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Visit with ?lab to flip styles and check coverage.","category":"other","icon":"beaker","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# 1. Hero + suffix","label":null,"prefix":null,"suffix":null,"section":"1. Hero + suffix","hero":false,"slider":null,"value":null,"display":null},{"text":"weight = 180 // lbs 80..400","label":null,"prefix":null,"suffix":"lbs","section":"1. Hero + suffix","hidden":false,"hero":false,"slider":{"min":80,"max":400,"step":1},"value":180,"display":"180"},{"text":"height = 70 // inches 48..84","label":null,"prefix":null,"suffix":"inches","section":"1. Hero + suffix","hidden":false,"hero":false,"slider":{"min":48,"max":84,"step":1},"value":70,"display":"70"},{"text":"_weight_kg = weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"1. Hero + suffix","hidden":true,"hero":false,"slider":null,"value":81.64656,"display":"81.65"},{"text":"_height_m = height * 0.0254","label":null,"prefix":null,"suffix":null,"section":"1. Hero + suffix","hidden":true,"hero":false,"slider":null,"value":1.778,"display":"1.778"},{"text":"body mass index = weight_kg / (height_m^2) // @hero @label(BMI) @suffix(kg/m²)","label":"BMI","prefix":null,"suffix":null,"section":"1. Hero + suffix","hidden":false,"hero":true,"slider":null,"value":25.82702471527392,"display":"25.83"},{"text":"# 2. Prefix + suffix","label":null,"prefix":null,"suffix":null,"section":"2. Prefix + suffix","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual income = $80000 // 20k..200k by 1k","label":null,"prefix":"$","suffix":null,"section":"2. Prefix + suffix","hidden":false,"hero":false,"slider":{"min":20000,"max":200000,"step":1000},"value":80000,"display":"$80,000.00"},{"text":"$annual expenses = $45000 // 10k..150k by 1k","label":null,"prefix":"$","suffix":null,"section":"2. Prefix + suffix","hidden":false,"hero":false,"slider":{"min":10000,"max":150000,"step":1000},"value":45000,"display":"$45,000.00"},{"text":"$annual savings = annual_income - annual_expenses","label":null,"prefix":"$","suffix":null,"section":"2. Prefix + suffix","hidden":false,"hero":false,"slider":null,"value":35000,"display":"$35,000.00"},{"text":"# 3. Hidden + advanced","label":null,"prefix":null,"suffix":null,"section":"3. Hidden + advanced","hero":false,"slider":null,"value":null,"display":null},{"text":"$_compound_seed = 100000","label":null,"prefix":"$","suffix":null,"section":"3. Hidden + advanced","hidden":true,"hero":false,"slider":null,"value":100000,"display":"$100,000.00"},{"text":"return rate = 7 // % 1..15 @advanced","label":null,"prefix":null,"suffix":"%","section":"3. Hidden + advanced","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.2},"value":7,"display":"7"},{"text":"years = 30 // 1..50 @advanced","label":null,"prefix":null,"suffix":null,"section":"3. Hidden + advanced","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":30,"display":"30"},{"text":"# 4. Long suffix — phrase","label":null,"prefix":null,"suffix":null,"section":"4. Long suffix — phrase","hero":false,"slider":null,"value":null,"display":null},{"text":"billable rate = 150 // dollars per hour","label":null,"prefix":null,"suffix":"dollars per hour","section":"4. Long suffix — phrase","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"output capacity = 145 // cubic feet per minute","label":null,"prefix":null,"suffix":"cubic feet per minute","section":"4. Long suffix — phrase","hidden":false,"hero":false,"slider":null,"value":145,"display":"145"},{"text":"monthly burn = 28500 // dollars per month","label":null,"prefix":null,"suffix":"dollars per month","section":"4. Long suffix — phrase","hidden":false,"hero":false,"slider":null,"value":28500,"display":"28,500"},{"text":"# 5. Hint-shaped suffix","label":null,"prefix":null,"suffix":null,"section":"5. Hint-shaped suffix","hero":false,"slider":null,"value":null,"display":null},{"text":"sex = 1 // 1 for male, 0 for female","label":null,"prefix":null,"suffix":"1 for male, 0 for female","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"material factor = 0.15 // Hard cheese: 0.1, Soft: 0.2","label":null,"prefix":null,"suffix":"Hard cheese: 0.1, Soft: 0.2","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"scope ratio = 7 // 7:1 is standard for overnight anchoring","label":null,"prefix":null,"suffix":"7:1 is standard for overnight anchoring","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"beam stress = 30000 // psi (steel)","label":null,"prefix":null,"suffix":"psi (steel)","section":"5. Hint-shaped suffix","hidden":false,"hero":false,"slider":null,"value":30000,"display":"30,000"},{"text":"# 6. Note decorator","label":null,"prefix":null,"suffix":null,"section":"6. Note decorator","hero":false,"slider":null,"value":null,"display":null},{"text":"$shipping cost = 9.99 // @note(Free over $50)","label":null,"prefix":"$","suffix":null,"section":"6. Note decorator","hidden":false,"hero":false,"slider":null,"value":9.99,"display":"$9.99"},{"text":"$tax rate = 8.25 // @suffix(%) @note(Varies by ZIP — verify before checkout)","label":null,"prefix":"$","suffix":null,"section":"6. Note decorator","hidden":false,"hero":false,"slider":null,"value":8.25,"display":"$8.25"},{"text":"# 7. Tooltip","label":null,"prefix":null,"suffix":null,"section":"7. Tooltip","hero":false,"slider":null,"value":null,"display":null},{"text":"sample size = 30 // @tooltip(Larger samples reduce confidence interval width)","label":null,"prefix":null,"suffix":null,"section":"7. Tooltip","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"confidence = 95 // % @tooltip(Standard for academic publication)","label":null,"prefix":null,"suffix":"%","section":"7. Tooltip","hidden":false,"hero":false,"slider":null,"value":95,"display":"95"},{"text":"# 8. Section + nested subsection","label":null,"prefix":null,"suffix":null,"section":"8. Section + nested subsection","hero":false,"slider":null,"value":null,"display":null},{"text":"# Group A — Inputs","label":null,"prefix":null,"suffix":null,"section":"Group A — Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"group_a_input_1 = 10","label":null,"prefix":null,"suffix":null,"section":"Group A — Inputs","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"group_a_input_2 = 20","label":null,"prefix":null,"suffix":null,"section":"Group A — Inputs","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"## Subsection","label":null,"prefix":null,"suffix":null,"section":"Subsection","hero":false,"slider":null,"value":null,"display":null},{"text":"nested_value = group_a_input_1 + group_a_input_2","label":null,"prefix":null,"suffix":null,"section":"Subsection","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# 9. Collapsed section","label":null,"prefix":null,"suffix":null,"section":"9. Collapsed section","hero":false,"slider":null,"value":null,"display":null},{"text":"# Advanced settings @collapsed","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hero":false,"slider":null,"value":null,"display":null},{"text":"fudge factor = 1.05","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hidden":false,"hero":false,"slider":null,"value":1.05,"display":"1.05"},{"text":"overhead = 0.12","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"margin = 0.25","label":null,"prefix":null,"suffix":null,"section":"Advanced settings","hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"# 10. Accent row","label":null,"prefix":null,"suffix":null,"section":"10. Accent row","hero":false,"slider":null,"value":null,"display":null},{"text":"$emergency reserve = 50000 // @accent","label":null,"prefix":"$","suffix":null,"section":"10. Accent row","hidden":false,"hero":false,"slider":null,"value":50000,"display":"$50,000.00"},{"text":"# 11. Readonly","label":null,"prefix":null,"suffix":null,"section":"11. Readonly","hero":false,"slider":null,"value":null,"display":null},{"text":"constant_pi = 3.14159 // @readonly","label":null,"prefix":null,"suffix":null,"section":"11. Readonly","hidden":false,"hero":false,"slider":null,"value":3.14159,"display":"3.142"},{"text":"# 12. Slider min..max syntax (inline range)","label":null,"prefix":null,"suffix":null,"section":"12. Slider min..max syntax (inline range)","hero":false,"slider":null,"value":null,"display":null},{"text":"slider quick = 50 // 0..100 by 5","label":null,"prefix":null,"suffix":null,"section":"12. Slider min..max syntax (inline range)","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":5},"value":50,"display":"50"},{"text":"slider with units = 250 // ml 0..1k by 25","label":null,"prefix":null,"suffix":"ml","section":"12. Slider min..max syntax (inline range)","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":25},"value":250,"display":"250"},{"text":"# 13. Dropdown","label":null,"prefix":null,"suffix":null,"section":"13. Dropdown","hero":false,"slider":null,"value":null,"display":null},{"text":"plan = {price: 9, name: 'Hobby'} // dropdown({Hobby: {price: 9, name: 'Hobby'}, Pro: {price: 29, name: 'Pro'}, Team: {price: 99, name: 'Team'}})","label":null,"prefix":null,"suffix":null,"section":"13. Dropdown","hidden":false,"hero":false,"slider":null,"value":{"price":9,"name":"Hobby"},"display":null},{"text":"$plan price = plan.price // @label(Selected price) @prefix($)","label":"Selected price","prefix":"$","suffix":null,"section":"13. Dropdown","hidden":false,"hero":false,"slider":null,"value":9,"display":"$9.00"},{"text":"# 14. Toggle","label":null,"prefix":null,"suffix":null,"section":"14. Toggle","hero":false,"slider":null,"value":null,"display":null},{"text":"includes_premium = false // @label(Premium add-on) toggle()","label":"Premium add-on","prefix":null,"suffix":null,"section":"14. Toggle","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"$base price = 49.99 // @prefix($)","label":null,"prefix":"$","suffix":null,"section":"14. Toggle","hidden":false,"hero":false,"slider":null,"value":49.99,"display":"$49.99"},{"text":"$total = base_price + (includes_premium ? 20 : 0) // @hero @prefix($)","label":null,"prefix":"$","suffix":null,"section":"14. Toggle","hidden":false,"hero":true,"slider":null,"value":49.99,"display":"$49.99"},{"text":"# 15. @icon on row","label":null,"prefix":null,"suffix":null,"section":"15. on row","hero":false,"slider":null,"value":null,"display":null},{"text":"fuel = 12.5 // @icon(droplet) gal","label":null,"prefix":null,"suffix":"gal","section":"15. on row","hidden":false,"hero":false,"slider":null,"value":12.5,"display":"12.5"},{"text":"distance = 320 // @icon(map-pin) mi","label":null,"prefix":null,"suffix":"mi","section":"15. on row","hidden":false,"hero":false,"slider":null,"value":320,"display":"320"},{"text":"# 16. Calc title @icon + @category in the first heading at the top of this file","label":null,"prefix":null,"suffix":null,"section":"16. Calc title + in the first heading at the top of this file","hero":false,"slider":null,"value":null,"display":null},{"text":"# 17. Layout: grid (peer outputs)","label":null,"prefix":null,"suffix":null,"section":"17. Layout: grid (peer outputs)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Color breakdown @layout(grid)","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"red = 255","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":255,"display":"255"},{"text":"green = 128","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":128,"display":"128"},{"text":"blue = 64","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":64,"display":"64"},{"text":"alpha = 1.0","label":null,"prefix":null,"suffix":null,"section":"Color breakdown","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# 18. Layout: split (inputs left, outputs right)","label":null,"prefix":null,"suffix":null,"section":"18. Layout: split (inputs left, outputs right)","hero":false,"slider":null,"value":null,"display":null},{"text":"# I/O scenario @layout(split)","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hero":false,"slider":null,"value":null,"display":null},{"text":"revenue = 150000","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":150000,"display":"150,000"},{"text":"expenses = 90000","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":90000,"display":"90,000"},{"text":"profit = revenue - expenses","label":null,"prefix":null,"suffix":null,"section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":60000,"display":"60,000"},{"text":"margin pct = (profit / revenue) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"I/O scenario","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"# 19. @wide — row spans full grid width","label":null,"prefix":null,"suffix":null,"section":"19. — row spans full grid width","hero":false,"slider":null,"value":null,"display":null},{"text":"$total quarterly revenue = 600000 // @wide @prefix($) @label(Q4 total revenue across all regions)","label":"Q4 total revenue across all regions","prefix":"$","suffix":null,"section":"19. — row spans full grid width","hidden":false,"hero":false,"slider":null,"value":600000,"display":"$600,000.00"},{"text":"# 20. Format: percent and currency","label":null,"prefix":null,"suffix":null,"section":"20. Format: percent and currency","hero":false,"slider":null,"value":null,"display":null},{"text":"percent rate = 0.075 // @format(percent)","label":null,"prefix":null,"suffix":null,"section":"20. Format: percent and currency","hidden":false,"hero":false,"slider":null,"value":0.075,"display":"7.5%"},{"text":"$compact dollars = 12345.67 // @format(currency) @decimals(0)","label":null,"prefix":"$","suffix":null,"section":"20. Format: percent and currency","hidden":false,"hero":false,"slider":null,"value":12345.67,"display":"$12.3K"},{"text":"raw count = 1234567 // @format(raw)","label":null,"prefix":null,"suffix":null,"section":"20. Format: percent and currency","hidden":false,"hero":false,"slider":null,"value":1234567,"display":"1,234,567"},{"text":"# 20b. Suppress unit on dimensioned results","label":null,"prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hero":false,"slider":null,"value":null,"display":null},{"text":"_w_kg = 82","label":null,"prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hidden":true,"hero":false,"slider":null,"value":82,"display":"82"},{"text":"_h_m = 1.78","label":null,"prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hidden":true,"hero":false,"slider":null,"value":1.78,"display":"1.78"},{"text":"body mass index = _w_kg / (_h_m^2) // @hero @label(BMI) @suffix()","label":"BMI","prefix":null,"suffix":null,"section":"20b. Suppress unit on dimensioned results","hidden":false,"hero":true,"slider":null,"value":25.88057063502083,"display":"25.88"},{"text":"# 21. Inline variable interpolation in prose","label":null,"prefix":null,"suffix":null,"section":"21. Inline variable interpolation in prose","hero":false,"slider":null,"value":null,"display":null},{"text":"# 22. Narrative row (markdown-friendly)","label":null,"prefix":null,"suffix":null,"section":"22. Narrative row (markdown-friendly)","hero":false,"slider":null,"value":null,"display":null},{"text":"# 23. Plain comment","label":null,"prefix":null,"suffix":null,"section":"23. Plain comment","hero":false,"slider":null,"value":null,"display":null},{"text":"# 24. Divider","label":null,"prefix":null,"suffix":null,"section":"24. Divider","hero":false,"slider":null,"value":null,"display":null},{"text":"# 25. Quoted string narrative","label":null,"prefix":null,"suffix":null,"section":"25. Quoted string narrative","hero":false,"slider":null,"value":null,"display":null},{"text":"# 26. Comment heading (level 3)","label":null,"prefix":null,"suffix":null,"section":"26. Comment heading (level 3)","hero":false,"slider":null,"value":null,"display":null},{"text":"### A level-3 sub-label","label":null,"prefix":null,"suffix":null,"section":"A level-3 sub-label","hero":false,"slider":null,"value":null,"display":null},{"text":"# 27. End cap — one final hero so the calc has a clear payoff","label":null,"prefix":null,"suffix":null,"section":"27. End cap — one final hero so the calc has a clear payoff","hero":false,"slider":null,"value":null,"display":null},{"text":"$grand total = annual_savings * years // @hero @label(Total saved over horizon) @prefix($)","label":"Total saved over horizon","prefix":"$","suffix":null,"section":"27. End cap — one final hero so the calc has a clear payoff","hidden":false,"hero":true,"slider":null,"value":1050000,"display":"$1,050,000.00"}]},{"id":"ac-impedance-rlc-circuit","title":"AC Impedance RLC Circuit","description":"Calculate total impedance and phase angle for AC circuits.","category":"engineering","icon":"zap","tags":["engineering","electrical","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"resistance_ohms = 100 // ohms","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"inductance_henries = 0.1 // henries","label":null,"prefix":null,"suffix":"henries","section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"capacitance_farads = 0.00001 // farads (10 uF)","label":null,"prefix":null,"suffix":"farads (10 uF)","section":null,"hidden":false,"hero":false,"slider":null,"value":0.00001,"display":"0.00001"},{"text":"frequency_hz = 60 // Hz","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"angular_frequency = 2 * 3.14159 * frequency_hz","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":376.9908,"display":"376.99"},{"text":"inductive_reactance = angular_frequency * inductance_henries","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":37.69908,"display":"37.7"},{"text":"capacitive_reactance = 1 / (angular_frequency * capacitance_farads)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":265.2584625407304,"display":"265.26"},{"text":"total_impedance_ohms = (resistance_ohms^2 + (inductive_reactance - capacitive_reactance)^2)^0.5 // ohms @hero","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":true,"slider":null,"value":248.5624118452315,"display":"248.56"},{"text":"phase_angle_degrees = atan((inductive_reactance - capacitive_reactance) / resistance_ohms) // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":-66.27711707071362,"display":"-66.2771"}]},{"id":"acceleration","title":"Acceleration","description":"a = (v − v₀) / t — average acceleration from change in velocity over time.","category":"formulas","icon":"gauge","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"final_velocity = 30 // m/s 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51","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":51,"display":"51"},{"text":"aqi_high = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"conc_low = 12.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12.1,"display":"12.1"},{"text":"conc_high = 35.4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":35.4,"display":"35.4"},{"text":"aqi = ((aqi_high - aqi_low) / (conc_high - conc_low)) * (pm25_concentration - conc_low) + aqi_low // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":99.15879828326179,"display":"99.16"}]},{"id":"alcohol-by-volume-brix","title":"Alcohol By Volume Brix","description":"Estimate alcohol by volume from original and final Brix 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100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"aluminum_scrap_valuation = aluminum_weight_pounds * aluminum_price_per_pound","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"amazon-fba-fee-estimate","title":"Amazon Fba Fee Estimate","description":"Estimate Amazon FBA referral and fulfillment fees and net proceeds per sale.","category":"other","icon":"calculator","tags":["fee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"item_price = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"item_weight_pounds = 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(transactionVolumeScore + geographicRiskScore + customerTypeScore) / 3 // scale 1-10 @hero","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":true,"slider":null,"value":5.666666666666667,"display":"5.667"}]},{"id":"among-us-imposter-probability","title":"Among Us Imposter Probability","description":"Calculate the probability of being assigned imposter or crewmate in Among Us.","category":"math","icon":"infinity","tags":["probability","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Game Settings","label":null,"prefix":null,"suffix":null,"section":"Game Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"total players = 10 // 4..15","label":null,"prefix":null,"suffix":null,"section":"Game Settings","hidden":false,"hero":false,"slider":{"min":4,"max":15,"step":0.2},"value":10,"display":"10"},{"text":"imposter count = 2 // 1..3","label":null,"prefix":null,"suffix":null,"section":"Game Settings","hidden":false,"hero":false,"slider":{"min":1,"max":3,"step":0.02},"value":2,"display":"2"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"imposter probability = (imposter count / total players) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":20,"display":"20"},{"text":"crewmate probability = 100 - imposter probability // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"amortization-schedule","title":"Amortization Schedule","description":"Calculate monthly payment, total interest, and total cost of a fixed-rate 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Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_monthly_rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"_num_payments = loan term * 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly payment = loan amount * (monthly_rate * (1 + monthly_rate)^num_payments) / ((1 + monthly_rate)^num_payments - 1) // @hero","label":null,"prefix":"$","suffix":null,"section":"Results","hidden":false,"hero":true,"slider":null,"value":1580.1700587324135,"display":"$1,580.17"},{"text":"$total payments = monthly payment * 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4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"scope_ratio = 7 // 7:1 is standard for overnight","label":null,"prefix":null,"suffix":"7:1 is standard for overnight","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"total_rode_length_feet = (water_depth_feet + freeboard_height_feet) * scope_ratio // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":168,"display":"168"}]},{"id":"anchoring-effect-strength","title":"Anchoring Effect Strength","description":"Estimate how much an anchor value biases a final numerical judgment.","category":"health","icon":"brain","tags":["effect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"anchor_value = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"actual_value = 500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"adjustment_percent = 0.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"final_estimate = anchor_value - (anchor_value - actual_value) * adjustment_percent // estimated value @hero","label":null,"prefix":null,"suffix":"estimated value","section":null,"hidden":false,"hero":true,"slider":null,"value":900,"display":"900"}]},{"id":"angle-conversion-degrees-radians","title":"Angle Conversion Degrees Radians","description":"Convert between degrees and radians: rad = deg × 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Radians)","label":"Degrees → Radians","prefix":null,"suffix":null,"section":"Conversions","hidden":false,"hero":true,"slider":null,"value":3.141592653589793,"display":"3.142"},{"text":"radians_to_degrees = radians * 180 / pi // @hero @label(Radians → Degrees)","label":"Radians → Degrees","prefix":null,"suffix":null,"section":"Conversions","hidden":false,"hero":true,"slider":null,"value":179.99984796050433,"display":"180"}]},{"id":"annuity-payment-calculator","title":"Annuity Payment Calculator","description":"Calculate the periodic payment of an annuity from present value, rate, and term.","category":"finance","icon":"dollar-sign","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"present_value = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"annual_rate = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"years = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"payment = present_value * (annual_rate / (1 - (1 + annual_rate) ** -years))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8024.258719069128,"display":"8,024.26"}]},{"id":"aperture-depth-of-field-blur","title":"Aperture Depth Of Field Blur","description":"Calculate the near and far depth-of-field limits for a given aperture and focus distance.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"focal_length = 50 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"aperture_f_stop = 1.8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.8,"display":"1.8"},{"text":"distance_to_subject = 2000 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"circle_of_confusion = 0.03 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"_hyperfocal_distance = focal_length^2 / (aperture_f_stop * circle_of_confusion)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":46296.2962962963,"display":"46,296.3"},{"text":"near_limit = (distance_to_subject * (hyperfocal_distance - focal_length)) / (hyperfocal_distance + distance_to_subject - 2 * focal_length) // mm @hero","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":true,"slider":null,"value":1919.080919080919,"display":"1,919.08"},{"text":"far_limit = (distance_to_subject * (hyperfocal_distance - focal_length)) / (hyperfocal_distance - distance_to_subject) // mm @hero","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":true,"slider":null,"value":2088.0434782608695,"display":"2,088.04"}]},{"id":"app-store-take-home-pay","title":"App Store Take Home Pay","description":"Estimate take-home pay from app sales after Apple or Google commission and taxes.","category":"everyday","icon":"home","tags":["home","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"total_app_sales_revenue = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"apple_google_commission_percentage = 0.30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"applicable_taxes_percentage = 0.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"revenue_after_commission = total_app_sales_revenue * (1 - apple_google_commission_percentage)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7000,"display":"7,000"},{"text":"net_take_home_pay = revenue_after_commission * (1 - applicable_taxes_percentage)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5950,"display":"5,950"}]},{"id":"appreciation-rate-projector","title":"Appreciation Rate Projector","description":"Project future property value based on historical growth rates.","category":"real-estate","icon":"trending-up","tags":["real-estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"currentValue = 300000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"annualAppreciationRate = 3 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"yearsProjected = 10 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"futureValue = currentValue * (1 + (annualAppreciationRate / 100)) ^ yearsProjected // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":403174.9138032367,"display":"403,174.91"}]},{"id":"aquifer-recharge-time","title":"Aquifer Recharge Time","description":"Estimate how long it takes for an underground aquifer to refill.","category":"science","icon":"droplet","tags":["science","water","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"aquifer_volume_cubic_meters = 1000000 // m3","label":null,"prefix":null,"suffix":"m3","section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"annual_recharge_liters_per_m2 = 50 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"catchment_area_m2 = 500000 // m2","label":null,"prefix":null,"suffix":"m2","section":null,"hidden":false,"hero":false,"slider":null,"value":500000,"display":"500,000"},{"text":"annual_recharge_m3 = (annual_recharge_liters_per_m2 * catchment_area_m2) / 1000 // m3","label":null,"prefix":null,"suffix":"m3","section":null,"hidden":false,"hero":false,"slider":null,"value":25000,"display":"25,000"},{"text":"years_to_full_recharge = aquifer_volume_cubic_meters / annual_recharge_m3 // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":40,"display":"40"}]},{"id":"arc-length","title":"Arc Length","description":"Find the length of a circular arc: s = r × θ (θ in radians).","category":"formulas","icon":"circle","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Arc","label":null,"prefix":null,"suffix":null,"section":"Arc","hero":false,"slider":null,"value":null,"display":null},{"text":"radius = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Arc","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"angle_degrees = 60 // 0..360","label":null,"prefix":null,"suffix":null,"section":"Arc","hidden":false,"hero":false,"slider":{"min":0,"max":360,"step":1},"value":60,"display":"60"},{"text":"# Convert to radians and compute arc length","label":null,"prefix":null,"suffix":null,"section":"Convert to radians and compute arc length","hero":false,"slider":null,"value":null,"display":null},{"text":"_angle_radians = angle_degrees * pi / 180","label":null,"prefix":null,"suffix":null,"section":"Convert to radians and compute arc length","hidden":true,"hero":false,"slider":null,"value":1.0471975511965976,"display":"1.047"},{"text":"arc_length = radius * angle_radians","label":null,"prefix":null,"suffix":null,"section":"Convert to radians and compute arc length","hidden":false,"hero":true,"slider":null,"value":10.471975511965976,"display":"10.47"}]},{"id":"archery-kinetic-energy","title":"Archery Kinetic Energy","description":"Calculate arrow kinetic energy in foot-pounds from arrow weight and velocity.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"arrow_weight_grains = 400","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"arrow_velocity_feet_per_second = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"kinetic_energy_foot_pounds = (arrow_weight_grains * arrow_velocity_feet_per_second^2) / 450240 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":79.95735607675905,"display":"79.96"}]},{"id":"arithmetic-sequence-nth-term","title":"Arithmetic Sequence nth Term","description":"Find the nth term of an arithmetic sequence: aₙ = a₁ + (n−1)·d.","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Sequence parameters","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence 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aₙ).","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Sequence parameters","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"d = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"n = 10 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Sum of first n terms","label":null,"prefix":null,"suffix":null,"section":"Sum of first n terms","hero":false,"slider":null,"value":null,"display":null},{"text":"an = a1 + (n - 1) * d // @label(aₙ)","label":"aₙ","prefix":null,"suffix":null,"section":"Sum of first n terms","hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"sum_n = n / 2 * (a1 + an) // @label(Sₙ)","label":"Sₙ","prefix":null,"suffix":null,"section":"Sum of first n terms","hidden":false,"hero":true,"slider":null,"value":255,"display":"255"}]},{"id":"aspect-ratio","title":"Aspect Ratio","description":"Scale dimensions proportionally while maintaining aspect ratio.","category":"design","icon":"maximize","tags":["aspect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Original Dimensions","label":null,"prefix":null,"suffix":null,"section":"Original Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"original width = 1920 // 1..7680","label":null,"prefix":null,"suffix":null,"section":"Original Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":7680,"step":100},"value":1920,"display":"1,920"},{"text":"original height = 1080 // 1..4320","label":null,"prefix":null,"suffix":null,"section":"Original Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":4320,"step":50},"value":1080,"display":"1,080"},{"text":"# Resize","label":null,"prefix":null,"suffix":null,"section":"Resize","hero":false,"slider":null,"value":null,"display":null},{"text":"new width = 1280 // 1..7680","label":null,"prefix":null,"suffix":null,"section":"Resize","hidden":false,"hero":false,"slider":{"min":1,"max":7680,"step":100},"value":1280,"display":"1,280"},{"text":"# Calculated","label":null,"prefix":null,"suffix":null,"section":"Calculated","hero":false,"slider":null,"value":null,"display":null},{"text":"new height = round(original height * (new width / original width)) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculated","hidden":false,"hero":true,"slider":null,"value":720,"display":"720"},{"text":"scale factor = round(new width / original width * 10000) / 10000","label":null,"prefix":null,"suffix":null,"section":"Calculated","hidden":false,"hero":false,"slider":null,"value":0.6667,"display":"0.6667"},{"text":"# Ratio","label":null,"prefix":null,"suffix":null,"section":"Ratio","hero":false,"slider":null,"value":null,"display":null},{"text":"ratio decimal = round(original width / original height * 10000) / 10000 // @label(Ratio (decimal))","label":"Ratio (decimal)","prefix":null,"suffix":null,"section":"Ratio","hidden":false,"hero":false,"slider":null,"value":1.7778,"display":"1.778"},{"text":"# Common Checks","label":null,"prefix":null,"suffix":null,"section":"Common Checks","hero":false,"slider":null,"value":null,"display":null},{"text":"original megapixels = round((original width * original height) / 1000000 * 100) / 100","label":null,"prefix":null,"suffix":null,"section":"Common Checks","hidden":false,"hero":false,"slider":null,"value":2.07,"display":"2.07"},{"text":"new megapixels = round((new width * new height) / 1000000 * 100) / 100","label":null,"prefix":null,"suffix":null,"section":"Common Checks","hidden":false,"hero":false,"slider":null,"value":0.92,"display":"0.92"}]},{"id":"asset-turnover-ratio","title":"Asset Turnover Ratio","description":"Calculate the asset turnover ratio from revenue and average total assets.","category":"math","icon":"ratio","tags":["turnover","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"total_revenue = 5000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000000,"display":"5,000,000"},{"text":"average_assets = 2500000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2500000,"display":"2,500,000"},{"text":"asset_turnover = total_revenue / average_assets","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"asteroid-impact-energy","title":"Asteroid Impact Energy","description":"Estimate the impact energy of an asteroid in megatons of TNT from size, density, and velocity.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"diameter_meters = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"density_kg_per_m3 = 3000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"velocity_km_per_s = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"volume = (4/3) * pi * (diameter_meters / 2)^3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":523598.7755982988,"display":"523,598.78"},{"text":"mass_kg = volume * density_kg_per_m3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1570796326.7948964,"display":"1,570,796,326.79"},{"text":"energy_joules = 0.5 * mass_kg * (velocity_km_per_s * 1000)^2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":314159265358979260,"display":"314,159,265,358,979,260"},{"text":"megatons_tnt = energy_joules / 4.184e15 // Megatons of TNT @hero","label":null,"prefix":null,"suffix":"Megatons of TNT","section":null,"hidden":false,"hero":true,"slider":null,"value":75.08586648159161,"display":"75.09"}]},{"id":"atmosphere-scale-height","title":"Atmosphere Scale Height","description":"Calculate the scale height of a planetary atmosphere from temperature and gravity.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"temperature_kelvin = 288","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":288,"display":"288"},{"text":"mean_molecular_mass_kilograms = 4.8e-26","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4.8e-26,"display":"4.8e-26"},{"text":"gravity_constant = 9.81","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"boltzmann_constant = 1.38e-23","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.38e-23,"display":"1.38e-23"},{"text":"scale_height_meters = (boltzmann_constant * temperature_kelvin) / (mean_molecular_mass_kilograms * gravity_constant) // meters @hero","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":true,"slider":null,"value":8440.366972477063,"display":"8,440.37"}]},{"id":"atmospheric-refraction-correction","title":"Atmospheric Refraction Correction","description":"Calculate atmospheric refraction correction for celestial altitude observations.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"apparent_altitude_degrees = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"pressure_millibars = 1013","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1013,"display":"1,013"},{"text":"temperature_celsius = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"refraction_arcminutes = (1.02 / tan(apparent_altitude_degrees + 10.3 / (apparent_altitude_degrees + 5.11))) * (pressure_millibars / 1010) * (283 / (273 + temperature_celsius))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.9980817482748903,"display":"0.9981"}]},{"id":"attack-speed-frames-per-second","title":"Attack Speed Frames Per Second","description":"Calculate attack speed in frames per second.","category":"math","icon":"sword","tags":["gaming","combat"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Attack Settings","label":null,"prefix":null,"suffix":null,"section":"Attack Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base attack speed = 1.0 // attacks per second","label":null,"prefix":null,"suffix":"attacks per second","section":"Attack Settings","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"increased attack speed percent = 50 // %","label":null,"prefix":null,"suffix":"%","section":"Attack Settings","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"frames per second = 60","label":null,"prefix":null,"suffix":null,"section":"Attack Settings","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_final_attack_speed = base attack speed * (1 + (increased attack speed percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"frames per attack = frames per second / final_attack_speed","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":40,"display":"40"}]},{"id":"attention-span-decay","title":"Attention Span Decay","description":"Estimate remaining attention as a percentage after a given number of minutes.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"time_minutes = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"initial_attention = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"decay_constant = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"current_attention = initial_attention * exp(-decay_constant * time_minutes) // percent remaining @suffix(%) @hero","label":null,"prefix":null,"suffix":"percent remaining","section":null,"hidden":false,"hero":true,"slider":null,"value":47.23665527410147,"display":"47.24"}]},{"id":"attic-fan-airflow-sizing","title":"Attic Fan Sizing","description":"Calculate CFM requirements for attic cooling fans.","category":"engineering","icon":"fan","tags":["engineering","home","cooling"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"attic_square_feet = 1500 // sq ft","label":null,"prefix":null,"suffix":"sq ft","section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"roof_color_dark = 1 // dropdown({Dark: 1, Light: 0})","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"multiplier = 0.7 + (roof_color_dark * 0.15)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.85,"display":"0.85"},{"text":"required_cfm = attic_square_feet * multiplier // cubic feet per minute @hero","label":null,"prefix":null,"suffix":"cubic feet per minute","section":null,"hidden":false,"hero":true,"slider":null,"value":1275,"display":"1,275"}]},{"id":"audio-delay-time-ms-to-bpm","title":"Audio Delay Time Ms To Bpm","description":"Calculate quarter, eighth, and dotted-eighth delay times in milliseconds for a given BPM.","category":"design","icon":"palette","tags":["delay"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"bpm = 120","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"beats_per_measure = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"quarter_note_delay = (60 / bpm) * 1000 // ms @hero","label":null,"prefix":null,"suffix":"ms","section":null,"hidden":false,"hero":true,"slider":null,"value":500,"display":"500"},{"text":"eighth_note_delay = quarter_note_delay / 2 // ms @hero","label":null,"prefix":null,"suffix":"ms","section":null,"hidden":false,"hero":true,"slider":null,"value":250,"display":"250"},{"text":"dotted_eighth_note_delay = eighth_note_delay * 1.5 // ms @hero","label":null,"prefix":null,"suffix":"ms","section":null,"hidden":false,"hero":true,"slider":null,"value":375,"display":"375"}]},{"id":"aurora-visibility-latitude","title":"Aurora Visibility Latitude","description":"Estimate the minimum latitude at which the aurora is visible for a given Kp index.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"kp_index = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"min_latitude = 67 - kp_index * 2 // minimum latitude for visibility @hero","label":null,"prefix":null,"suffix":"minimum latitude for 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Terms","hidden":false,"hero":false,"slider":{"min":10000,"max":100000,"step":500},"value":32000,"display":"$32,000.00"},{"text":"$down payment = 3000 // 0..20k by 100","label":null,"prefix":"$","suffix":null,"section":"Lease Terms","hidden":false,"hero":false,"slider":{"min":0,"max":20000,"step":100},"value":3000,"display":"$3,000.00"},{"text":"residual value percent = 60 // % 30..80","label":null,"prefix":null,"suffix":"%","section":"Lease Terms","hidden":false,"hero":false,"slider":{"min":30,"max":80,"step":1},"value":60,"display":"60"},{"text":"money factor = 0.00125 // 0.0001..0.005 by 0.0001","label":null,"prefix":null,"suffix":null,"section":"Lease Terms","hidden":false,"hero":false,"slider":{"min":0.0001,"max":0.005,"step":0.0001},"value":0.00125,"display":"0.00125"},{"text":"lease term = 36 // months 12..60","label":null,"prefix":null,"suffix":"months","section":"Lease Terms","hidden":false,"hero":false,"slider":{"min":12,"max":60,"step":1},"value":36,"display":"36"},{"text":"tax rate = 8 // % 0..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Lease Terms","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.1},"value":8,"display":"8"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_capitalized_cost = negotiated price - down payment","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":29000,"display":"$29,000.00"},{"text":"$_residual_value = msrp * (residual value percent / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":21000,"display":"$21,000.00"},{"text":"$_monthly_depreciation = (capitalized_cost - residual_value) / lease term","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":222.22222222222223,"display":"$222.22"},{"text":"$_monthly_finance_fee = (capitalized_cost + residual_value) * money factor","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":62.5,"display":"$62.50"},{"text":"$_base_monthly_payment = monthly_depreciation + monthly_finance_fee","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":284.72222222222223,"display":"$284.72"},{"text":"$_monthly_tax = base_monthly_payment * (tax rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":22.77777777777778,"display":"$22.78"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$total monthly lease payment = base_monthly_payment + monthly_tax // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":307.5,"display":"$307.50"},{"text":"$total cost of lease = total monthly lease payment * lease term + down payment","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":14070,"display":"$14,070.00"}]},{"id":"average-days-to-ship","title":"Average Days to Ship","description":"Calculate the average time from order receipt to shipping.","category":"business","icon":"clock","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"totalDaysForAllOrders = 450 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":450,"display":"450"},{"text":"totalOrdersShipped = 150 // orders","label":null,"prefix":null,"suffix":"orders","section":null,"hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"averageDaysToShip = totalDaysForAllOrders / totalOrdersShipped // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"avogadros-law-moles-volume","title":"Avogadros Law Moles Volume","description":"Calculate the final gas volume after changing moles at constant temperature and pressure.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"volume_initial = 22.4 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":22.4,"display":"22.4"},{"text":"moles_initial = 1.0 // mol","label":null,"prefix":null,"suffix":"mol","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"moles_final = 1.5 // mol","label":null,"prefix":null,"suffix":"mol","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"volume_final = volume_initial * (moles_final / moles_initial) // liters @hero","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":33.6,"display":"33.6"}]},{"id":"baby-name-randomizer","title":"Baby Name Randomizer","description":"Calculate the probability and 1-in-X odds of a baby name occurring among newborns.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Name Stats","label":null,"prefix":null,"suffix":null,"section":"Name Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"babies with name = 15000","label":null,"prefix":null,"suffix":null,"section":"Name Stats","hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"total babies born = 4000000","label":null,"prefix":null,"suffix":null,"section":"Name Stats","hidden":false,"hero":false,"slider":null,"value":4000000,"display":"4,000,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"probability of name = (babies with name / total babies born) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":0.375,"display":"0.375"},{"text":"odds = total babies born / babies with name // 1 in X @hero","label":null,"prefix":null,"suffix":"1 in X","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":266.6666666666667,"display":"266.67"}]},{"id":"back-end-load-impact","title":"Back End Load Impact","description":"Estimate the impact of a back-end load fee on an investment after years of growth.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"investment_amount = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"annual_growth = 0.07","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.07,"display":"0.07"},{"text":"years = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"back_end_load_rate = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"future_value_pre_fee = investment_amount * (1 + annual_growth) ** years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14025.517307000004,"display":"14,025.52"},{"text":"fee_amount = future_value_pre_fee * back_end_load_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":420.76551921000015,"display":"420.77"},{"text":"final_value = future_value_pre_fee - fee_amount","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":13604.751787790003,"display":"13,604.75"}]},{"id":"backorder-rate","title":"Backorder Rate","description":"Calculate the percentage of orders that cannot be filled immediately.","category":"business","icon":"list","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"backorderedOrders = 40 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"totalOrdersPlaced = 1000 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"backorderRatePercent = (backorderedOrders / totalOrdersPlaced) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"baking-ratio","title":"Baker's Percentage","description":"Calculate ingredient weights using baker's percentages relative to flour weight.","category":"cooking","icon":"egg-fried","tags":["baking"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Baker's Percentage (relative to flour)","label":null,"prefix":null,"suffix":null,"section":"Baker's Percentage (relative to flour)","hero":false,"slider":null,"value":null,"display":null},{"text":"flour = 500 // g 100..5k","label":null,"prefix":null,"suffix":"g","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":100,"max":5000,"step":50},"value":500,"display":"500"},{"text":"hydration = 65 // % 40..100","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":40,"max":100,"step":1},"value":65,"display":"65"},{"text":"salt pct = 2 // % 0..5 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.1},"value":2,"display":"2"},{"text":"yeast pct = 1 // % 0..5 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.1},"value":1,"display":"1"},{"text":"sugar pct = 5 // % 0..20","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":5,"display":"5"},{"text":"fat pct = 3 // % 0..20","label":null,"prefix":null,"suffix":"%","section":"Baker's Percentage (relative to flour)","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":3,"display":"3"},{"text":"# Ingredient Amounts","label":null,"prefix":null,"suffix":null,"section":"Ingredient Amounts","hero":false,"slider":null,"value":null,"display":null},{"text":"water = flour * hydration / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":325,"display":"325"},{"text":"salt = flour * salt_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"yeast = flour * yeast_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"sugar = flour * sugar_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"fat = flour * fat_pct / 100 // g","label":null,"prefix":null,"suffix":"g","section":"Ingredient Amounts","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"# Total","label":null,"prefix":null,"suffix":null,"section":"Total","hero":false,"slider":null,"value":null,"display":null},{"text":"total dough weight = flour + water + salt + yeast + sugar + fat // g @hero","label":null,"prefix":null,"suffix":"g","section":"Total","hidden":false,"hero":true,"slider":null,"value":880,"display":"880"},{"text":"total in ounces = round(total_dough_weight / 28.35, 1) // oz","label":null,"prefix":null,"suffix":"oz","section":"Total","hidden":false,"hero":false,"slider":null,"value":31,"display":"31"}]},{"id":"baking-scale","title":"Baking Time Scale","description":"Adjusted bake time when scaling a recipe up or down (heat-conduction model).","category":"cooking","icon":"chef-hat","tags":["baking","recipe"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Original Recipe","label":null,"prefix":null,"suffix":null,"section":"Original Recipe","hero":false,"slider":null,"value":null,"display":null},{"text":"original servings = 8 // 1..50","label":null,"prefix":null,"suffix":null,"section":"Original Recipe","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":8,"display":"8"},{"text":"original bake minutes = 30 // min 5..240","label":null,"prefix":null,"suffix":"min","section":"Original Recipe","hidden":false,"hero":false,"slider":{"min":5,"max":240,"step":1},"value":30,"display":"30"},{"text":"# Desired Recipe","label":null,"prefix":null,"suffix":null,"section":"Desired Recipe","hero":false,"slider":null,"value":null,"display":null},{"text":"desired servings = 16 // 1..100","label":null,"prefix":null,"suffix":null,"section":"Desired Recipe","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":16,"display":"16"},{"text":"# Scale Factor","label":null,"prefix":null,"suffix":null,"section":"Scale Factor","hero":false,"slider":null,"value":null,"display":null},{"text":"scale = desired servings / original servings // @label(Recipe scale)","label":"Recipe scale","prefix":null,"suffix":null,"section":"Scale Factor","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"# Bake Time Heuristic (heat conducts through cross-section, not volume)","label":null,"prefix":null,"suffix":null,"section":"Bake Time Heuristic (heat conducts through cross-section, not volume)","hero":false,"slider":null,"value":null,"display":null},{"text":"time exponent = 0.32 // 0.2..0.66 by 0.01","label":null,"prefix":null,"suffix":null,"section":"Bake Time Heuristic (heat conducts through cross-section, not volume)","hidden":false,"hero":false,"slider":{"min":0.2,"max":0.66,"step":0.01},"value":0.32,"display":"0.32"},{"text":"new bake minutes = round(original bake minutes * scale^time exponent, 1) // min @hero @label(New bake time)","label":"New bake time","prefix":null,"suffix":"min","section":"Bake Time Heuristic (heat conducts through cross-section, not volume)","hidden":false,"hero":true,"slider":null,"value":37.4,"display":"37.4"},{"text":"# Increase","label":null,"prefix":null,"suffix":null,"section":"Increase","hero":false,"slider":null,"value":null,"display":null},{"text":"extra minutes = round(new bake minutes - original bake minutes, 1) // min @label(Extra bake time)","label":"Extra bake time","prefix":null,"suffix":"min","section":"Increase","hidden":false,"hero":false,"slider":null,"value":7.4,"display":"7.4"},{"text":"percent longer = round((new bake minutes / original bake minutes - 1) * 100, 1) // % @label(% longer)","label":"% longer","prefix":null,"suffix":"%","section":"Increase","hidden":false,"hero":false,"slider":null,"value":24.7,"display":"24.7"}]},{"id":"baking-substitution","title":"Baking Substitution","description":"Egg replacements (banana, applesauce, flax) by mass for any recipe.","category":"cooking","icon":"egg-fried","tags":["baking","recipe"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Recipe Calls For","label":null,"prefix":null,"suffix":null,"section":"Recipe Calls For","hero":false,"slider":null,"value":null,"display":null},{"text":"eggs in recipe = 2 // 1..12","label":null,"prefix":null,"suffix":null,"section":"Recipe Calls For","hidden":false,"hero":false,"slider":{"min":1,"max":12,"step":0.2},"value":2,"display":"2"},{"text":"# Egg Mass","label":null,"prefix":null,"suffix":null,"section":"Egg Mass","hero":false,"slider":null,"value":null,"display":null},{"text":"_grams_per_egg = 60 // g","label":null,"prefix":null,"suffix":"g","section":"Egg Mass","hidden":true,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"total egg mass = eggs in recipe * grams_per_egg // g","label":null,"prefix":null,"suffix":"g","section":"Egg Mass","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"# Substitutes (per egg = 60 g moisture + binder)","label":null,"prefix":null,"suffix":null,"section":"Substitutes (per egg = 60 g moisture + binder)","hero":false,"slider":null,"value":null,"display":null},{"text":"banana mashed g = total egg mass // g @hero @label(Mashed banana) @suffix(g)","label":"Mashed banana","prefix":null,"suffix":"g","section":"Substitutes (per egg = 60 g moisture + binder)","hidden":false,"hero":true,"slider":null,"value":120,"display":"120"},{"text":"applesauce g = total egg mass // g @label(Unsweetened applesauce) @suffix(g)","label":"Unsweetened applesauce","prefix":null,"suffix":"g","section":"Substitutes (per egg = 60 g moisture + binder)","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"flax water mix g = eggs in recipe * 3 + eggs in recipe * 8 // g @label(Ground flax + water (1 tbsp + 3 tbsp))","label":"Ground flax + water (1 tbsp + 3 tbsp)","prefix":null,"suffix":"g","section":"Substitutes (per egg = 60 g moisture + binder)","hidden":false,"hero":false,"slider":null,"value":22,"display":"22"},{"text":"yogurt g = total egg mass // g @label(Plain yogurt) @suffix(g)","label":"Plain yogurt","prefix":null,"suffix":"g","section":"Substitutes (per egg = 60 g moisture + binder)","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"silken tofu g = eggs in recipe * 64 // g @label(Silken tofu) @suffix(g)","label":"Silken tofu","prefix":null,"suffix":"g","section":"Substitutes (per egg = 60 g moisture + binder)","hidden":false,"hero":false,"slider":null,"value":128,"display":"128"},{"text":"# Conversion","label":null,"prefix":null,"suffix":null,"section":"Conversion","hero":false,"slider":null,"value":null,"display":null},{"text":"bananas needed = round(banana mashed g / 120, 1) // @label(Medium bananas (≈120 g each))","label":"Medium bananas (≈120 g each)","prefix":null,"suffix":null,"section":"Conversion","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"}]},{"id":"balloon-inflation-volume","title":"Balloon Inflation Volume","description":"Calculate the volume of an inflated spherical balloon in liters from its radius.","category":"everyday","icon":"smile","tags":["inflation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"balloon_radius_cm = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"volume_liters = (4/3 * pi * balloon_radius_cm^3) / 1000 // liters @hero","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":14.137166941154067,"display":"14.14"}]},{"id":"bandwidth-calculator","title":"Bandwidth Calculator","description":"Calculate file transfer times and streaming data usage from bandwidth.","category":"programming","icon":"gauge","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Connection","label":null,"prefix":null,"suffix":null,"section":"Connection","hero":false,"slider":null,"value":null,"display":null},{"text":"bandwidth = 100 // Mbps 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@hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":0.02482758620689655,"display":"0.0248"}]},{"id":"beam-load","title":"Beam Load Calculator","description":"Calculate bending moment, shear force, and deflection for simply supported beams.","category":"engineering","icon":"ruler","tags":["engineering"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"# Beam Properties","label":null,"prefix":null,"suffix":null,"section":"Beam Properties","hero":false,"slider":null,"value":null,"display":null},{"text":"beam span = 10 // ft 2..40","label":null,"prefix":null,"suffix":"ft","section":"Beam Properties","hidden":false,"hero":false,"slider":{"min":2,"max":40,"step":1},"value":10,"display":"10"},{"text":"beam width = 6 // in 2..24","label":null,"prefix":null,"suffix":"in","section":"Beam 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* (beam_width * beam_depth^3 / 12)) // in","label":null,"prefix":null,"suffix":"in","section":"Results","hidden":false,"hero":false,"slider":null,"value":0.11029411764705882,"display":"0.1103"}]},{"id":"beat-matching-bpm-transition","title":"Beat Matching Bpm Transition","description":"Calculate the pitch adjustment percentage needed to match two tracks of different BPM.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"current_bpm = 120","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"target_bpm = 128","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":128,"display":"128"},{"text":"pitch_adjustment_percent = ((target_bpm / current_bpm) - 1) * 100 // @suffix(%) 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carbonation.","category":"other","icon":"beer","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"beer_volume_liters = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"desired_volumes_of_carbonation = 2.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"beer_temperature_celsius = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"residual_carbon_dioxide = 1.2 * (2.71828 ** (-0.019 * beer_temperature_celsius))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.8206339008154173,"display":"0.8206"},{"text":"sugar_needed_grams = (desired_volumes_of_carbonation - residual_carbon_dioxide) * 4 * beer_volume_liters","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":134.34928793476664,"display":"134.35"}]},{"id":"belt-drive-length-tension","title":"Belt Drive Length","description":"Calculate required belt length for a two-pulley drive.","category":"engineering","icon":"circle","tags":["engineering","mechanical","drive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.677Z"},"rows":[{"text":"pulley_1_diameter_inches = 4 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"pulley_2_diameter_inches = 10 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"center_distance_inches = 20 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"belt_length_inches = (2 * center_distance_inches) + (1.57 * (pulley_1_diameter_inches + pulley_2_diameter_inches)) + (((pulley_2_diameter_inches - pulley_1_diameter_inches)^2) / (4 * center_distance_inches)) // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":62.43,"display":"62.43"}]},{"id":"benjamin-graham-formula-value","title":"Benjamin Graham Formula Value","description":"Estimate a stock's intrinsic value using the Benjamin Graham formula.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"earnings_per_share = 5.00","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"expected_growth_rate = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"corporate_bond_yield = 0.04","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"},{"text":"intrinsic_value = (earnings_per_share * (8.5 + 2 * expected_growth_rate * 100) * 4.4) / (corporate_bond_yield * 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":101.75,"display":"101.75"}]},{"id":"bernoulli-principle-venturi","title":"Bernoulli Principle Venturi","description":"Calculate pressure change in a Venturi tube throat.","category":"engineering","icon":"wind","tags":["engineering","fluids","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"inlet_velocity_m_per_s = 1 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"inlet_pressure_pa = 200000 // Pa","label":null,"prefix":null,"suffix":"Pa","section":null,"hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"throat_velocity_m_per_s = 4 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"fluid_density_kg_m3 = 1000 // kg/m3","label":null,"prefix":null,"suffix":"kg/m3","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"throat_pressure_pa = inlet_pressure_pa - 0.5 * fluid_density_kg_m3 * (throat_velocity_m_per_s^2 - 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Pascals","label":null,"prefix":null,"suffix":"Pascals","section":null,"hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"velocity_2 = 5 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"pressure_2 = pressure_1 + 0.5 * fluid_density * (velocity_1^2 - velocity_2^2) // Pascals @hero","label":null,"prefix":null,"suffix":"Pascals","section":null,"hidden":false,"hero":true,"slider":null,"value":189500,"display":"189,500"}]},{"id":"beta-coefficient-stock","title":"Beta Coefficient Stock","description":"Calculate a stock's beta from stock return, market return, and risk-free rate.","category":"finance","icon":"dollar-sign","tags":["coefficient","stock","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"stock_return = 0.12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"market_return = 0.10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"risk_free_rate = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"beta = (stock_return - risk_free_rate) / (market_return - risk_free_rate)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.2857142857142858,"display":"1.286"}]},{"id":"bicycle-cadence-to-speed","title":"Bicycle Cadence To Speed","description":"Calculate bicycle speed in mph from cadence, gear ratio, and wheel 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cog_teeth","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.3333333333333335,"display":"3.333"},{"text":"distance_per_minute_mm = cadence_rpm * gear_ratio * wheel_circumference_millimeters","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":630000,"display":"630,000"},{"text":"speed_miles_per_hour = (distance_per_minute_mm * 60) / (25.4 * 12 * 5280) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":23.487831066571225,"display":"23.49"}]},{"id":"big-mac-index-valuation","title":"Big Mac Index Valuation","description":"Estimate currency over- or under-valuation using The Economist's Big Mac index.","category":"business","icon":"briefcase","tags":["index","valuation","business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"price_big_mac_local = 6.50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.5,"display":"6.5"},{"text":"price_big_mac_us = 5.60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5.6,"display":"5.6"},{"text":"actual_exchange_rate = 1.10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.1,"display":"1.1"},{"text":"implied_exchange_rate = price_big_mac_local / price_big_mac_us","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.1607142857142858,"display":"1.161"},{"text":"valuation = (actual_exchange_rate / implied_exchange_rate) - 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":-0.0523076923076924,"display":"-0.0523"}]},{"id":"big-o-complexity-growth","title":"Big O Complexity Growth","description":"Compare growth rates 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@hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":100,"display":"100"},{"text":"o n log n = n * log2(n) // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":664.3856189774725,"display":"664.39"},{"text":"o n squared = n^2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":10000,"display":"10,000"},{"text":"o 2 to the n = 2^n // @hero","label":null,"prefix":null,"suffix":null,"section":"Complexities","hidden":false,"hero":true,"slider":null,"value":1.2676506002282294e+30,"display":"1.2677e30"}]},{"id":"billable-hour-annual-income","title":"Billable Hour Annual Income","description":"Calculate gross annual income from hourly rate and weekly billable 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50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"millet_percentage = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"cracked_corn_percentage = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"total_mix_weight_kilograms = 5 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"sunflower_weight = total_mix_weight_kilograms * (sunflower_seeds_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"millet_weight = total_mix_weight_kilograms * (millet_percentage / 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Rules","label":null,"prefix":null,"suffix":null,"section":"Rules","hero":false,"slider":null,"value":null,"display":null},{"text":"number of decks = 6 // 1..8","label":null,"prefix":null,"suffix":null,"section":"Rules","hidden":false,"hero":false,"slider":{"min":1,"max":8,"step":0.1},"value":6,"display":"6"},{"text":"dealer hits soft 17 = 1 // toggle()","label":null,"prefix":null,"suffix":null,"section":"Rules","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Base Edge","label":null,"prefix":null,"suffix":null,"section":"Base Edge","hero":false,"slider":null,"value":null,"display":null},{"text":"base edge = 0.5 // % (typical)","label":null,"prefix":null,"suffix":"% (typical)","section":"Base Edge","hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_deck_penalty = (number of decks - 1) * 0.02","label":null,"prefix":null,"suffix":null,"section":"Base 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1..100","label":null,"prefix":null,"suffix":"%","section":"Option Parameters","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":20,"display":"20"},{"text":"# Intermediate Steps (Black-Scholes d1, d2)","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hero":false,"slider":null,"value":null,"display":null},{"text":"_s = share_price","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_k = strike_price","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_t = time_to_expiry","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_r = risk free rate / 100","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"_v = volatility / 100","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"_d1 = (ln(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t))","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.35,"display":"0.35"},{"text":"_d2 = d1 - v * sqrt(t)","label":null,"prefix":null,"suffix":null,"section":"Intermediate Steps (Black-Scholes d1, d2)","hidden":true,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"# Normal CDF Approximation (Logistic)","label":null,"prefix":null,"suffix":null,"section":"Normal CDF Approximation 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@hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":10.40364478039402,"display":"$10.40"},{"text":"$put option price = call option price + k * exp(-r * t) - s","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":5.52658723046542,"display":"$5.53"},{"text":"$intrinsic value = if(s > k, s - k, 0)","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":0,"display":"$0.00"},{"text":"$time value = call option price - intrinsic value","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":10.40364478039402,"display":"$10.40"}]},{"id":"block-wall-estimator","title":"Block Wall Estimator","description":"Estimate the number of standard CMU blocks needed for a wall, including 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144","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":17280,"display":"17,280"},{"text":"total blocks needed = roundup(wall_area_square_inches / block_area_square_inches) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":135,"display":"135"},{"text":"waste factor percent = 5 // 0..20","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":5,"display":"5"},{"text":"total blocks with waste = roundup(total blocks needed * (1 + waste factor percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":142,"display":"142"}]},{"id":"blood-alcohol-content","title":"Blood Alcohol Content","description":"Estimate blood alcohol content using the Widmark formula from drinks, weight, and 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60","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"bowling-average-calculator","title":"Bowling Average Calculator","description":"Calculate bowling average over multiple games.","category":"health","icon":"activity","tags":["sports"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Stats","label":null,"prefix":null,"suffix":null,"section":"Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"total pins = 2150","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":2150,"display":"2,150"},{"text":"total games = 12","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"bowling average = total pins / total games","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":179.16666666666666,"display":"179.17"}]},{"id":"bowling-score-projector","title":"Bowling Score Projector","description":"Project a final bowling score from current frame, current score, and season average.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Current Game","label":null,"prefix":null,"suffix":null,"section":"Current Game","hero":false,"slider":null,"value":null,"display":null},{"text":"current frame = 6 // 1..10","label":null,"prefix":null,"suffix":null,"section":"Current Game","hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":6,"display":"6"},{"text":"current score = 120","label":null,"prefix":null,"suffix":null,"section":"Current Game","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"season average = 180","label":null,"prefix":null,"suffix":null,"section":"Current Game","hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_frames_remaining = 10 - current frame","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"_projected_remaining = frames_remaining * (season average / 10)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":72,"display":"72"},{"text":"projected final score = current score + projected_remaining","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":192,"display":"192"}]},{"id":"boxing-punch-accuracy","title":"Boxing Punch Accuracy","description":"Calculate boxing punch accuracy.","category":"health","icon":"activity","tags":["sports"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Stats","label":null,"prefix":null,"suffix":null,"section":"Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"punches landed = 120","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"punches thrown = 350","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"punch accuracy percentage = (punches landed / punches thrown) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":34.28571428571429,"display":"34.29"}]},{"id":"boyles-law-pressure-volume","title":"Boyles Law Pressure Volume","description":"Calculate final gas volume after a pressure change at constant temperature using Boyle's Law.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"pressure_initial = 1.0 // atm","label":null,"prefix":null,"suffix":"atm","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"volume_initial = 2.0 // 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fahrenheit = 450","label":null,"prefix":null,"suffix":null,"section":"Fluid Stats","hidden":false,"hero":false,"slider":null,"value":450,"display":"450"},{"text":"wet boiling point fahrenheit = 300","label":null,"prefix":null,"suffix":null,"section":"Fluid Stats","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"months since change = 12","label":null,"prefix":null,"suffix":null,"section":"Fluid Stats","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_degradation_per_month = (dry boiling point fahrenheit - wet boiling point fahrenheit) / 24","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":6.25,"display":"6.25"},{"text":"estimated boiling point fahrenheit = dry boiling point fahrenheit - (months since change * 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costs.","category":"business","icon":"chart-bar","tags":["revenue","profit"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Revenue & Costs","label":null,"prefix":null,"suffix":null,"section":"Revenue & Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$price per unit = 49.99 // 1..500","label":null,"prefix":"$","suffix":null,"section":"Revenue & Costs","hidden":false,"hero":false,"slider":{"min":1,"max":500,"step":1},"value":49.99,"display":"$49.99"},{"text":"$variable cost per unit = 22.50 // 0.01..400","label":null,"prefix":"$","suffix":null,"section":"Revenue & Costs","hidden":false,"hero":false,"slider":{"min":0.01,"max":400,"step":5},"value":22.5,"display":"$22.50"},{"text":"$fixed costs monthly = 15000 // 1k..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Revenue & 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(including mortar joint)","label":null,"prefix":null,"suffix":null,"section":"Brick Dimensions (including mortar joint)","hero":false,"slider":null,"value":null,"display":null},{"text":"brick length = 8 // inches","label":null,"prefix":null,"suffix":"inches","section":"Brick Dimensions (including mortar joint)","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"brick height = 2.25 // inches","label":null,"prefix":null,"suffix":"inches","section":"Brick Dimensions (including mortar joint)","hidden":false,"hero":false,"slider":null,"value":2.25,"display":"2.25"},{"text":"mortar joint = 0.5 // inches","label":null,"prefix":null,"suffix":"inches","section":"Brick Dimensions (including mortar joint)","hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_effective_brick_length = brick length + 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bricks needed = roundup(wall_area_square_inches / brick_area_square_inches) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":986,"display":"986"},{"text":"waste factor percent = 10 // 0..25","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":{"min":0,"max":25,"step":1},"value":10,"display":"10"},{"text":"total bricks with waste = roundup(total bricks needed * (1 + waste factor percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":1085,"display":"1,085"}]},{"id":"brine-salt-percentage","title":"Brine Salt Percentage","description":"Calculate brine salt percentage from water volume and salt weight.","category":"health","icon":"activity","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"water_volume_milliliters = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"salt_weight_grams = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"salt_percentage = (salt_weight_grams / (water_volume_milliliters + salt_weight_grams)) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4.761904761904762,"display":"4.762"}]},{"id":"btu-air-conditioner-sizing","title":"Btu Air Conditioner Sizing","description":"Estimate BTU air conditioner size needed from room area, occupants, and sun exposure.","category":"other","icon":"calculator","tags":["air"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Room Info","label":null,"prefix":null,"suffix":null,"section":"Room 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kitchen_adjustment","label":null,"prefix":null,"suffix":null,"section":"Adjustments","hidden":true,"hero":false,"slider":null,"value":6000,"display":"6,000"},{"text":"_sun_adjustment = is sunny * (subtotal_btu * 0.1)","label":null,"prefix":null,"suffix":null,"section":"Adjustments","hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"total btu needed = roundup(subtotal_btu + sun_adjustment) // @hero","label":null,"prefix":null,"suffix":null,"section":"Adjustments","hidden":false,"hero":true,"slider":null,"value":6000,"display":"6,000"},{"text":"# Common Unit Size","label":null,"prefix":null,"suffix":null,"section":"Common Unit Size","hero":false,"slider":null,"value":null,"display":null},{"text":"# ACs are often sold in 1000s","label":null,"prefix":null,"suffix":null,"section":"ACs are often sold in 1000s","hero":false,"slider":null,"value":null,"display":null},{"text":"recommended ac size = roundup(total btu needed / 1000) * 1000","label":null,"prefix":null,"suffix":null,"section":"ACs are often sold in 1000s","hidden":false,"hero":false,"slider":null,"value":6000,"display":"6,000"}]},{"id":"bubble-wrap-pop-time","title":"Bubble Wrap Pop Time","description":"Calculate how long it takes to pop a sheet of bubble wrap at a given rate.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"number_of_bubbles = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"pops_per_second = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"time_minutes = (number_of_bubbles / pops_per_second) / 60 // minutes @hero","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":true,"slider":null,"value":0.8333333333333334,"display":"0.8333"}]},{"id":"buckling-load-euler-column","title":"Buckling Load Euler Column","description":"Calculate critical buckling load for structural columns.","category":"engineering","icon":"layers","tags":["engineering","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"elastic_modulus_psi = 29000000 // psi (steel)","label":null,"prefix":null,"suffix":"psi (steel)","section":null,"hidden":false,"hero":false,"slider":null,"value":29000000,"display":"29,000,000"},{"text":"moment_of_inertia_in4 = 0.5 // in^4","label":null,"prefix":null,"suffix":"in^4","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"column_length_inches = 60 // 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balances.","category":"science","icon":"flame","tags":["burn","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Startup Cash","label":null,"prefix":null,"suffix":null,"section":"Startup Cash","hero":false,"slider":null,"value":null,"display":null},{"text":"$starting cash balance = 500000 // 10k..10M","label":null,"prefix":"$","suffix":null,"section":"Startup Cash","hidden":false,"hero":false,"slider":{"min":10000,"max":10000000,"step":100000},"value":500000,"display":"$500,000.00"},{"text":"$ending cash balance = 350000 // 0..10M","label":null,"prefix":"$","suffix":null,"section":"Startup Cash","hidden":false,"hero":false,"slider":{"min":0,"max":10000000,"step":100000},"value":350000,"display":"$350,000.00"},{"text":"number of months = 6 // months 1..24","label":null,"prefix":null,"suffix":"months","section":"Startup 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rate","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"$annual burn = monthly burn rate * 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":300000,"display":"$300,000.00"}]},{"id":"burnout-risk-score","title":"Burnout Risk Score","description":"Estimate burnout risk from weekly work hours, stress, and autonomy levels.","category":"health","icon":"brain","tags":["risk"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"work_hours_per_week = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"stress_level_1_to_10 = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"autonomy_level_1_to_10 = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"risk_score = (work_hours_per_week * stress_level_1_to_10) / autonomy_level_1_to_10 // risk index @hero","label":null,"prefix":null,"suffix":"risk index","section":null,"hidden":false,"hero":true,"slider":null,"value":133.33333333333334,"display":"133.33"}]},{"id":"business-downtime-cost-per-minute","title":"Business Downtime Cost Per Minute","description":"Estimate the revenue cost of one hour of business downtime.","category":"productivity","icon":"clock","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"annual_revenue = 1000000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"business_hours_per_year = 2080 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":2080,"display":"2,080"},{"text":"_revenue_per_minute = annual_revenue / (business_hours_per_year * 60)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":8.012820512820513,"display":"8.013"},{"text":"downtime_cost_60_minutes = revenue_per_minute * 60 // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":480.7692307692308,"display":"480.77"}]},{"id":"bystander-effect-probability","title":"Bystander Effect Probability","description":"Calculate the probability that at least one bystander helps in an emergency.","category":"health","icon":"brain","tags":["effect","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"number_of_bystanders = 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@label(∫ₐᵇ x² dx)","label":"∫ₐᵇ x² dx","prefix":null,"suffix":null,"section":"Definite integral: the area under x² from a to b","hidden":false,"hero":true,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"# Indefinite integral — the antiderivative x³/3, as a graphable curve","label":null,"prefix":null,"suffix":null,"section":"Indefinite integral — the antiderivative x³/3, as a graphable curve","hero":false,"slider":null,"value":null,"display":null},{"text":"# Fundamental theorem check: the antiderivative of x³ is x⁴/4,","label":null,"prefix":null,"suffix":null,"section":"Fundamental theorem check: the antiderivative of x³ is x⁴/4,","hero":false,"slider":null,"value":null,"display":null},{"text":"# so ∫₀² x³ dx should equal (2⁴ − 0)/4 = 4.","label":null,"prefix":null,"suffix":null,"section":"so ∫₀² x³ dx should equal (2⁴ − 0)/4 = 4.","hero":false,"slider":null,"value":null,"display":null},{"text":"cubic_area = integral(x^3, 0, 2) // @label(∫₀² x³ dx)","label":"∫₀² x³ dx","prefix":null,"suffix":null,"section":"so ∫₀² x³ dx should equal (2⁴ − 0)/4 = 4.","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"}]},{"id":"calorie-deficit","title":"Calorie Deficit","description":"Calculate your TDEE and calorie targets for weight loss using the Mifflin-St Jeor equation.","category":"health","icon":"utensils","tags":["calories"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Your Stats","label":null,"prefix":null,"suffix":null,"section":"Your Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"current weight = 180 // lbs 80..400","label":null,"prefix":null,"suffix":"lbs","section":"Your Stats","hidden":false,"hero":false,"slider":{"min":80,"max":400,"step":1},"value":180,"display":"180"},{"text":"height = 70 // inches 48..84","label":null,"prefix":null,"suffix":"inches","section":"Your Stats","hidden":false,"hero":false,"slider":{"min":48,"max":84,"step":1},"value":70,"display":"70"},{"text":"age = 30 // years 15..80","label":null,"prefix":null,"suffix":"years","section":"Your Stats","hidden":false,"hero":false,"slider":{"min":15,"max":80,"step":1},"value":30,"display":"30"},{"text":"activity factor = 1.55 // 1.2..1.9 by 0.05","label":null,"prefix":null,"suffix":null,"section":"Your Stats","hidden":false,"hero":false,"slider":{"min":1.2,"max":1.9,"step":0.05},"value":1.55,"display":"1.55"},{"text":"# Metabolic Rate","label":null,"prefix":null,"suffix":null,"section":"Metabolic Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"_weight_kg = current_weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"Metabolic Rate","hidden":true,"hero":false,"slider":null,"value":81.64656,"display":"81.65"},{"text":"_height_cm = height * 2.54","label":null,"prefix":null,"suffix":null,"section":"Metabolic Rate","hidden":true,"hero":false,"slider":null,"value":177.8,"display":"177.8"},{"text":"_basal_metabolic_rate = round(10 * weight_kg + 6.25 * height_cm - 5 * age + 5) // cal","label":null,"prefix":null,"suffix":"cal","section":"Metabolic Rate","hidden":true,"hero":false,"slider":null,"value":1783,"display":"1,783"},{"text":"total daily energy = round(basal_metabolic_rate * activity_factor) // cal @hero","label":null,"prefix":null,"suffix":"cal","section":"Metabolic Rate","hidden":false,"hero":true,"slider":null,"value":2764,"display":"2,764"},{"text":"# Weight Loss Targets @layout(grid)","label":null,"prefix":null,"suffix":null,"section":"Weight Loss Targets","hero":false,"slider":null,"value":null,"display":null},{"text":"mild loss = total_daily_energy - 250 // cal/day","label":null,"prefix":null,"suffix":"cal/day","section":"Weight Loss Targets","hidden":false,"hero":false,"slider":null,"value":2514,"display":"2,514"},{"text":"moderate loss = total_daily_energy - 500 // cal/day","label":null,"prefix":null,"suffix":"cal/day","section":"Weight Loss Targets","hidden":false,"hero":false,"slider":null,"value":2264,"display":"2,264"},{"text":"aggressive loss = total_daily_energy - 1000 // cal/day","label":null,"prefix":null,"suffix":"cal/day","section":"Weight Loss Targets","hidden":false,"hero":false,"slider":null,"value":1764,"display":"1,764"}]},{"id":"calories-burned-standing-desk","title":"Calories Burned Standing Desk","description":"Estimate extra calories burned standing instead of sitting at a desk.","category":"health","icon":"activity","tags":["calories","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"user_weight_pounds = 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"standing_hours = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"additional_calories_burned = standing_hours * 60 * 0.15 * (user_weight_pounds / 150) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":43.2,"display":"43.2"}]},{"id":"camera-iso-noise-estimate","title":"Camera Iso Noise Estimate","description":"Estimate camera noise increase as ISO rises above the base ISO.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"base_iso = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"current_iso = 3200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3200,"display":"3,200"},{"text":"base_noise_percent = 0.5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"estimated_noise_percent = base_noise_percent * (current_iso / base_iso)^0.5 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.8284271247461903,"display":"2.828"}]},{"id":"camera-sensor-crop-factor","title":"Camera Sensor Crop Factor","description":"Calculate a camera sensor's crop factor relative to full-frame 35mm.","category":"math","icon":"camera","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"sensor_width_millimeters = 23.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":23.5,"display":"23.5"},{"text":"sensor_height_millimeters = 15.6","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15.6,"display":"15.6"},{"text":"full_frame_diagonal = (36^2 + 24^2)^0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":43.266615305567875,"display":"43.27"},{"text":"sensor_diagonal = (sensor_width_millimeters^2 + sensor_height_millimeters^2)^0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":28.20655952079232,"display":"28.21"},{"text":"crop_factor = full_frame_diagonal / sensor_diagonal // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.5339203377027997,"display":"1.534"}]},{"id":"camshaft-lift-duration","title":"Camshaft Lift Duration","description":"Calculate valve lift from lobe lift and rocker ratio.","category":"engineering","icon":"settings","tags":["automotive","engine"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Cam Specs","label":null,"prefix":null,"suffix":null,"section":"Cam Specs","hero":false,"slider":null,"value":null,"display":null},{"text":"lobe lift inches = 0.35","label":null,"prefix":null,"suffix":null,"section":"Cam Specs","hidden":false,"hero":false,"slider":null,"value":0.35,"display":"0.35"},{"text":"rocker ratio = 1.5","label":null,"prefix":null,"suffix":null,"section":"Cam Specs","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"valve lift inches = lobe lift inches * rocker ratio","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":0.525,"display":"0.525"}]},{"id":"candle-burn-duration","title":"Candle Burn Duration","description":"Calculate total candle burn time in hours from height and burn rate.","category":"everyday","icon":"smile","tags":["burn"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"candle_height_cm = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"burn_rate_cm_per_hour = 1.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"total_burn_time = candle_height_cm / burn_rate_cm_per_hour // hours @hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":13.333333333333334,"display":"13.33"}]},{"id":"canning-processing-time-altitude","title":"Canning Processing Time Altitude","description":"Adjust home canning processing time for altitude above sea level.","category":"productivity","icon":"clock","tags":["altitude","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"standard_time_minutes = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"altitude_feet = 4500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4500,"display":"4,500"},{"text":"time_increase = (altitude_feet > 6000) ? 15 : (altitude_feet > 3000) ? 10 : (altitude_feet > 1000) ? 5 : 0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"adjusted_time_minutes = standard_time_minutes + time_increase // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"cantilever-beam-stress","title":"Cantilever Beam Stress","description":"Calculate max bending stress for a cantilever beam.","category":"engineering","icon":"ruler","tags":["engineering","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"force_at_tip_lbs = 200 // lbs","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"beam_length_inches = 48 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"section_modulus_in3 = 2 // in^3","label":null,"prefix":null,"suffix":"in^3","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"max_bending_stress_psi = (force_at_tip_lbs * beam_length_inches) / section_modulus_in3 // psi @hero","label":null,"prefix":null,"suffix":"psi","section":null,"hidden":false,"hero":true,"slider":null,"value":4800,"display":"4,800"}]},{"id":"canvas-dpi-print-resolution","title":"Canvas Dpi Print Resolution","description":"Calculate pixel dimensions needed to print a canvas at a target DPI.","category":"design","icon":"palette","tags":["print"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"width_inches = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"height_inches = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"dpi = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"width_pixels = width_inches * dpi // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":2400,"display":"2,400"},{"text":"height_pixels = height_inches * dpi // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":3000,"display":"3,000"}]},{"id":"cap-rate-by-neighborhood","title":"Cap Rate by Neighborhood","description":"Calculate the capitalization rate for specific local real 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voltage.","category":"health","icon":"activity","tags":["storage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"capacitance_microfarads = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"voltage_volts = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"energy_stored_joules = 0.5 * (capacitance_microfarads / 1000000) * voltage_volts ** 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.3125,"display":"0.3125"}]},{"id":"capacitor-rc-time-constant","title":"Capacitor Rc Time Constant","description":"Calculate the RC time constant in seconds for a resistor-capacitor 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percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":true,"hero":false,"slider":null,"value":99.3,"display":"99.3"}]},{"id":"capital-expenditure-capex-reserve","title":"CapEx Reserve","description":"Calculate the recommended monthly reserve for major repairs.","category":"real-estate","icon":"archive","tags":["capital"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"grossMonthlyRent = 2000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"capexReservePercentage = 8 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"monthlyCapexReserve = grossMonthlyRent * (capexReservePercentage / 100) // @prefix($) @suffix(/mo) 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%","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":56.25,"display":"56.25"}]},{"id":"car-affordability","title":"Car Affordability","description":"Find the max car price you can afford from your monthly budget.","category":"finance","icon":"car","tags":["car","budget"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Budget","label":null,"prefix":null,"suffix":null,"section":"Budget","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly budget = 500 // 100..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Budget","hidden":false,"hero":false,"slider":{"min":100,"max":2000,"step":25},"value":500,"display":"$500.00"},{"text":"interest rate = 6 // % 0..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Budget","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.1},"value":6,"display":"6"},{"text":"loan term = 60 // 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100","label":null,"prefix":"$","suffix":null,"section":"Affordability","hidden":false,"hero":false,"slider":null,"value":4137.22,"display":"$4,137.22"}]},{"id":"car-depreciation","title":"Car Depreciation","description":"Calculate a car's current value, total depreciation, and percent retained.","category":"other","icon":"car","tags":["car","depreciation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Car Value","label":null,"prefix":null,"suffix":null,"section":"Car Value","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchase price = 35000 // 5k..150k by 500","label":null,"prefix":"$","suffix":null,"section":"Car Value","hidden":false,"hero":false,"slider":{"min":5000,"max":150000,"step":500},"value":35000,"display":"$35,000.00"},{"text":"annual depreciation rate = 15 // % 5..30","label":null,"prefix":null,"suffix":"%","section":"Car 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Details","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":500},"value":5000,"display":"$5,000.00"},{"text":"interest rate = 5.5 // % 0..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Car Details","hidden":false,"hero":false,"slider":{"min":0,"max":15,"step":0.1},"value":5.5,"display":"5.5"},{"text":"loan term = 60 // months 12..84","label":null,"prefix":null,"suffix":"months","section":"Car Details","hidden":false,"hero":false,"slider":{"min":12,"max":84,"step":1},"value":60,"display":"60"},{"text":"# Loan Calculation","label":null,"prefix":null,"suffix":null,"section":"Loan Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = car price - down payment","label":null,"prefix":"$","suffix":null,"section":"Loan Calculation","hidden":false,"hero":false,"slider":null,"value":30000,"display":"$30,000.00"},{"text":"monthly rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Loan Calculation","hidden":false,"hero":false,"slider":null,"value":0.004583333333333333,"display":"0.004583"},{"text":"$monthly payment = loan amount * (monthly rate * (1 + monthly rate)^loan term) / ((1 + monthly rate)^loan term - 1) // @hero","label":null,"prefix":"$","suffix":null,"section":"Loan Calculation","hidden":false,"hero":true,"slider":null,"value":573.0348651534617,"display":"$573.03"},{"text":"# Total Cost","label":null,"prefix":null,"suffix":null,"section":"Total Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$total paid = round(monthly payment * loan term * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Total Cost","hidden":false,"hero":false,"slider":null,"value":34382.09,"display":"$34,382.09"},{"text":"$total interest = round((total paid - loan amount) * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Total Cost","hidden":false,"hero":false,"slider":null,"value":4382.09,"display":"$4,382.09"},{"text":"$total car cost = round((total paid + down payment) * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Total Cost","hidden":false,"hero":false,"slider":null,"value":39382.09,"display":"$39,382.09"}]},{"id":"car-rental-vs-own","title":"Car Rental vs Own","description":"Compare monthly cost of owning a car against renting one as needed.","category":"other","icon":"car","tags":["car","rental"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Ownership Costs","label":null,"prefix":null,"suffix":null,"section":"Ownership Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly car payment = 500 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Ownership Costs","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":500,"display":"$500.00"},{"text":"$monthly insurance = 150 // 0..500 by 10","label":null,"prefix":"$","suffix":null,"section":"Ownership Costs","hidden":false,"hero":false,"slider":{"min":0,"max":500,"step":10},"value":150,"display":"$150.00"},{"text":"$monthly maintenance and gas = 200 // 0..1k by 25","label":null,"prefix":"$","suffix":null,"section":"Ownership Costs","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":25},"value":200,"display":"$200.00"},{"text":"# Rental Costs","label":null,"prefix":null,"suffix":null,"section":"Rental Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$rental cost per day = 80 // 20..500","label":null,"prefix":"$","suffix":null,"section":"Rental Costs","hidden":false,"hero":false,"slider":{"min":20,"max":500,"step":1},"value":80,"display":"$80.00"},{"text":"days needed per month = 10 // days 0..31","label":null,"prefix":null,"suffix":"days","section":"Rental Costs","hidden":false,"hero":false,"slider":{"min":0,"max":31,"step":1},"value":10,"display":"10"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_monthly_ownership_cost = monthly car payment + monthly insurance + monthly maintenance and gas","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":850,"display":"$850.00"},{"text":"$_total_monthly_rental_cost = rental cost per day * days needed per month","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":800,"display":"$800.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly savings by renting = total_monthly_ownership_cost - total_monthly_rental_cost // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":50,"display":"$50.00"},{"text":"$annual ownership cost = total_monthly_ownership_cost * 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":10200,"display":"$10,200.00"},{"text":"$annual rental cost = total_monthly_rental_cost * 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":9600,"display":"$9,600.00"},{"text":"break even days per month = total_monthly_ownership_cost / rental cost per day","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":10.625,"display":"10.63"}]},{"id":"carbon-sequestration-per-tree","title":"Carbon Sequestration Per Tree","description":"Estimate annual CO2 sequestered by a tree from age and growth rate.","category":"health","icon":"activity","tags":["carbon","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"tree_age_years = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"growth_rate_factor = 1.0 // 1.0 for average, 1.5 for fast","label":null,"prefix":null,"suffix":"1.0 for average, 1.5 for fast","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"annual_co2_sequestered_pounds = 48 * growth_rate_factor * (min(tree_age_years, 25) / 25) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":38.4,"display":"38.4"}]},{"id":"carpet-area-calculator","title":"Carpet Area Calculator","description":"Calculate carpet square yardage and total cost from room dimensions and waste.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"# Room Dimensions","label":null,"prefix":null,"suffix":null,"section":"Room 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10..100","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":{"min":10,"max":100,"step":1},"value":30,"display":"$30.00"},{"text":"$total cost = round(total yards with waste * price per square yard, 2)","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":null,"value":660,"display":"$660.00"}]},{"id":"carpooling-emissions-savings","title":"Carpooling Emissions Savings","description":"Calculate annual CO2 savings by sharing your commute.","category":"science","icon":"users","tags":["eco","travel","emissions"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.680Z"},"rows":[{"text":"commute_distance_km = 30 // km","label":null,"prefix":null,"suffix":"km","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"days_per_year = 240 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":240,"display":"240"},{"text":"carpool_members = 3 // people","label":null,"prefix":null,"suffix":"people","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"emissions_per_km = 0.15 // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"total_annual_emissions_solo = commute_distance_km * 2 * days_per_year * emissions_per_km // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":2160,"display":"2,160"},{"text":"annual_emissions_per_person_carpool = total_annual_emissions_solo / carpool_members // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":720,"display":"720"},{"text":"annual_co2_savings_per_person = total_annual_emissions_solo - annual_emissions_per_person_carpool // kg CO2 @hero","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":true,"slider":null,"value":1440,"display":"1,440"}]},{"id":"cash-conversion-cycle","title":"Cash Conversion Cycle","description":"Calculate the cash conversion cycle from inventory, receivable, and payable days.","category":"finance","icon":"dollar-sign","tags":["cash","cycle","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"days_inventory_outstanding = 60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"days_sales_outstanding = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"days_payable_outstanding = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"cash_conversion_cycle = days_inventory_outstanding + days_sales_outstanding - days_payable_outstanding","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":75,"display":"75"}]},{"id":"cash-on-cash-return-advanced","title":"Cash on Cash Return","description":"Calculate annual return based on the actual cash invested.","category":"real-estate","icon":"dollar-sign","tags":["cash"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"annualPreTaxCashFlow = 5000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"totalCashInvested = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"cashOnCashReturn = (annualPreTaxCashFlow / totalCashInvested) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"cash-on-cash-return","title":"Cash On Cash Return","description":"Calculate cash-on-cash return and recoup time from down payment and annual cash flow.","category":"finance","icon":"dollar-sign","tags":["cash","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Investment Analysis","label":null,"prefix":null,"suffix":null,"section":"Investment Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchase price = 300000 // 50k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":50000,"max":1000000,"step":5000},"value":300000,"display":"$300,000.00"},{"text":"$down payment = 60000 // 0..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":1000},"value":60000,"display":"$60,000.00"},{"text":"$closing costs = 9000 // 0..50k","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":500},"value":9000,"display":"$9,000.00"},{"text":"$total annual pre tax cash flow = 7200 // 0..50k by 100","label":null,"prefix":"$","suffix":null,"section":"Investment Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":100},"value":7200,"display":"$7,200.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_cash_invested = down payment + closing costs","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":69000,"display":"$69,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"cash on cash return = (total annual pre tax cash flow / total_cash_invested) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":10.434782608695652,"display":"10.43"},{"text":"$monthly cash flow = total annual pre tax cash flow / 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":600,"display":"$600.00"},{"text":"years to recoup investment = total_cash_invested / total annual pre tax cash flow","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":9.583333333333334,"display":"9.583"}]},{"id":"cat-years-to-human-years","title":"Cat Years To Human Years","description":"Convert a cat's age in years to its equivalent human age.","category":"everyday","icon":"cat","tags":["human","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"actual_cat_age_years = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"first_year_human_equivalent = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"second_year_human_equivalent = 9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"additional_years_multiplier = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"equivalent_human_age = first_year_human_equivalent + second_year_human_equivalent + (actual_cat_age_years - 2) * additional_years_multiplier","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"cell-turnover","title":"Cell Turnover","description":"Total cells in the body and how many are replaced each day or year.","category":"health","icon":"atom","tags":["biology","body","turnover"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Person","label":null,"prefix":null,"suffix":null,"section":"Person","hero":false,"slider":null,"value":null,"display":null},{"text":"body weight kg = 70 // kg 1..200","label":null,"prefix":null,"suffix":"kg","section":"Person","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":70,"display":"70"},{"text":"turnover years = 7 // years 1..80","label":null,"prefix":null,"suffix":"years","section":"Person","hidden":false,"hero":false,"slider":{"min":1,"max":80,"step":1},"value":7,"display":"7"},{"text":"# Cell Count (≈ 528 billion per kg)","label":null,"prefix":null,"suffix":null,"section":"Cell Count (≈ 528 billion per kg)","hero":false,"slider":null,"value":null,"display":null},{"text":"_cells_per_kg = 528000000000","label":null,"prefix":null,"suffix":null,"section":"Cell Count (≈ 528 billion per kg)","hidden":true,"hero":false,"slider":null,"value":528000000000,"display":"528,000,000,000"},{"text":"total cells = body weight kg * cells_per_kg // @hero @label(Total cells in body)","label":"Total cells in body","prefix":null,"suffix":null,"section":"Cell Count (≈ 528 billion per kg)","hidden":false,"hero":true,"slider":null,"value":36960000000000,"display":"36,960,000,000,000"},{"text":"# Replacement Rate","label":null,"prefix":null,"suffix":null,"section":"Replacement Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"cells per year = total cells / turnover years // @label(Cells replaced per year)","label":"Cells replaced per year","prefix":null,"suffix":null,"section":"Replacement Rate","hidden":false,"hero":false,"slider":null,"value":5280000000000,"display":"5,280,000,000,000"},{"text":"cells per day = cells per year / 365 // @label(Cells replaced per day)","label":"Cells replaced per day","prefix":null,"suffix":null,"section":"Replacement Rate","hidden":false,"hero":false,"slider":null,"value":14465753424.657534,"display":"14,465,753,424.66"},{"text":"cells per second = round(cells per day / 86400) // @label(Cells replaced per second)","label":"Cells replaced per second","prefix":null,"suffix":null,"section":"Replacement Rate","hidden":false,"hero":false,"slider":null,"value":167428,"display":"167,428"},{"text":"# Lifetime","label":null,"prefix":null,"suffix":null,"section":"Lifetime","hero":false,"slider":null,"value":null,"display":null},{"text":"lifetime years = 80 // years 1..120","label":null,"prefix":null,"suffix":"years","section":"Lifetime","hidden":false,"hero":false,"slider":{"min":1,"max":120,"step":1},"value":80,"display":"80"},{"text":"total replacements = round(lifetime years / turnover years, 1) // @label(Full-body replacements in a lifetime)","label":"Full-body replacements in a lifetime","prefix":null,"suffix":null,"section":"Lifetime","hidden":false,"hero":false,"slider":null,"value":11.4,"display":"11.4"}]},{"id":"centripetal-acceleration-rotation","title":"Centripetal Acceleration Rotation","description":"Calculate centripetal acceleration from rotational radius and velocity.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"radius = 5 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"velocity = 10 // meters per second","label":null,"prefix":null,"suffix":"meters per second","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"centripetal_acceleration = velocity^2 / radius // meters per second squared @hero","label":null,"prefix":null,"suffix":"meters per second squared","section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"chain-drive-speed-ratio","title":"Chain Drive Speed Ratio","description":"Calculate driven RPM and ratio for chain and sprocket.","category":"engineering","icon":"settings","tags":["engineering","mechanical","drive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"driver_sprocket_teeth = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"driven_sprocket_teeth = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"driver_rpm = 1000 // RPM","label":null,"prefix":null,"suffix":"RPM","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"driven_rpm = driver_rpm * (driver_sprocket_teeth / driven_sprocket_teeth) // RPM @hero","label":null,"prefix":null,"suffix":"RPM","section":null,"hidden":false,"hero":true,"slider":null,"value":333.3333333333333,"display":"333.33"},{"text":"speed_ratio = driven_sprocket_teeth / driver_sprocket_teeth","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"}]},{"id":"champagne-bottle-pressure","title":"Champagne Bottle Pressure","description":"Estimate the internal pressure of a champagne bottle at a given temperature.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"temperature_celsius = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"pressure_atmospheres = 5 + 0.2 * (temperature_celsius - 10) // atmospheres @hero","label":null,"prefix":null,"suffix":"atmospheres","section":null,"hidden":false,"hero":true,"slider":null,"value":7,"display":"7"}]},{"id":"charitable-donation-tax-savings","title":"Charitable Donation Tax Savings","description":"Calculate tax savings and net cost of a charitable donation at your tax bracket.","category":"finance","icon":"dollar-sign","tags":["tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"donation_amount = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"tax_rate = 0.35","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.35,"display":"0.35"},{"text":"tax_savings = donation_amount * tax_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"net_cost = donation_amount - tax_savings","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":650,"display":"650"}]},{"id":"charles-law-volume-temperature","title":"Charles Law Volume Temperature","description":"Calculate the final gas volume after a temperature change using Charles's Law.","category":"education","icon":"book-open","tags":["temperature"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"volume_initial = 1.5 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"temperature_initial_celsius = 25 // Celsius","label":null,"prefix":null,"suffix":"Celsius","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"temperature_final_celsius = 100 // Celsius","label":null,"prefix":null,"suffix":"Celsius","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_t1_kelvin = temperature_initial_celsius + 273.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":298.15,"display":"298.15"},{"text":"_t2_kelvin = temperature_final_celsius + 273.15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":373.15,"display":"373.15"},{"text":"volume_final = volume_initial * (t2_kelvin / t1_kelvin) // liters @hero","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":1.8773268489015598,"display":"1.877"}]},{"id":"cheese-yield-from-milk","title":"Cheese Yield From Milk","description":"Estimate cheese yield in pounds from milk volume, fat content, and cheese type.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"milk_volume_gallons = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"milk_fat_percent = 3.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.5,"display":"3.5"},{"text":"cheese_type_factor = 0.1 // Hard cheese: 0.1, Soft: 0.2","label":null,"prefix":null,"suffix":"Hard cheese: 0.1, Soft: 0.2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"estimated_cheese_weight_pounds = milk_volume_gallons * 8.6 * cheese_type_factor * (milk_fat_percent / 3.5) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.72,"display":"1.72"}]},{"id":"chemical-balancing-stoichiometry","title":"Chemical Balancing Stoichiometry","description":"Calculate the total mass of reactants from moles and molar masses.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"reactant_1_moles = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"reactant_1_molar_mass = 18.02 // g/mol","label":null,"prefix":null,"suffix":"g/mol","section":null,"hidden":false,"hero":false,"slider":null,"value":18.02,"display":"18.02"},{"text":"reactant_2_moles = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"reactant_2_molar_mass = 32.00 // g/mol","label":null,"prefix":null,"suffix":"g/mol","section":null,"hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"total_mass = (reactant_1_moles * reactant_1_molar_mass) + (reactant_2_moles * reactant_2_molar_mass) // grams @hero","label":null,"prefix":null,"suffix":"grams","section":null,"hidden":false,"hero":true,"slider":null,"value":82.02,"display":"82.02"}]},{"id":"chess-elo-rating-change","title":"Chess Elo Rating Change","description":"Calculate Elo rating change after a chess game from K-factor and outcome.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Ratings","label":null,"prefix":null,"suffix":null,"section":"Ratings","hero":false,"slider":null,"value":null,"display":null},{"text":"your rating = 1500","label":null,"prefix":null,"suffix":null,"section":"Ratings","hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"opponent rating = 1600","label":null,"prefix":null,"suffix":null,"section":"Ratings","hidden":false,"hero":false,"slider":null,"value":1600,"display":"1,600"},{"text":"k factor = 32 // stability factor","label":null,"prefix":null,"suffix":"stability factor","section":"Ratings","hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"# Outcome","label":null,"prefix":null,"suffix":null,"section":"Outcome","hero":false,"slider":null,"value":null,"display":null},{"text":"score = 1 // 1 for win, 0.5 for draw, 0 for loss","label":null,"prefix":null,"suffix":"1 for win, 0.5 for draw, 0 for loss","section":"Outcome","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_expected_score = 1 / (1 + 10 ^ ((opponent rating - your rating) / 400))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":0.35993500019711494,"display":"0.3599"},{"text":"rating change = k factor * (score - expected_score) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":20.48207999369232,"display":"20.48"},{"text":"new rating = your rating + rating change // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":1520.4820799936922,"display":"1,520.48"}]},{"id":"chicken-egg-production-timer","title":"Chicken Egg Production Timer","description":"Estimate total eggs from a flock over a collection period.","category":"productivity","icon":"clock","tags":["timer","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"number_of_hens = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"eggs_per_hen_per_week = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"days_to_collect = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"estimated_total_eggs = number_of_hens * (eggs_per_hen_per_week / 7) * days_to_collect // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":25,"display":"25"}]},{"id":"child-support-estimate","title":"Child Support Estimate","description":"Estimate monthly child support based on parental income.","category":"other","icon":"users","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"nonCustodialMonthlyIncome = 5000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"numberOfChildren = 2 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"supportPercentagePerChild = 17 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":17,"display":"17"},{"text":"monthlySupport = nonCustodialMonthlyIncome * (supportPercentagePerChild / 100) * numberOfChildren // @prefix($) @suffix(/mo) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1700,"display":"1,700"}]},{"id":"churn-rate","title":"Churn Rate","description":"Calculate monthly customer churn rate, retention, and estimated customer half-life.","category":"business","icon":"briefcase","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Customer Retention","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hero":false,"slider":null,"value":null,"display":null},{"text":"customers at start of month = 1200 // 1..100k","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hidden":false,"hero":false,"slider":{"min":1,"max":100000,"step":1000},"value":1200,"display":"1,200"},{"text":"customers lost during month = 60 // 0..10k","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":60,"display":"60"},{"text":"new customers added = 80 // 0..10k","label":null,"prefix":null,"suffix":null,"section":"Customer Retention","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":80,"display":"80"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly churn rate = (customers lost during month / customers at start of month) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"retention rate = 100 - monthly churn rate // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":95,"display":"95"},{"text":"estimated customer half life = 70 / monthly churn rate // months (Rule of 70 approx)","label":null,"prefix":null,"suffix":"months (Rule of 70 approx)","section":"Result","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"$net change = new customers added - customers lost during month","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":20,"display":"$20.00"}]},{"id":"cinematic-aspect-ratio-letterbox","title":"Cinematic Aspect Ratio Letterbox","description":"Calculate letterbox bar height for displaying a cinematic aspect ratio on a screen.","category":"design","icon":"palette","tags":["aspect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"screen_width = 1920 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":1920,"display":"1,920"},{"text":"screen_height = 1080 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":1080,"display":"1,080"},{"text":"target_aspect_ratio = 2.39 // cinematic wide","label":null,"prefix":null,"suffix":"cinematic wide","section":null,"hidden":false,"hero":false,"slider":null,"value":2.39,"display":"2.39"},{"text":"_content_height = screen_width / target_aspect_ratio","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":803.347280334728,"display":"803.35"},{"text":"letterbox_bar_height = (screen_height - content_height) / 2 // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":138.326359832636,"display":"138.33"}]},{"id":"circle-area","title":"Circle Area","description":"Find the area of a circle from its radius: A = π × r².","category":"formulas","icon":"circle","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Radius","label":null,"prefix":null,"suffix":null,"section":"Radius","hero":false,"slider":null,"value":null,"display":null},{"text":"radius = 5 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Radius","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"# Area","label":null,"prefix":null,"suffix":null,"section":"Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = pi * radius^2","label":null,"prefix":null,"suffix":null,"section":"Area","hidden":false,"hero":true,"slider":null,"value":78.53981633974483,"display":"78.54"}]},{"id":"circle-circumference","title":"Circle Circumference","description":"Find the circumference of a circle from its radius: C = 2 × π × r.","category":"formulas","icon":"circle","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Radius","label":null,"prefix":null,"suffix":null,"section":"Radius","hero":false,"slider":null,"value":null,"display":null},{"text":"radius = 5 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Radius","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"# Circumference and diameter","label":null,"prefix":null,"suffix":null,"section":"Circumference and diameter","hero":false,"slider":null,"value":null,"display":null},{"text":"circumference = 2 * pi * radius // @hero","label":null,"prefix":null,"suffix":null,"section":"Circumference and diameter","hidden":false,"hero":true,"slider":null,"value":31.415926535897928,"display":"31.42"},{"text":"diameter = 2 * radius","label":null,"prefix":null,"suffix":null,"section":"Circumference and diameter","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"}]},{"id":"class-grade","title":"Class Grade","description":"Calculate your weighted class grade from assignments and exams.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Homework","label":null,"prefix":null,"suffix":null,"section":"Homework","hero":false,"slider":null,"value":null,"display":null},{"text":"homework_score = 92 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Homework","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":92,"display":"92"},{"text":"homework_weight = 30 // % 5..50 by 5","label":null,"prefix":null,"suffix":"%","section":"Homework","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":5},"value":30,"display":"30"},{"text":"# Midterm","label":null,"prefix":null,"suffix":null,"section":"Midterm","hero":false,"slider":null,"value":null,"display":null},{"text":"midterm_score = 78 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Midterm","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":78,"display":"78"},{"text":"midterm_weight = 30 // % 5..50 by 5","label":null,"prefix":null,"suffix":"%","section":"Midterm","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":5},"value":30,"display":"30"},{"text":"# Final Exam","label":null,"prefix":null,"suffix":null,"section":"Final Exam","hero":false,"slider":null,"value":null,"display":null},{"text":"final_score = 85 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Final Exam","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":85,"display":"85"},{"text":"final_weight = 40 // % 5..50 by 5","label":null,"prefix":null,"suffix":"%","section":"Final Exam","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":5},"value":40,"display":"40"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"total_weight = homework_weight + midterm_weight + final_weight // %","label":null,"prefix":null,"suffix":"%","section":"Results","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"weighted_average = round((homework_score * homework_weight + midterm_score * midterm_weight + final_score * final_weight) / total_weight * 10) / 10 // %","label":null,"prefix":null,"suffix":"%","section":"Results","hidden":false,"hero":true,"slider":null,"value":85,"display":"85"}]},{"id":"clay-shrinkage-pottery-percent","title":"Clay Shrinkage Pottery Percent","description":"Calculate clay shrinkage percentage between wet and fired pottery dimensions.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"wet_length = 10 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"fired_length = 8.8 // cm","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":false,"slider":null,"value":8.8,"display":"8.8"},{"text":"shrinkage_percentage = ((wet_length - fired_length) / wet_length) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12,"display":"12"}]},{"id":"click-to-solve-logistic","title":"Click-to-solve logistic growth","description":"A logistic curve has three knobs: carrying capacity, midpoint, and steepness.","category":"science","icon":"activity","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Logistic parameters","label":null,"prefix":null,"suffix":null,"section":"Logistic parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"K = 100 // 1..200 — carrying capacity (the eventual plateau)","label":null,"prefix":null,"suffix":"1..200 — carrying capacity (the eventual plateau)","section":"Logistic parameters","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"x_0 = 5 // -5..15 — midpoint (where growth peaks)","label":null,"prefix":null,"suffix":"-5..15 — midpoint (where growth peaks)","section":"Logistic parameters","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"k = 1 // 0.1..3 — steepness","label":null,"prefix":null,"suffix":"0.1..3 — steepness","section":"Logistic parameters","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# The logistic curve. Click any point — the solver will move the","label":null,"prefix":null,"suffix":null,"section":"The logistic curve. Click any point — the solver will move the","hero":false,"slider":null,"value":null,"display":null},{"text":"# midpoint `x_0` to land the curve through your click.","label":null,"prefix":null,"suffix":null,"section":"midpoint `x_0` to land the curve through your click.","hero":false,"slider":null,"value":null,"display":null},{"text":"# Click at (8, 90) to see the midpoint shift right so 90% adoption","label":null,"prefix":null,"suffix":null,"section":"Click at (8, 90) to see the midpoint shift right so 90% adoption","hero":false,"slider":null,"value":null,"display":null},{"text":"# lands at x = 8. Then click (3, 50) to shift it left for \"halfway by 3\".","label":null,"prefix":null,"suffix":null,"section":"lands at x = 8. Then click (3, 50) to shift it left for \"halfway by 3\".","hero":false,"slider":null,"value":null,"display":null},{"text":"# Inspect: when does the curve hit 50% of capacity?","label":null,"prefix":null,"suffix":null,"section":"Inspect: when does the curve hit 50% of capacity?","hero":false,"slider":null,"value":null,"display":null},{"text":"half_x = x_0 // by definition, half-capacity is at the midpoint","label":null,"prefix":null,"suffix":"by definition, half-capacity is at the midpoint","section":"Inspect: when does the curve hit 50% of capacity?","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"click-to-solve-parabola","title":"Click-to-solve a parabola","description":"Click any point on the curve to set a goal. The engine reverse-solves the","category":"math","icon":"trending-up","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Coefficients you can vary","label":null,"prefix":null,"suffix":null,"section":"Coefficients you can vary","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 1 // -5..5 — click on the curve to let the solver set this","label":null,"prefix":null,"suffix":"-5..5 — click on the curve to let the solver set this","section":"Coefficients you can vary","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"b = 0 // -10..10 — linear term","label":null,"prefix":null,"suffix":"-10..10 — linear term","section":"Coefficients you can vary","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"c = 0 // -20..20 — constant","label":null,"prefix":null,"suffix":"-20..20 — constant","section":"Coefficients you can vary","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# The parabola — click anywhere on the curve to fit `a` to that point","label":null,"prefix":null,"suffix":null,"section":"The parabola — click anywhere on the curve to fit `a` to that point","hero":false,"slider":null,"value":null,"display":null},{"text":"# Try clicking at (3, 9). The solver will land `a = 1` (since 1*9 + 0 + 0 = 9).","label":null,"prefix":null,"suffix":null,"section":"Try clicking at (3, 9). The solver will land `a = 1` (since 1*9 + 0 + 0 = 9).","hero":false,"slider":null,"value":null,"display":null},{"text":"# Then drag `b` away from 0 and click again at the same spot — `a` re-solves","label":null,"prefix":null,"suffix":null,"section":"Then drag `b` away from 0 and click again at the same spot — `a` re-solves","hero":false,"slider":null,"value":null,"display":null},{"text":"# to land the new curve through (3, 9).","label":null,"prefix":null,"suffix":null,"section":"to land the new curve through (3, 9).","hero":false,"slider":null,"value":null,"display":null},{"text":"# Inspect the roots once the curve fits","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hero":false,"slider":null,"value":null,"display":null},{"text":"disc = b^2 - 4*a*c","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"root_1 = (-b - sqrt(disc)) / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hidden":false,"hero":false,"slider":null,"value":0,"display":"-0"},{"text":"root_2 = (-b + sqrt(disc)) / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Inspect the roots once the curve fits","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"climb-gradient","title":"Climb Gradient","description":"Calculate climb gradient as percent and degrees from elevation gain and distance.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Terrain Info","label":null,"prefix":null,"suffix":null,"section":"Terrain Info","hero":false,"slider":null,"value":null,"display":null},{"text":"elevation gain = 500 // feet 0..5k","label":null,"prefix":null,"suffix":"feet","section":"Terrain Info","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":50},"value":500,"display":"500"},{"text":"horizontal distance = 5280 // feet 0..50k","label":null,"prefix":null,"suffix":"feet","section":"Terrain Info","hidden":false,"hero":false,"slider":{"min":0,"max":50000,"step":500},"value":5280,"display":"5,280"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"slope decimal = elevation gain / horizontal distance","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":0.0946969696969697,"display":"0.0947"},{"text":"slope percentage = slope decimal * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":9.469696969696969,"display":"9.47"},{"text":"# Degree conversion","label":null,"prefix":null,"suffix":null,"section":"Degree conversion","hero":false,"slider":null,"value":null,"display":null},{"text":"angle degrees = atan(slope decimal)","label":null,"prefix":null,"suffix":null,"section":"Degree conversion","hidden":false,"hero":false,"slider":null,"value":5.409604944473391,"display":"5.4096"},{"text":"grade category = slope percentage","label":null,"prefix":null,"suffix":null,"section":"Degree conversion","hidden":false,"hero":false,"slider":null,"value":9.469696969696969,"display":"9.47"},{"text":"# Classification","label":null,"prefix":null,"suffix":null,"section":"Classification","hero":false,"slider":null,"value":null,"display":null},{"text":"flat = 3","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"moderate = 6","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"steep = 10","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"extreme = 15","label":null,"prefix":null,"suffix":null,"section":"Classification","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"}]},{"id":"closing-costs","title":"Closing Costs","description":"Estimate closing costs and total cash due at closing.","category":"real-estate","icon":"file-text","tags":["home"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Home Purchase","label":null,"prefix":null,"suffix":null,"section":"Home Purchase","hero":false,"slider":null,"value":null,"display":null},{"text":"$home price = 350000 // 50k..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Home Purchase","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":5000},"value":350000,"display":"$350,000.00"},{"text":"down payment pct = 10 // % 0..100","label":null,"prefix":null,"suffix":"%","section":"Home Purchase","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":10,"display":"10"},{"text":"$down payment = home price * down payment pct / 100","label":null,"prefix":"$","suffix":null,"section":"Home Purchase","hidden":false,"hero":false,"slider":null,"value":35000,"display":"$35,000.00"},{"text":"# Closing Cost Breakdown","label":null,"prefix":null,"suffix":null,"section":"Closing Cost Breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"$lender fees = home price * 0.01 // @label(Lender/Origination Fees ~1%)","label":"Lender/Origination Fees ~1%","prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":null,"value":3500,"display":"$3,500.00"},{"text":"$title insurance = 1500 // 500..5k by 100","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":500,"max":5000,"step":100},"value":1500,"display":"$1,500.00"},{"text":"$appraisal fee = 500 // 200..1k by 50","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":200,"max":1000,"step":50},"value":500,"display":"$500.00"},{"text":"$home inspection = 450 // 200..800 by 50","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":200,"max":800,"step":50},"value":450,"display":"$450.00"},{"text":"$escrow and recording = 750 // 200..2k by 50","label":null,"prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":{"min":200,"max":2000,"step":50},"value":750,"display":"$750.00"},{"text":"$prepaid taxes and insurance = home price * 0.005 // @label(Prepaid Taxes & Insurance ~0.5%)","label":"Prepaid Taxes & Insurance ~0.5%","prefix":"$","suffix":null,"section":"Closing Cost Breakdown","hidden":false,"hero":false,"slider":null,"value":1750,"display":"$1,750.00"},{"text":"# Totals","label":null,"prefix":null,"suffix":null,"section":"Totals","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated closing costs = lender fees + title insurance + appraisal fee + home inspection + escrow and recording + prepaid taxes and insurance","label":null,"prefix":"$","suffix":null,"section":"Totals","hidden":false,"hero":false,"slider":null,"value":8450,"display":"$8,450.00"},{"text":"closing cost pct = round(estimated closing costs / home price * 100 * 10) / 10 // %","label":null,"prefix":null,"suffix":"%","section":"Totals","hidden":false,"hero":false,"slider":null,"value":2.4,"display":"2.4"},{"text":"$total due at closing = down payment + estimated closing costs","label":null,"prefix":"$","suffix":null,"section":"Totals","hidden":false,"hero":true,"slider":null,"value":43450,"display":"$43,450.00"}]},{"id":"cloud-egress-cost-calculator","title":"Cloud Egress Cost Calculator","description":"Estimate total cost of cloud data egress at a given price per gigabyte.","category":"other","icon":"cloud","tags":["cloud"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"egress_data_terabytes = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"cost_per_gigabyte = 0.09","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.09,"display":"0.09"},{"text":"total_egress_cost_dollars = egress_data_terabytes * 1000 * cost_per_gigabyte // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":450,"display":"450"}]},{"id":"cloud-storage-cost-comparison","title":"Cloud Storage Cost Comparison","description":"Compare monthly cloud storage costs across three providers at a given data size.","category":"health","icon":"cloud","tags":["cloud","storage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"data_size_terabytes = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"cost_per_terabyte_month_provider_a = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"cost_per_terabyte_month_provider_b = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"cost_per_terabyte_month_provider_c = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"monthly_cost_provider_a = data_size_terabytes * cost_per_terabyte_month_provider_a","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"monthly_cost_provider_b = data_size_terabytes * cost_per_terabyte_month_provider_b // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"monthly_cost_provider_c = data_size_terabytes * cost_per_terabyte_month_provider_c","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"}]},{"id":"cloud-weight-estimate","title":"Cloud Weight Estimate","description":"Estimate the total weight of a cumulus cloud from its volume and water density.","category":"everyday","icon":"smile","tags":["cloud"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"cloud_volume_m3 = 1e9 // 1 cubic km","label":null,"prefix":null,"suffix":"1 cubic km","section":null,"hidden":false,"hero":false,"slider":null,"value":1000000000,"display":"1,000,000,000"},{"text":"water_density_g_per_m3 = 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"total_weight_kilograms = (cloud_volume_m3 * water_density_g_per_m3) / 1000 // kilograms @hero","label":null,"prefix":null,"suffix":"kilograms","section":null,"hidden":false,"hero":true,"slider":null,"value":500000,"display":"500,000"}]},{"id":"cmyk-to-rgb-color-converter","title":"Cmyk To Rgb Color Converter","description":"Convert CMYK percentages to RGB color values.","category":"design","icon":"palette","tags":["rgb","color"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"cyan_percent = 100 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"magenta_percent = 0 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"yellow_percent = 0 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"black_percent = 0 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"_c = cyan_percent / 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_m = magenta_percent / 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"_y = yellow_percent / 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"_k = black_percent / 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"red_rgb = 255 * (1 - c) * (1 - k) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0,"display":"0"},{"text":"green_rgb = 255 * (1 - m) * (1 - k) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":255,"display":"255"},{"text":"blue_rgb = 255 * (1 - y) * (1 - k) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":255,"display":"255"}]},{"id":"coffee-cost","title":"Coffee Cost","description":"See the true cost of your daily coffee habit.","category":"everyday","icon":"coffee","tags":["coffee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Coffee Habit","label":null,"prefix":null,"suffix":null,"section":"Coffee Habit","hero":false,"slider":null,"value":null,"display":null},{"text":"coffees per day = 2 // 1..10","label":null,"prefix":null,"suffix":null,"section":"Coffee Habit","hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":2,"display":"2"},{"text":"$price per coffee = 5.50 // 1..15 by 0.25","label":null,"prefix":"$","suffix":null,"section":"Coffee Habit","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.25},"value":5.5,"display":"$5.50"},{"text":"# Daily & Weekly","label":null,"prefix":null,"suffix":null,"section":"Daily & Weekly","hero":false,"slider":null,"value":null,"display":null},{"text":"$daily cost = coffees per day * price per coffee","label":null,"prefix":"$","suffix":null,"section":"Daily & Weekly","hidden":false,"hero":false,"slider":null,"value":11,"display":"$11.00"},{"text":"$weekly cost = daily cost * 7","label":null,"prefix":"$","suffix":null,"section":"Daily & Weekly","hidden":false,"hero":false,"slider":null,"value":77,"display":"$77.00"},{"text":"# Monthly & Yearly","label":null,"prefix":null,"suffix":null,"section":"Monthly & Yearly","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly cost = round(daily cost * 30.44 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Monthly & Yearly","hidden":false,"hero":false,"slider":null,"value":334.84,"display":"$334.84"},{"text":"$yearly cost = round(daily cost * 365.25 * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Monthly & Yearly","hidden":false,"hero":true,"slider":null,"value":4017.75,"display":"$4,017.75"},{"text":"# Long Term","label":null,"prefix":null,"suffix":null,"section":"Long Term","hero":false,"slider":null,"value":null,"display":null},{"text":"$five year cost = round(yearly cost * 5 * 100) / 100 // @label(5-Year Cost)","label":"5-Year Cost","prefix":"$","suffix":null,"section":"Long Term","hidden":false,"hero":false,"slider":null,"value":20088.75,"display":"$20,088.75"},{"text":"$ten year cost = round(yearly cost * 10 * 100) / 100 // @label(10-Year Cost)","label":"10-Year Cost","prefix":"$","suffix":null,"section":"Long Term","hidden":false,"hero":false,"slider":null,"value":40177.5,"display":"$40,177.50"},{"text":"$ten year invested = round(yearly cost * ((1.07^10 - 1) / 0.07) * 100) / 100 // @label(10-Year If Invested at 7%)","label":"10-Year If Invested at 7%","prefix":"$","suffix":null,"section":"Long Term","hidden":false,"hero":false,"slider":null,"value":55511.03,"display":"$55,511.03"}]},{"id":"coffee-extraction-yield","title":"Coffee Extraction Yield","description":"Calculate coffee extraction yield percentage from brew weight, TDS, and dose.","category":"other","icon":"coffee","tags":["coffee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"brewed_coffee_weight_grams = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"coffee_tds_percent = 1.35","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.35,"display":"1.35"},{"text":"dry_coffee_weight_grams = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"extraction_yield_percent = (brewed_coffee_weight_grams * coffee_tds_percent) / dry_coffee_weight_grams // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":20.25,"display":"20.25"}]},{"id":"coffee-roast-weight-loss","title":"Coffee Roast Weight Loss","description":"Calculate percentage weight loss between green and roasted coffee beans.","category":"health","icon":"coffee","tags":["coffee","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"green_coffee_weight_grams = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"roasted_coffee_weight_grams = 850","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":850,"display":"850"},{"text":"weight_loss_grams = green_coffee_weight_grams - roasted_coffee_weight_grams","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"percentage_weight_loss = (weight_loss_grams / green_coffee_weight_grams) * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":15,"display":"15"}]},{"id":"coffee-stain-radius","title":"Coffee Stain Radius","description":"Estimate the spread radius of a coffee spill on an absorbent surface.","category":"everyday","icon":"smile","tags":["coffee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"spill_volume_ml = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"surface_absorbency = 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"stain_radius_cm = sqrt(spill_volume_ml / (pi * surface_absorbency)) // centimeters @hero","label":null,"prefix":null,"suffix":"centimeters","section":null,"hidden":false,"hero":true,"slider":null,"value":1.7841241161527712,"display":"1.784"}]},{"id":"coffee-to-water-ratio","title":"Coffee To Water Ratio","description":"Calculate water needed in grams and ounces for a given coffee dose and ratio.","category":"health","icon":"coffee","tags":["coffee","water","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Brewing Input","label":null,"prefix":null,"suffix":null,"section":"Brewing Input","hero":false,"slider":null,"value":null,"display":null},{"text":"coffee weight = 20 // grams 5..100","label":null,"prefix":null,"suffix":"grams","section":"Brewing Input","hidden":false,"hero":false,"slider":{"min":5,"max":100,"step":1},"value":20,"display":"20"},{"text":"target ratio = 16 // 1:12 to 1:20","label":null,"prefix":null,"suffix":null,"section":"Brewing Input","hidden":false,"hero":false,"slider":{"min":4320,"max":4800,"step":1},"value":16,"display":"16"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"water weight needed = coffee weight * target ratio // grams @hero","label":null,"prefix":null,"suffix":"grams","section":"Result","hidden":false,"hero":true,"slider":null,"value":320,"display":"320"},{"text":"water in milliliters = water weight needed","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":320,"display":"320"},{"text":"water in ounces = water weight needed * 0.033814","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":10.82048,"display":"10.82"},{"text":"# Strength Guide","label":null,"prefix":null,"suffix":null,"section":"Strength Guide","hero":false,"slider":null,"value":null,"display":null},{"text":"ratio one to twelve = coffee weight * 12 // Strong","label":null,"prefix":null,"suffix":"Strong","section":"Strength Guide","hidden":false,"hero":false,"slider":null,"value":240,"display":"240"},{"text":"ratio one to fifteen = coffee weight * 15 // Balanced","label":null,"prefix":null,"suffix":"Balanced","section":"Strength Guide","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"ratio one to eighteen = coffee weight * 18 // 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@hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":14400,"display":"14,400"},{"text":"lifetime_time_cost_value = lifetime_commute_hours * hourly_wage_value // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":720000,"display":"720,000"}]},{"id":"complementary-color-hue-finder","title":"Complementary Color Hue Finder","description":"Find the complementary HSL hue 180 degrees opposite a given hue.","category":"design","icon":"palette","tags":["color"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"original_hue = 45 // degrees (HSL)","label":null,"prefix":null,"suffix":"degrees (HSL)","section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"complementary_hue = mod(original_hue + 180, 360) // degrees 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1..50","label":null,"prefix":null,"suffix":null,"section":"Footing Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":4,"display":"4"},{"text":"# Volume Calculations","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_volume_per_footing_cubic_inches = length * width * depth","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":6912,"display":"6,912"},{"text":"_total_volume_cubic_inches = volume_per_footing_cubic_inches * number of footings","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":27648,"display":"27,648"},{"text":"_total_volume_cubic_feet = total_volume_cubic_inches / 1728","label":null,"prefix":null,"suffix":null,"section":"Volume 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meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":1.2,"display":"1.2"},{"text":"step_rise_meters = 0.18 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.18,"display":"0.18"},{"text":"step_run_meters = 0.3 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"volume_per_step = step_width_meters * step_rise_meters * step_run_meters // m3","label":null,"prefix":null,"suffix":"m3","section":null,"hidden":false,"hero":false,"slider":null,"value":0.0648,"display":"0.0648"},{"text":"total_step_volume = volume_per_step * (number_of_steps * (number_of_steps + 1) / 2) // m3","label":null,"prefix":null,"suffix":"m3","section":null,"hidden":false,"hero":false,"slider":null,"value":0.972,"display":"0.972"},{"text":"total_concrete_cubic_meters = total_step_volume 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// ft 1..100","label":null,"prefix":null,"suffix":"ft","section":"Slab Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":8,"display":"8"},{"text":"depth = 4 // in 2..24","label":null,"prefix":null,"suffix":"in","section":"Slab Dimensions","hidden":false,"hero":false,"slider":{"min":2,"max":24,"step":1},"value":4,"display":"4"},{"text":"# Volume","label":null,"prefix":null,"suffix":null,"section":"Volume","hero":false,"slider":null,"value":null,"display":null},{"text":"_depth_ft = depth / 12","label":null,"prefix":null,"suffix":null,"section":"Volume","hidden":true,"hero":false,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"_volume_cubic_feet = length * width * depth_ft // cu ft","label":null,"prefix":null,"suffix":"cu ft","section":"Volume","hidden":true,"hero":false,"slider":null,"value":26.66666666666666,"display":"26.67"},{"text":"volume cubic yards = round(volume_cubic_feet / 27, 2) // cu yd @hero 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50..300","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":{"min":50,"max":300,"step":1},"value":150,"display":"$150.00"},{"text":"$total concrete cost = round(yards_to_order * price_per_cubic_yard, 2)","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":null,"value":163.5,"display":"$163.50"},{"text":"bags needed = roundup(volume_cubic_feet * 1.1 / 0.6) // 80lb bags @label(80lb bags needed)","label":"80lb bags needed","prefix":null,"suffix":"80lb bags","section":"Cost","hidden":false,"hero":false,"slider":null,"value":49,"display":"49"}]},{"id":"conditional-probability","title":"Conditional Probability","description":"Compute P(A|B) = P(A ∩ B) / P(B).","category":"formulas","icon":"percent","tags":["probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Probabilities","label":null,"prefix":null,"suffix":null,"section":"Probabilities","hero":false,"slider":null,"value":null,"display":null},{"text":"prob_a_and_b = 0.2 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Probabilities","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.2,"display":"0.2"},{"text":"prob_b = 0.5 // 0.01..1","label":null,"prefix":null,"suffix":null,"section":"Probabilities","hidden":false,"hero":false,"slider":{"min":0.01,"max":1,"step":0.01},"value":0.5,"display":"0.5"},{"text":"# Conditional probability","label":null,"prefix":null,"suffix":null,"section":"Conditional probability","hero":false,"slider":null,"value":null,"display":null},{"text":"prob_a_given_b = prob_a_and_b / prob_b // @label(P(A|B))","label":"P(A|B)","prefix":null,"suffix":null,"section":"Conditional probability","hidden":false,"hero":true,"slider":null,"value":0.4,"display":"0.4"}]},{"id":"cone-surface-area","title":"Cone Surface Area","description":"Find the surface area of a cone (lateral + base).","category":"formulas","icon":"cone","tags":["surface-area","geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.684Z"},"rows":[{"text":"# Cone","label":null,"prefix":null,"suffix":null,"section":"Cone","hero":false,"slider":null,"value":null,"display":null},{"text":"radius = 5 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Cone","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"height = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Cone","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"# Slant height and surface area","label":null,"prefix":null,"suffix":null,"section":"Slant height and surface area","hero":false,"slider":null,"value":null,"display":null},{"text":"slant_height = sqrt(radius^2 + 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damage = 150","label":null,"prefix":null,"suffix":null,"section":"Damage Settings","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"crit multiplier = 2.0","label":null,"prefix":null,"suffix":null,"section":"Damage Settings","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"crit damage bonus percent = 50 // %","label":null,"prefix":null,"suffix":"%","section":"Damage Settings","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_crit_multiplier = crit multiplier + (crit damage bonus percent / 100)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"final damage = base damage * total_crit_multiplier","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":375,"display":"375"}]},{"id":"crochet-yarn-estimator","title":"Crochet Yarn Estimator","description":"Estimate yards of yarn needed for a crochet project from dimensions and stitch density.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Project Type","label":null,"prefix":null,"suffix":null,"section":"Project Type","hero":false,"slider":null,"value":null,"display":null},{"text":"# Yarn per square inch (varies by stitch)","label":null,"prefix":null,"suffix":null,"section":"Yarn per square inch (varies by stitch)","hero":false,"slider":null,"value":null,"display":null},{"text":"yarn factor = 4.5 // yards per sq inch (typical)","label":null,"prefix":null,"suffix":"yards per sq inch (typical)","section":"Yarn per square inch (varies by 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Fabric","label":null,"prefix":null,"suffix":null,"section":"Fabric","hero":false,"slider":null,"value":null,"display":null},{"text":"fabric count = 14 // stitches per inch","label":null,"prefix":null,"suffix":"stitches per inch","section":"Fabric","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"# Margins","label":null,"prefix":null,"suffix":null,"section":"Margins","hero":false,"slider":null,"value":null,"display":null},{"text":"margin inches = 3 // per side","label":null,"prefix":null,"suffix":"per side","section":"Margins","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_design_width = stitches wide / fabric 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@hero","label":null,"prefix":null,"suffix":null,"section":"Volume and surface area","hidden":false,"hero":true,"slider":null,"value":125,"display":"125"},{"text":"surface_area = 6 * side^2","label":null,"prefix":null,"suffix":null,"section":"Volume and surface area","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"diagonal = side * sqrt(3) // @label(Space Diagonal)","label":"Space Diagonal","prefix":null,"suffix":null,"section":"Volume and surface area","hidden":false,"hero":false,"slider":null,"value":8.660254037844386,"display":"8.66"}]},{"id":"curb-weight-to-gvwr","title":"Curb Weight To GVWR","description":"Calculate percentage of GVWR used.","category":"engineering","icon":"settings","tags":["automotive","truck"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Weight Stats","label":null,"prefix":null,"suffix":null,"section":"Weight 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Marketing","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":25000,"display":"$25,000.00"},{"text":"$sales team spend = 15000 // 0..1M","label":null,"prefix":"$","suffix":null,"section":"Sales and Marketing","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":15000,"display":"$15,000.00"},{"text":"new customers acquired = 200 // 1..10k","label":null,"prefix":null,"suffix":null,"section":"Sales and Marketing","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":200,"display":"200"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$customer acquisition cost = (marketing spend + sales team spend) / new customers acquired // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":200,"display":"$200.00"},{"text":"$total spend = marketing spend + sales 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1..10k","label":null,"prefix":"$","suffix":null,"section":"Customer Value","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":120,"display":"$120.00"},{"text":"average purchase frequency = 4 // per year 1..52","label":null,"prefix":null,"suffix":"per year","section":"Customer Value","hidden":false,"hero":false,"slider":{"min":1,"max":52,"step":1},"value":4,"display":"4"},{"text":"average customer lifespan = 5 // years 1..50","label":null,"prefix":null,"suffix":"years","section":"Customer Value","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":5,"display":"5"},{"text":"profit margin percent = 30 // % 1..100","label":null,"prefix":null,"suffix":"%","section":"Customer Value","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":30,"display":"30"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$customer lifetime value = average purchase value * average purchase frequency * average customer lifespan * (profit margin percent / 100) // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":720,"display":"$720.00"},{"text":"$annual value per customer = average purchase value * average purchase frequency","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":480,"display":"$480.00"},{"text":"$total lifetime revenue = average purchase value * average purchase frequency * average customer lifespan","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":2400,"display":"$2,400.00"}]},{"id":"customer-response-time-average","title":"Customer Response Time Average","description":"Calculate average customer response time per support 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Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"drag force newtons = 0.5 * cda * air density * (speed meters per second ^ 2)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":18.375,"display":"18.38"}]},{"id":"cycling-estimated-time","title":"Cycling Estimated Time","description":"Calculate estimated time for a cycling distance.","category":"health","icon":"activity","tags":["sports","cycling"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Ride Settings","label":null,"prefix":null,"suffix":null,"section":"Ride Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"distance kilometers = 40","label":null,"prefix":null,"suffix":null,"section":"Ride Settings","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"average speed 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0.453592","label":null,"prefix":null,"suffix":null,"section":"Totals","hidden":false,"hero":false,"slider":null,"value":83.91452,"display":"83.91"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"power to weight ratio = average power / (rider weight * 0.453592) // w/kg @hero","label":null,"prefix":null,"suffix":"w/kg","section":"Result","hidden":false,"hero":true,"slider":null,"value":3.340340030581481,"display":"3.34"},{"text":"# Category Guide","label":null,"prefix":null,"suffix":null,"section":"Category Guide","hero":false,"slider":null,"value":null,"display":null},{"text":"untrained = 2.0","label":null,"prefix":null,"suffix":null,"section":"Category Guide","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"cat five = 2.5","label":null,"prefix":null,"suffix":null,"section":"Category 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0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Cylinder","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"height = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Cylinder","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"# Volume","label":null,"prefix":null,"suffix":null,"section":"Volume","hero":false,"slider":null,"value":null,"display":null},{"text":"volume = pi * radius^2 * height","label":null,"prefix":null,"suffix":null,"section":"Volume","hidden":false,"hero":true,"slider":null,"value":785.3981633974483,"display":"785.4"}]},{"id":"daily-productivity-score-weighted","title":"Daily Productivity Score Weighted","description":"Calculate a daily productivity score from tasks completed, difficulty, and focus 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100","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":5.319148936170214,"display":"5.319"}]},{"id":"damage-reduction-armor-diminishing","title":"Damage Reduction Armor Diminishing","description":"Calculate damage reduction with diminishing returns.","category":"math","icon":"shield","tags":["gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Defense Settings","label":null,"prefix":null,"suffix":null,"section":"Defense Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"armor value = 1200","label":null,"prefix":null,"suffix":null,"section":"Defense Settings","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"constant = 3000","label":null,"prefix":null,"suffix":null,"section":"Defense Settings","hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"damage reduction percent = (armor value / (armor value + constant)) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":28.57142857142857,"display":"28.57"}]},{"id":"data-center-cooling-load","title":"Data Center Cooling Load","description":"Calculate data center cooling load in BTU/hour from IT equipment and heat sources.","category":"other","icon":"calculator","tags":["cooling"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"it_equipment_power_watts = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"other_heat_sources_watts = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"cooling_load_btu_per_hour = (it_equipment_power_watts + other_heat_sources_watts) * 3.412 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":375320,"display":"375,320"}]},{"id":"debt-equity-ratio","title":"Debt Equity Ratio","description":"Calculate debt-to-equity ratio and leverage status from liabilities and equity.","category":"finance","icon":"ratio","tags":["debt","equity","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Balance Sheet","label":null,"prefix":null,"suffix":null,"section":"Balance Sheet","hero":false,"slider":null,"value":null,"display":null},{"text":"$total liabilities = 1500000 // 0..100M","label":null,"prefix":"$","suffix":null,"section":"Balance 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> 2, \"High Leverage\", if(debt to equity ratio > 1, \"Moderate\", \"Conservative\"))","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Moderate","display":"Moderate"}]},{"id":"debt-payoff","title":"Debt Payoff","description":"Calculate how long to pay off debt and total interest costs.","category":"finance","icon":"credit-card","tags":["debt","payoff","interest"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Debt Details","label":null,"prefix":null,"suffix":null,"section":"Debt Details","hero":false,"slider":null,"value":null,"display":null},{"text":"total debt = $15000 // 500..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Debt Details","hidden":false,"hero":false,"slider":{"min":500,"max":100000,"step":500},"value":15000,"display":"$15,000.00"},{"text":"annual interest rate = 18 // % 1..30","label":null,"prefix":null,"suffix":"%","section":"Debt Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":18,"display":"18"},{"text":"monthly payment = $400 // 50..5k by 25","label":null,"prefix":"$","suffix":null,"section":"Debt Details","hidden":false,"hero":false,"slider":{"min":50,"max":5000,"step":25},"value":400,"display":"$400.00"},{"text":"# Payoff Timeline","label":null,"prefix":null,"suffix":null,"section":"Payoff Timeline","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly rate = annual interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Payoff Timeline","hidden":false,"hero":false,"slider":null,"value":0.015,"display":"0.015"},{"text":"months to payoff = -ln(1 - (total debt * monthly rate / monthly payment)) / ln(1 + monthly rate)","label":null,"prefix":null,"suffix":null,"section":"Payoff Timeline","hidden":false,"hero":false,"slider":null,"value":55.52421849460205,"display":"55.52"},{"text":"years to payoff = round(months to payoff / 12 * 10) / 10 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@hero","label":null,"prefix":null,"suffix":"ratio","section":null,"hidden":false,"hero":true,"slider":null,"value":1.3333333333333333,"display":"1.333"}]},{"id":"debt-to-income-ratio","title":"Debt To Income Ratio","description":"Calculate debt-to-income ratio (DTI) from monthly income and debt payments.","category":"finance","icon":"ratio","tags":["debt","income","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Monthly Income and Debt","label":null,"prefix":null,"suffix":null,"section":"Monthly Income and Debt","hero":false,"slider":null,"value":null,"display":null},{"text":"$gross monthly income = 6000 // 1k..50k by 100","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":1000,"max":50000,"step":100},"value":6000,"display":"$6,000.00"},{"text":"$monthly mortgage or rent = 1800 // 0..10k by 50","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":50},"value":1800,"display":"$1,800.00"},{"text":"$monthly car payments = 400 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":400,"display":"$400.00"},{"text":"$monthly credit card minimums = 150 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":150,"display":"$150.00"},{"text":"$other monthly debt payments = 200 // 0..5k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Income and Debt","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":25},"value":200,"display":"$200.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_total_monthly_debt = monthly mortgage or rent + monthly car payments + monthly credit card minimums + other monthly debt payments","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2550,"display":"$2,550.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"debt to income ratio = (total_monthly_debt / gross monthly income) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":42.5,"display":"42.5"},{"text":"$remaining monthly income = gross monthly income - total_monthly_debt","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":3450,"display":"$3,450.00"},{"text":"health = if(debt to income ratio < 36, \"Healthy\", if(debt to income ratio < 43, \"Moderate\", \"High\"))","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Moderate","display":"Moderate"}]},{"id":"debuff-resistance-probability","title":"Debuff Resistance Probability","description":"Calculate probability to resist a debuff.","category":"math","icon":"shield-off","tags":["gaming","combat"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Resistance Settings","label":null,"prefix":null,"suffix":null,"section":"Resistance Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"attacker debuff chance percent = 80 // %","label":null,"prefix":null,"suffix":"%","section":"Resistance Settings","hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"defender resistance percent = 30 // %","label":null,"prefix":null,"suffix":"%","section":"Resistance Settings","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"final debuff chance percent = attacker debuff chance percent * (1 - (defender resistance percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":56,"display":"56"}]},{"id":"decision-fatigue-level","title":"Decision Fatigue Level","description":"Estimate decision fatigue from daily decision count and complexity.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"decisions_today = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"avg_decision_complexity = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"fatigue_index = (decisions_today * avg_decision_complexity) / 100 // scale 0-10 @hero","label":null,"prefix":null,"suffix":"scale 0-10","section":null,"hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"deck-board-estimator","title":"Deck Board Estimator","description":"Estimate deck boards and linear feet needed from deck size and board width.","category":"everyday","icon":"home","tags":["deck","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Deck Dimensions","label":null,"prefix":null,"suffix":null,"section":"Deck Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"deck length = 16 // feet 1..100","label":null,"prefix":null,"suffix":"feet","section":"Deck Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":16,"display":"16"},{"text":"deck width = 12 // feet 1..100","label":null,"prefix":null,"suffix":"feet","section":"Deck Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":12,"display":"12"},{"text":"# Board Dimensions","label":null,"prefix":null,"suffix":null,"section":"Board Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"board nominal width = 6 // inches","label":null,"prefix":null,"suffix":"inches","section":"Board Dimensions","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"actual board width = 5.5 // inches","label":null,"prefix":null,"suffix":"inches","section":"Board Dimensions","hidden":false,"hero":false,"slider":null,"value":5.5,"display":"5.5"},{"text":"gap width = 0.125 // inches","label":null,"prefix":null,"suffix":"inches","section":"Board Dimensions","hidden":false,"hero":false,"slider":null,"value":0.125,"display":"0.125"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_effective_board_width_inches = actual board width + gap width","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":5.625,"display":"5.625"},{"text":"_effective_board_width_feet = effective_board_width_inches / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.46875,"display":"0.4688"},{"text":"# Assuming boards run along the length","label":null,"prefix":null,"suffix":null,"section":"Assuming boards run along the length","hero":false,"slider":null,"value":null,"display":null},{"text":"boards needed = roundup(deck width / effective_board_width_feet) // @hero","label":null,"prefix":null,"suffix":null,"section":"Assuming boards run along the length","hidden":false,"hero":true,"slider":null,"value":26,"display":"26"},{"text":"# Total linear feet","label":null,"prefix":null,"suffix":null,"section":"Total linear feet","hero":false,"slider":null,"value":null,"display":null},{"text":"total linear feet = boards needed * deck length","label":null,"prefix":null,"suffix":null,"section":"Total linear feet","hidden":false,"hero":false,"slider":null,"value":416,"display":"416"},{"text":"# With 10% waste","label":null,"prefix":null,"suffix":null,"section":"With 10% waste","hero":false,"slider":null,"value":null,"display":null},{"text":"total linear feet with waste = total linear feet * 1.1","label":null,"prefix":null,"suffix":null,"section":"With 10% waste","hidden":false,"hero":false,"slider":null,"value":457.6,"display":"457.6"}]},{"id":"deck-of-cards-shuffles","title":"Deck Of Cards Shuffles","description":"Show the recommended number of riffle shuffles to randomize a 52-card deck.","category":"everyday","icon":"smile","tags":["deck"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"number_of_cards = 52","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":52,"display":"52"},{"text":"shuffles_for_randomness = 7 // recommended shuffles @hero","label":null,"prefix":null,"suffix":"recommended shuffles","section":null,"hidden":false,"hero":true,"slider":null,"value":7,"display":"7"}]},{"id":"deck-railing-baluster-spacing","title":"Deck Railing Baluster Spacing","description":"Calculate even spacing for deck balusters to meet code.","category":"construction","icon":"fence","tags":["construction","deck","woodworking"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"railing_length_inches = 96 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"baluster_width_inches = 1.5 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"max_spacing_inches = 4 // inches (standard code)","label":null,"prefix":null,"suffix":"inches (standard code)","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"total_balusters = ceil(railing_length_inches / (baluster_width_inches + max_spacing_inches))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"actual_spacing_inches = (railing_length_inches - (total_balusters * baluster_width_inches)) / (total_balusters + 1) // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":3.6315789473684212,"display":"3.632"}]},{"id":"deep-work-uninterrupted-ratio","title":"Deep Work Uninterrupted Ratio","description":"Calculate the percentage of a work day spent in deep, uninterrupted focus.","category":"productivity","icon":"clock","tags":["work"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"total_work_hours = 8 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"deep_work_hours = 3 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"deep_work_ratio_percent = (deep_work_hours / total_work_hours) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":37.5,"display":"37.5"}]},{"id":"definite-integral","title":"Definite Integral — Power Rule","description":"Evaluate ∫ₐᵇ c·xⁿ dx = c·(b^(n+1) − a^(n+1))/(n+1).","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Function: f(x) = c · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"c = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 2 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":2,"display":"2"},{"text":"# Bounds","label":null,"prefix":null,"suffix":null,"section":"Bounds","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 0 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Bounds","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":0,"display":"0"},{"text":"b = 4 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Bounds","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":4,"display":"4"},{"text":"# Definite integral","label":null,"prefix":null,"suffix":null,"section":"Definite integral","hero":false,"slider":null,"value":null,"display":null},{"text":"integral = c * (b^(n + 1) - a^(n + 1)) / (n + 1) // @label(∫ₐᵇ f(x) dx)","label":"∫ₐᵇ f(x) dx","prefix":null,"suffix":null,"section":"Definite integral","hidden":false,"hero":true,"slider":null,"value":64,"display":"64"}]},{"id":"deforestation-rate-per-second","title":"Deforestation Rate Per Second","description":"See how many hectares of forest are lost in real-time.","category":"science","icon":"tree-pine","tags":["science","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"annual_deforestation_hectares = 10000000 // hectares per year","label":null,"prefix":null,"suffix":"hectares per year","section":null,"hidden":false,"hero":false,"slider":null,"value":10000000,"display":"10,000,000"},{"text":"seconds_per_year = 31536000 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":31536000,"display":"31,536,000"},{"text":"hectares_lost_per_second = annual_deforestation_hectares / seconds_per_year // hectares @hero","label":null,"prefix":null,"suffix":"hectares","section":null,"hidden":false,"hero":true,"slider":null,"value":0.31709791983764585,"display":"0.3171"},{"text":"football_fields_per_second = hectares_lost_per_second / 0.7 // approx size of football field","label":null,"prefix":null,"suffix":"approx size of football field","section":null,"hidden":false,"hero":false,"slider":null,"value":0.4529970283394941,"display":"0.453"}]},{"id":"delta-v-orbit-change","title":"Delta V Orbit Change","description":"Calculate the delta-V for an orbit change using the Tsiolkovsky rocket equation.","category":"science","icon":"globe","tags":["orbit"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"specific_impulse_seconds = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"gravity_constant = 9.806","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9.806,"display":"9.806"},{"text":"mass_initial_kilograms = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"mass_final_kilograms = 800","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":800,"display":"800"},{"text":"delta_v_meters_per_second = specific_impulse_seconds * gravity_constant * ln(mass_initial_kilograms / mass_final_kilograms) // m/s @hero","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":false,"hero":true,"slider":null,"value":656.4436992561423,"display":"656.44"}]},{"id":"density-altitude","title":"Density Altitude","description":"Calculate density altitude from pressure altitude, temperature, and ISA 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Impact","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hero":false,"slider":null,"value":null,"display":null},{"text":"isa deviation = temp celsius - isa temperature celsius","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":24.344444444444445,"display":"24.34"},{"text":"takeoff distance factor = 1 + (density altitude / 1000) * 0.1","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":1.7921333333333336,"display":"1.792"},{"text":"engine power loss percent = (density altitude / 1000) * 3 // %","label":null,"prefix":null,"suffix":"%","section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":23.764000000000003,"display":"23.76"},{"text":"density ratio = (518.67 / (459.67 + outside air temperature)) * (1 - 0.0000068756 * pressure altitude)^5.2559","label":null,"prefix":null,"suffix":null,"section":"Performance Impact","hidden":false,"hero":false,"slider":null,"value":0.7923290569713252,"display":"0.7923"}]},{"id":"density","title":"Density","description":"Convert mass and volume into density and per-teaspoon weight.","category":"science","icon":"atom","tags":["mass","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Sample","label":null,"prefix":null,"suffix":null,"section":"Sample","hero":false,"slider":null,"value":null,"display":null},{"text":"mass kg = 6000000000000 // kg 0.001..1e20","label":null,"prefix":null,"suffix":"kg","section":"Sample","hidden":false,"hero":false,"slider":{"min":0.001,"max":100000000000000000000,"step":1000000000000000000},"value":6000000000000,"display":"6,000,000,000,000"},{"text":"volume ml = 5 // mL 0.001..100k","label":null,"prefix":null,"suffix":"mL","section":"Sample","hidden":false,"hero":false,"slider":{"min":0.001,"max":100000,"step":1000},"value":5,"display":"5"},{"text":"# Density","label":null,"prefix":null,"suffix":null,"section":"Density","hero":false,"slider":null,"value":null,"display":null},{"text":"_volume_m3 = volume ml / 1000000 // m³","label":null,"prefix":null,"suffix":"m³","section":"Density","hidden":true,"hero":false,"slider":null,"value":0.000005,"display":"0.000005"},{"text":"density kg per m3 = mass kg / volume_m3 // kg/m³ @label(Density (kg/m³))","label":"Density (kg/m³)","prefix":null,"suffix":"kg/m³","section":"Density","hidden":false,"hero":false,"slider":null,"value":1200000000000000000,"display":"1.2e18"},{"text":"density g per cc = density kg per m3 / 1000 // g/cm³ @label(Density (g/cm³))","label":"Density (g/cm³)","prefix":null,"suffix":"g/cm³","section":"Density","hidden":false,"hero":false,"slider":null,"value":1200000000000000,"display":"1,200,000,000,000,000"},{"text":"# Mass per Teaspoon (5 mL)","label":null,"prefix":null,"suffix":null,"section":"Mass per Teaspoon (5 mL)","hero":false,"slider":null,"value":null,"display":null},{"text":"mass per tsp kg = density kg per m3 * 5 / 1000000 // @label(Mass per teaspoon)","label":"Mass per teaspoon","prefix":null,"suffix":null,"section":"Mass per Teaspoon (5 mL)","hidden":false,"hero":false,"slider":null,"value":6000000000000,"display":"6,000,000,000,000"},{"text":"mass per tsp tons = mass per tsp kg / 1000 // tons @hero @label(Mass per teaspoon (metric tons))","label":"Mass per teaspoon (metric tons)","prefix":null,"suffix":"tons","section":"Mass per Teaspoon (5 mL)","hidden":false,"hero":true,"slider":null,"value":6000000000,"display":"6,000,000,000"},{"text":"# Reference","label":null,"prefix":null,"suffix":null,"section":"Reference","hero":false,"slider":null,"value":null,"display":null},{"text":"_water_density = 1000 // kg/m³","label":null,"prefix":null,"suffix":"kg/m³","section":"Reference","hidden":true,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"times denser than water = round(density kg per m3 / water_density)","label":null,"prefix":null,"suffix":null,"section":"Reference","hidden":false,"hero":false,"slider":null,"value":1200000000000000,"display":"1,200,000,000,000,000"}]},{"id":"depth-of-field","title":"Depth of Field","description":"Calculate near, far, and total depth of field for a given lens, aperture, and distance.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Camera Specs","label":null,"prefix":null,"suffix":null,"section":"Camera Specs","hero":false,"slider":null,"value":null,"display":null},{"text":"focal length = 50 // mm 10..600","label":null,"prefix":null,"suffix":"mm","section":"Camera Specs","hidden":false,"hero":false,"slider":{"min":10,"max":600,"step":1},"value":50,"display":"50"},{"text":"aperture = 2.8 // f-number 1.0..32","label":null,"prefix":null,"suffix":"f-number","section":"Camera Specs","hidden":false,"hero":false,"slider":{"min":1,"max":32,"step":1},"value":2.8,"display":"2.8"},{"text":"subject distance = 10 // feet 1..500","label":null,"prefix":null,"suffix":"feet","section":"Camera Specs","hidden":false,"hero":false,"slider":{"min":1,"max":500,"step":1},"value":10,"display":"10"},{"text":"sensor crop factor = 1.0 // 1.0 for Full Frame, 1.5 for APS-C","label":null,"prefix":null,"suffix":"1.0 for Full Frame, 1.5 for APS-C","section":"Camera Specs","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Constants","label":null,"prefix":null,"suffix":null,"section":"Constants","hero":false,"slider":null,"value":null,"display":null},{"text":"coc = 0.03 / sensor crop factor // mm (Circle of Confusion)","label":null,"prefix":null,"suffix":"mm (Circle of Confusion)","section":"Constants","hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"distance mm = subject distance * 304.8","label":null,"prefix":null,"suffix":null,"section":"Constants","hidden":false,"hero":false,"slider":null,"value":3048,"display":"3,048"},{"text":"# Hyperfocal Distance","label":null,"prefix":null,"suffix":null,"section":"Hyperfocal Distance","hero":false,"slider":null,"value":null,"display":null},{"text":"hyperfocal mm = (focal length^2 / (aperture * coc)) + focal length","label":null,"prefix":null,"suffix":null,"section":"Hyperfocal Distance","hidden":false,"hero":false,"slider":null,"value":29811.904761904763,"display":"29,811.9"},{"text":"hyperfocal feet = hyperfocal mm / 304.8","label":null,"prefix":null,"suffix":null,"section":"Hyperfocal Distance","hidden":false,"hero":false,"slider":null,"value":97.80808648918885,"display":"97.81"},{"text":"# DoF Calculation","label":null,"prefix":null,"suffix":null,"section":"DoF Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"near point mm = (hyperfocal mm * distance mm) / (hyperfocal mm + (distance mm - focal length))","label":null,"prefix":null,"suffix":null,"section":"DoF Calculation","hidden":false,"hero":false,"slider":null,"value":2769.4894689176317,"display":"2,769.49"},{"text":"far point mm = (hyperfocal mm * distance mm) / (hyperfocal mm - (distance mm - focal length))","label":null,"prefix":null,"suffix":null,"section":"DoF Calculation","hidden":false,"hero":false,"slider":null,"value":3388.789753716977,"display":"3,388.79"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"total depth of field = (far point mm - near point mm) / 304.8 // feet @hero","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":true,"slider":null,"value":2.0318250813626806,"display":"2.032"},{"text":"near limit = near point mm / 304.8 // feet","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":false,"slider":null,"value":9.086251538443673,"display":"9.086"},{"text":"far limit = far point mm / 304.8 // feet","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":false,"slider":null,"value":11.118076619806356,"display":"11.12"},{"text":"is infinite = distance mm >= hyperfocal mm","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"dof display = if(is infinite, 9999, total depth of field)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":2.0318250813626806,"display":"2.032"}]},{"id":"derivative-chain-rule","title":"Derivative — Chain Rule","description":"Evaluate (f∘g)'(x) = f'(g(x)) · g'(x).","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Values","label":null,"prefix":null,"suffix":null,"section":"Values","hero":false,"slider":null,"value":null,"display":null},{"text":"fprime_at_g = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"gprime_at_x = 7 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":7,"display":"7"},{"text":"# Chain rule","label":null,"prefix":null,"suffix":null,"section":"Chain rule","hero":false,"slider":null,"value":null,"display":null},{"text":"derivative = fprime_at_g * gprime_at_x // @label((f∘g)'(x))","label":"(f∘g)'(x)","prefix":null,"suffix":null,"section":"Chain rule","hidden":false,"hero":true,"slider":null,"value":28,"display":"28"}]},{"id":"derivative-power-rule","title":"Derivative — Power Rule","description":"Evaluate d/dx [a·xⁿ] = a·n·x^(n−1) at a given point.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Function: f(x) = a · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 4 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":4,"display":"4"},{"text":"x = 2 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":2,"display":"2"},{"text":"# Original and derivative at x","label":null,"prefix":null,"suffix":null,"section":"Original and derivative at x","hero":false,"slider":null,"value":null,"display":null},{"text":"f_x = a * x^n // @label(f(x))","label":"f(x)","prefix":null,"suffix":null,"section":"Original and derivative at x","hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"fprime_x = a * n * x^(n - 1) // @label(f'(x))","label":"f'(x)","prefix":null,"suffix":null,"section":"Original and derivative at x","hidden":false,"hero":true,"slider":null,"value":96,"display":"96"}]},{"id":"derivative-product-rule","title":"Derivative — Product Rule","description":"Evaluate (f·g)' = f'·g + f·g' at a given x using user-supplied f, g, f', g'.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Values at x","label":null,"prefix":null,"suffix":null,"section":"Values at x","hero":false,"slider":null,"value":null,"display":null},{"text":"f = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"g = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"fprime = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"gprime = 6 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Values at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":6,"display":"6"},{"text":"# Product rule","label":null,"prefix":null,"suffix":null,"section":"Product rule","hero":false,"slider":null,"value":null,"display":null},{"text":"derivative = fprime * g + f * gprime // @label((fg)')","label":"(fg)","prefix":null,"suffix":null,"section":"Product rule","hidden":false,"hero":true,"slider":null,"value":38,"display":"38"}]},{"id":"differential-gear-ratio-impact","title":"Differential Gear Ratio Impact","description":"Calculate RPM change after differential gear 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parity","hidden":false,"hero":true,"slider":null,"value":40,"display":"40"},{"text":"parity overhead terabytes = 2 * drive capacity terabytes // @hero","label":null,"prefix":null,"suffix":null,"section":"RAID 6 uses two drives worth of space for parity","hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"distance-converter","title":"Distance Converter","description":"Convert miles to kilometers, feet, meters, yards, and nautical miles.","category":"conversion","icon":"ruler","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Input Distance","label":null,"prefix":null,"suffix":null,"section":"Input Distance","hero":false,"slider":null,"value":null,"display":null},{"text":"miles = 26.2 // mi 0.1..1k","label":null,"prefix":null,"suffix":"mi","section":"Input Distance","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":26.2,"display":"26.2"},{"text":"# Metric","label":null,"prefix":null,"suffix":null,"section":"Metric","hero":false,"slider":null,"value":null,"display":null},{"text":"kilometers = miles * 1.60934 // km @hero","label":null,"prefix":null,"suffix":"km","section":"Metric","hidden":false,"hero":true,"slider":null,"value":42.164708,"display":"42.16"},{"text":"meters = kilometers * 1000 // m","label":null,"prefix":null,"suffix":"m","section":"Metric","hidden":false,"hero":false,"slider":null,"value":42164.708,"display":"42,164.71"},{"text":"centimeters = meters * 100 // cm","label":null,"prefix":null,"suffix":"cm","section":"Metric","hidden":false,"hero":false,"slider":null,"value":4216470.8,"display":"4,216,470.8"},{"text":"# Imperial","label":null,"prefix":null,"suffix":null,"section":"Imperial","hero":false,"slider":null,"value":null,"display":null},{"text":"yards = miles * 1760 // 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ls","label":null,"prefix":null,"suffix":"ls","section":"Other","hidden":false,"hero":false,"slider":null,"value":0.00014064632673314284,"display":"0.0001406"}]},{"id":"distance-formula","title":"Distance Formula","description":"Find the distance between two points: d = √((x₂-x₁)² + (y₂-y₁)²).","category":"formulas","icon":"ruler","tags":["coordinate-geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Two points","label":null,"prefix":null,"suffix":null,"section":"Two points","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"y1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"x2 = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"y2 = 6 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":6,"display":"6"},{"text":"# Distance","label":null,"prefix":null,"suffix":null,"section":"Distance","hero":false,"slider":null,"value":null,"display":null},{"text":"distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)","label":null,"prefix":null,"suffix":null,"section":"Distance","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"distance-time","title":"Distance, Speed, Time","description":"Travel time and distance for any speed, from walking pace to light-speed.","category":"science","icon":"gauge","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"distance km = 149600000 // km 0.001..1e10 by 1","label":null,"prefix":null,"suffix":"km","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000000000,"step":1},"value":149600000,"display":"149,600,000"},{"text":"speed km per s = 299792.458 // km/s 0.0001..299793","label":null,"prefix":null,"suffix":"km/s","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.0001,"max":299793,"step":5000},"value":299792.458,"display":"299,792.46"},{"text":"# Time","label":null,"prefix":null,"suffix":null,"section":"Time","hero":false,"slider":null,"value":null,"display":null},{"text":"time seconds = distance km / speed km per s // s","label":null,"prefix":null,"suffix":"s","section":"Time","hidden":false,"hero":false,"slider":null,"value":499.01188641643546,"display":"499.01"},{"text":"time minutes = time seconds / 60 // min @hero","label":null,"prefix":null,"suffix":"min","section":"Time","hidden":false,"hero":true,"slider":null,"value":8.316864773607257,"display":"8.317"},{"text":"time hours = time minutes / 60 // hr","label":null,"prefix":null,"suffix":"hr","section":"Time","hidden":false,"hero":false,"slider":null,"value":0.13861441289345428,"display":"0.1386"},{"text":"# Inverse: distance at this speed in a given duration","label":null,"prefix":null,"suffix":null,"section":"Inverse: distance at this speed in a given duration","hero":false,"slider":null,"value":null,"display":null},{"text":"duration sec = 1 // s 0..3.6k","label":null,"prefix":null,"suffix":"s","section":"Inverse: distance at this speed in a given duration","hidden":false,"hero":false,"slider":{"min":0,"max":3600,"step":50},"value":1,"display":"1"},{"text":"distance covered km = speed km per s * duration sec // km","label":null,"prefix":null,"suffix":"km","section":"Inverse: distance at this speed in a given 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6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"distance_km = (2 * earth_radius_km * (eye_height_meters / 1000) + (eye_height_meters / 1000) ** 2) ** 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4.654181226596146,"display":"4.654"}]},{"id":"dive-decompression-penalty","title":"Dive Decompression Penalty","description":"Check whether a scuba dive exceeds the no-decompression limit at a given depth.","category":"other","icon":"calculator","tags":["penalty"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"depth_feet = 80","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"bottom_time_minutes = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"no_deco_limit_minutes = 480 / (depth_feet - 30) // Very rough approximation","label":null,"prefix":null,"suffix":"Very rough approximation","section":null,"hidden":false,"hero":false,"slider":null,"value":9.6,"display":"9.6"},{"text":"deco_penalty_status = bottom_time_minutes > no_deco_limit_minutes ? 1 : 0 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"dividend-payout-ratio","title":"Dividend Payout Ratio","description":"Calculate dividend payout ratio from dividends per share and earnings per share.","category":"finance","icon":"ratio","tags":["dividend","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"dividends_per_share = 2.50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"earnings_per_share = 5.00","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"payout_ratio = dividends_per_share / earnings_per_share","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"dividend-yield","title":"Dividend Yield","description":"Calculate dividend yield from annual dividends per share and stock price.","category":"finance","icon":"dollar-sign","tags":["dividend","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Dividend Data","label":null,"prefix":null,"suffix":null,"section":"Dividend Data","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual_dividends_per_share = 4.50 // dollars 0..100","label":null,"prefix":"$","suffix":"dollars","section":"Dividend Data","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":4.5,"display":"$4.50"},{"text":"$share_price = 120 // dollars 1..5k","label":null,"prefix":"$","suffix":"dollars","section":"Dividend Data","hidden":false,"hero":false,"slider":{"min":1,"max":5000,"step":50},"value":120,"display":"$120.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"dividend_yield = (annual_dividends_per_share / share_price) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":3.75,"display":"3.75"},{"text":"$quarterly_dividend = annual_dividends_per_share / 4","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":1.125,"display":"$1.13"},{"text":"$investment_for_1000_monthly = (1000 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Adjustments","label":null,"prefix":null,"suffix":null,"section":"Adjustments","hero":false,"slider":null,"value":null,"display":null},{"text":"target strength = 5 // % 0.5..50","label":null,"prefix":null,"suffix":"%","section":"Adjustments","hidden":false,"hero":false,"slider":{"min":0.5,"max":50,"step":0.5},"value":5,"display":"5"},{"text":"mixer needed for target = round(concentrate_volume * (concentrate_strength - target_strength) / (target_strength - mixer_strength), 1) // oz","label":null,"prefix":null,"suffix":"oz","section":"Adjustments","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"total volume at target = concentrate_volume + mixer_needed_for_target // oz","label":null,"prefix":null,"suffix":"oz","section":"Adjustments","hidden":false,"hero":false,"slider":null,"value":16,"display":"16"}]},{"id":"drive-shaft-critical-speed","title":"Drive Shaft Critical Speed","description":"Calculate drive shaft critical 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material constant * (diameter inches / (length inches ^ 2))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":5760,"display":"5,760"}]},{"id":"driveway-sealant-volume","title":"Driveway Sealant Volume","description":"Calculate gallons of sealant needed for your driveway.","category":"construction","icon":"container","tags":["construction","maintenance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"driveway_width_feet = 20 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"driveway_length_feet = 40 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"coverage_sq_ft_per_gallon = 80 // sq ft","label":null,"prefix":null,"suffix":"sq 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panel_area) // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":25,"display":"25"},{"text":"# Materials","label":null,"prefix":null,"suffix":null,"section":"Materials","hero":false,"slider":null,"value":null,"display":null},{"text":"waste factor percent = 15 // 5..30","label":null,"prefix":null,"suffix":null,"section":"Materials","hidden":false,"hero":false,"slider":{"min":5,"max":30,"step":1},"value":15,"display":"15"},{"text":"total panels with waste = roundup(panels needed * (1 + waste factor percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Materials","hidden":false,"hero":false,"slider":null,"value":29,"display":"29"},{"text":"# Accessories","label":null,"prefix":null,"suffix":null,"section":"Accessories","hero":false,"slider":null,"value":null,"display":null},{"text":"# Rule of thumb: 1 gallon of joint compound per 100 sq ft","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 gallon of joint compound per 100 sq ft","hero":false,"slider":null,"value":null,"display":null},{"text":"joint compound gallons = round(total area / 100, 1)","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 gallon of joint compound per 100 sq ft","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Rule of thumb: 1 roll of tape per 200 sq ft","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 roll of tape per 200 sq ft","hero":false,"slider":null,"value":null,"display":null},{"text":"tape rolls = roundup(total area / 200)","label":null,"prefix":null,"suffix":null,"section":"Rule of thumb: 1 roll of tape per 200 sq ft","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"}]},{"id":"dunning-kruger-confidence-gap","title":"Dunning Kruger Confidence Gap","description":"Calculate the gap between actual and perceived competence 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Share","description":"Calculate earnings per share (EPS) from net income, preferred dividends, and shares.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.688Z"},"rows":[{"text":"# Earnings Data","label":null,"prefix":null,"suffix":null,"section":"Earnings Data","hero":false,"slider":null,"value":null,"display":null},{"text":"$net income = 1200000 // 0..100M","label":null,"prefix":"$","suffix":null,"section":"Earnings Data","hidden":false,"hero":false,"slider":{"min":0,"max":100000000,"step":1000000},"value":1200000,"display":"$1,200,000.00"},{"text":"$preferred dividends = 200000 // 0..10M","label":null,"prefix":"$","suffix":null,"section":"Earnings Data","hidden":false,"hero":false,"slider":{"min":0,"max":10000000,"step":100000},"value":200000,"display":"$200,000.00"},{"text":"weighted average shares = 500000 // 1k..10M","label":null,"prefix":null,"suffix":null,"section":"Earnings 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div)","section":"Result","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"}]},{"id":"earth-curvature-hidden-height","title":"Earth Curvature Hidden Height","description":"Calculate how much of a distant object is hidden by Earth's curvature.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Geography","label":null,"prefix":null,"suffix":null,"section":"Geography","hero":false,"slider":null,"value":null,"display":null},{"text":"distance to object = 10 // miles 1..500","label":null,"prefix":null,"suffix":"miles","section":"Geography","hidden":false,"hero":false,"slider":{"min":1,"max":500,"step":1},"value":10,"display":"10"},{"text":"observer height = 6 // feet 1..1k","label":null,"prefix":null,"suffix":"feet","section":"Geography","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":6,"display":"6"},{"text":"# Constants","label":null,"prefix":null,"suffix":null,"section":"Constants","hero":false,"slider":null,"value":null,"display":null},{"text":"earth radius miles = 3959","label":null,"prefix":null,"suffix":null,"section":"Constants","hidden":false,"hero":false,"slider":null,"value":3959,"display":"3,959"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"distance to horizon = sqrt(2 * earth radius miles * (observer height / 5280)) // miles","label":null,"prefix":null,"suffix":"miles","section":"Calculation","hidden":false,"hero":false,"slider":null,"value":2.999621188204816,"display":"3"},{"text":"is visible = distance to object <= distance to horizon","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"# Hidden Height Formula","label":null,"prefix":null,"suffix":null,"section":"Hidden Height 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@hero","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":true,"slider":null,"value":32.6784544740555,"display":"32.68"},{"text":"horizon distance = distance to horizon // miles","label":null,"prefix":null,"suffix":"miles","section":"Result","hidden":false,"hero":false,"slider":null,"value":2.999621188204816,"display":"3"},{"text":"total drop = (distance to object^2) / (2 * earth radius miles) * 5280 // feet","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":false,"slider":null,"value":66.68350593584239,"display":"66.68"}]},{"id":"easing-curves","title":"Easing Curves","description":"Hermite-fit cubics that smoothly interpolate between two values with chosen slopes at the endpoints — the basis for animation easing, monotone interpolation, and CAGD splines.","category":"math","icon":"activity","tags":["553","interpolation","animation","spline"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Constraints","label":null,"prefix":null,"suffix":null,"section":"Constraints","hero":false,"slider":null,"value":null,"display":null},{"text":"# Smoothstep — start and end flat (zero slopes), used in GLSL / CSS ease-in-out","label":null,"prefix":null,"suffix":null,"section":"Smoothstep — start and end flat (zero slopes), used in GLSL / CSS ease-in-out","hero":false,"slider":null,"value":null,"display":null},{"text":"smoothstep = hermite(0, 0, 0, 1, 1, 0)","label":null,"prefix":null,"suffix":null,"section":"Smoothstep — start and end flat (zero slopes), used in GLSL / CSS ease-in-out","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"__hermiteEval","text":"__hermiteEval"},[["folded",[0,0,3,-2]],{"type":"id","value":"x","text":"x","canonicalName":"x"}]],"__hermiteCoeffs":[0,0,3,-2],"name":"smoothstep"},"display":null},{"text":"# Accelerate — start flat, end with slope 2 (ease-in)","label":null,"prefix":null,"suffix":null,"section":"Accelerate — start flat, end with slope 2 (ease-in)","hero":false,"slider":null,"value":null,"display":null},{"text":"accelerate = hermite(0, 0, 0, 1, 1, 2)","label":null,"prefix":null,"suffix":null,"section":"Accelerate — start flat, end with slope 2 (ease-in)","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"__hermiteEval","text":"__hermiteEval"},[["folded",[0,0,1,0]],{"type":"id","value":"x","text":"x","canonicalName":"x"}]],"__hermiteCoeffs":[0,0,1,0],"name":"accelerate"},"display":null},{"text":"# Decelerate — start with slope 2, end flat (ease-out)","label":null,"prefix":null,"suffix":null,"section":"Decelerate — start with slope 2, end flat (ease-out)","hero":false,"slider":null,"value":null,"display":null},{"text":"decelerate = hermite(0, 0, 2, 1, 1, 0)","label":null,"prefix":null,"suffix":null,"section":"Decelerate — start with slope 2, end flat (ease-out)","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"__hermiteEval","text":"__hermiteEval"},[["folded",[0,2,-1,0]],{"type":"id","value":"x","text":"x","canonicalName":"x"}]],"__hermiteCoeffs":[0,2,-1,0],"name":"decelerate"},"display":null},{"text":"# Three curves, one per chart","label":null,"prefix":null,"suffix":null,"section":"Three curves, one per chart","hero":false,"slider":null,"value":null,"display":null},{"text":"# Try a custom fit","label":null,"prefix":null,"suffix":null,"section":"Try a custom fit","hero":false,"slider":null,"value":null,"display":null},{"text":"slope_start = 0 // -3..3 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Try a custom fit","hidden":false,"hero":false,"slider":{"min":-3,"max":3,"step":0.1},"value":0,"display":"0"},{"text":"slope_end = 0 // -3..3 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Try a custom fit","hidden":false,"hero":false,"slider":{"min":-3,"max":3,"step":0.1},"value":0,"display":"0"},{"text":"custom = hermite(0, 0, slope_start, 1, 1, slope_end)","label":null,"prefix":null,"suffix":null,"section":"Try a custom fit","hidden":false,"hero":true,"slider":null,"value":{"type":"function","params":["x"],"body":["callExp",{"type":"id","value":"__hermiteEval","text":"__hermiteEval"},[["folded",[0,0,3,-2]],{"type":"id","value":"x","text":"x","canonicalName":"x"}]],"__hermiteCoeffs":[0,0,3,-2],"name":"custom"},"display":null}]},{"id":"ebay-profit-calculator","title":"Ebay Profit Calculator","description":"Calculate net profit on an eBay sale after item cost, shipping, and fees.","category":"finance","icon":"dollar-sign","tags":["profit","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"selling_price = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"shipping_charged = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"item_cost = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"shipping_cost = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"ebay_fee_percentage = 0.1325","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1325,"display":"0.1325"},{"text":"ebay_per_order_fee = 0.30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"total_revenue = selling_price + shipping_charged","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":110,"display":"110"},{"text":"ebay_fee = (total_revenue * ebay_fee_percentage) + ebay_per_order_fee","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14.875,"display":"14.88"},{"text":"total_cost = item_cost + shipping_cost + ebay_fee","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":66.875,"display":"66.88"},{"text":"net_profit = total_revenue - total_cost","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":43.125,"display":"43.13"}]},{"id":"ebitda-calculator","title":"Ebitda Calculator","description":"Calculate EBITDA from net income, interest, taxes, depreciation, and amortization.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Company Financials","label":null,"prefix":null,"suffix":null,"section":"Company Financials","hero":false,"slider":null,"value":null,"display":null},{"text":"$net income = 500000 // 0..10M","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":10000000,"step":100000},"value":500000,"display":"$500,000.00"},{"text":"$interest expense = 50000 // 0..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":5000},"value":50000,"display":"$50,000.00"},{"text":"$income tax expense = 120000 // 0..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":5000},"value":120000,"display":"$120,000.00"},{"text":"$depreciation = 80000 // 0..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":5000},"value":80000,"display":"$80,000.00"},{"text":"$amortization = 20000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"Company Financials","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":20000,"display":"$20,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$ebitda = net income + interest expense + income tax expense + depreciation + amortization // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":770000,"display":"$770,000.00"},{"text":"$ebit = net income + interest expense + income tax expense","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":670000,"display":"$670,000.00"},{"text":"ebitda margin = (ebitda / (net income * 4)) * 100 // % (assumes revenue is 4x net income for context)","label":null,"prefix":null,"suffix":"% (assumes revenue is 4x net income for context)","section":"Result","hidden":false,"hero":false,"slider":null,"value":38.5,"display":"38.5"}]},{"id":"eco-label-product-premium","title":"Eco Label Product Premium","description":"Compare costs of eco-labeled vs standard products.","category":"finance","icon":"tag","tags":["finance","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"standard_product_price = 10 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"eco_label_premium_percent = 15 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"eco_product_price = standard_product_price * (1 + eco_label_premium_percent / 100) // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11.5,"display":"11.5"},{"text":"annual_extra_cost_if_buying_weekly = (eco_product_price - standard_product_price) * 52 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":78,"display":"78"}]},{"id":"economic-order-quantity","title":"Economic Order Quantity","description":"Find the optimal order size to minimize total inventory costs.","category":"business","icon":"shopping-cart","tags":["order"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"annualDemand = 10000 // units","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"orderCost = 50 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"holdingCostPerUnit = 2.50 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"eoq = sqrt((2 * annualDemand * orderCost) / holdingCostPerUnit) // units @hero","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":true,"slider":null,"value":632.4555320336759,"display":"632.46"}]},{"id":"effective-annual-rate","title":"Effective Annual Rate","description":"Effective annual rate from a nominal rate compounded n times per year: EAR = (1 + r/n)ⁿ − 1.","category":"formulas","icon":"percent","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"nominal_rate = 6 // % 0..50","label":null,"prefix":null,"suffix":"%","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":6,"display":"6"},{"text":"compounding_periods = 12 // per year 1..365","label":null,"prefix":null,"suffix":"per year","section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":365,"step":1},"value":12,"display":"12"},{"text":"# Effective rate","label":null,"prefix":null,"suffix":null,"section":"Effective rate","hero":false,"slider":null,"value":null,"display":null},{"text":"effective_rate = ((1 + nominal_rate / 100 / compounding_periods)^compounding_periods - 1) * 100 // @label(EAR (%))","label":"EAR (%)","prefix":null,"suffix":null,"section":"Effective rate","hidden":false,"hero":true,"slider":null,"value":6.16778118644982,"display":"6.168"}]},{"id":"effective-gross-income","title":"Effective Gross Income","description":"Property income after accounting for vacancy and credit losses.","category":"real-estate","icon":"dollar-sign","tags":["income"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"potentialRentalIncome = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"vacancyAndCreditLoss = 5000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"otherIncome = 3000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"egi = potentialRentalIncome - vacancyAndCreditLoss + otherIncome // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":98000,"display":"98,000"}]},{"id":"eisenhower-matrix-task-priority","title":"Eisenhower Matrix Task Priority","description":"Calculate task priority index from urgency and importance scores.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"urgency_score = 8 // 1..10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":8,"display":"8"},{"text":"importance_score = 9 // 1..10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":{"min":1,"max":10,"step":0.1},"value":9,"display":"9"},{"text":"priority_index = urgency_score * importance_score // max 100 @hero","label":null,"prefix":null,"suffix":"max 100","section":null,"hidden":false,"hero":true,"slider":null,"value":72,"display":"72"},{"text":"_quadrant = if (urgency_score > 5) { if (importance_score > 5) { \"Do First\" } else { \"Delegate\" } } else { if (importance_score > 5) { \"Schedule\" } else { \"Eliminate\" } }","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":"Do First","display":"Do First"}]},{"id":"electric-car-emissions-savings","title":"Electric Car Emissions Savings","description":"Compare EV emissions to gas vehicle emissions.","category":"science","icon":"zap","tags":["eco","ev","emissions"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"annual_km_driven = 15000 // km","label":null,"prefix":null,"suffix":"km","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"gas_car_emissions_per_km = 0.12 // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"electric_car_emissions_per_km = 0.05 // kg CO2 (grid dependent)","label":null,"prefix":null,"suffix":"kg CO2 (grid dependent)","section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"annual_co2_savings_kg = annual_km_driven * (gas_car_emissions_per_km - electric_car_emissions_per_km) // kg CO2 @hero","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":true,"slider":null,"value":1050,"display":"1,050"}]},{"id":"electric-circuit-total-resistance-parallel","title":"Electric Circuit Total Resistance Parallel","description":"Calculate total resistance of three resistors in parallel.","category":"education","icon":"book-open","tags":["electric"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"r1 = 100 // ohms","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"r2 = 200 // ohms","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"r3 = 300 // ohms","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"total_resistance_parallel = 1 / (1/r1 + 1/r2 + 1/r3) // ohms @hero","label":null,"prefix":null,"suffix":"ohms","section":null,"hidden":false,"hero":true,"slider":null,"value":54.54545454545455,"display":"54.55"}]},{"id":"electric-field-point-charge","title":"Electric Field Point Charge","description":"Calculate the electric field magnitude at a distance from a point charge.","category":"education","icon":"book-open","tags":["electric","charge"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"charge = 1e-6 // Coulombs","label":null,"prefix":null,"suffix":"Coulombs","section":null,"hidden":false,"hero":false,"slider":null,"value":0.000001,"display":"0.000001"},{"text":"distance = 0.1 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"_k = 8.987e9 // N*m^2/C^2","label":null,"prefix":null,"suffix":"N*m^2/C^2","section":null,"hidden":true,"hero":false,"slider":null,"value":8987000000,"display":"8,987,000,000"},{"text":"electric_field_magnitude = k * charge / distance^2 // Newtons per Coulomb @hero","label":null,"prefix":null,"suffix":"Newtons per Coulomb","section":null,"hidden":false,"hero":true,"slider":null,"value":898699.9999999999,"display":"898,700"}]},{"id":"electric-power-efficiency","title":"Electric Power Efficiency","description":"Calculate electric power efficiency and power loss from input and output watts.","category":"education","icon":"book-open","tags":["electric"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"power_input = 1000 // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"power_output = 850 // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":850,"display":"850"},{"text":"efficiency_percentage = (power_output / power_input) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":85,"display":"85"},{"text":"power_loss = power_input - power_output // Watts @hero","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"}]},{"id":"electrical-wire","title":"Wire Gauge","description":"Calculate minimum wire gauge for an electrical circuit.","category":"engineering","icon":"zap","tags":["electrical"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Circuit Requirements","label":null,"prefix":null,"suffix":null,"section":"Circuit Requirements","hero":false,"slider":null,"value":null,"display":null},{"text":"amps = 20 // 1..200","label":null,"prefix":null,"suffix":null,"section":"Circuit Requirements","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":20,"display":"20"},{"text":"distance ft = 100 // 10..1k","label":null,"prefix":null,"suffix":null,"section":"Circuit Requirements","hidden":false,"hero":false,"slider":{"min":10,"max":1000,"step":1},"value":100,"display":"100"},{"text":"voltage = 120 // V 12..480 by 12","label":null,"prefix":null,"suffix":"V","section":"Circuit Requirements","hidden":false,"hero":false,"slider":{"min":12,"max":480,"step":12},"value":120,"display":"120"},{"text":"# Wire Sizing (copper, NEC)","label":null,"prefix":null,"suffix":null,"section":"Wire Sizing (copper, NEC)","hero":false,"slider":null,"value":null,"display":null},{"text":"max voltage drop pct = 3 // % 1..5 by 0.5","label":null,"prefix":null,"suffix":"%","section":"Wire Sizing (copper, NEC)","hidden":false,"hero":false,"slider":{"min":1,"max":5,"step":0.5},"value":3,"display":"3"},{"text":"_resistivity = 10.4 // ohm-cmil/ft (copper at 75°C)","label":null,"prefix":null,"suffix":"ohm-cmil/ft (copper at 75°C)","section":"Wire Sizing (copper, NEC)","hidden":true,"hero":false,"slider":null,"value":10.4,"display":"10.4"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"total wire length = distance ft * 2 // @label(Round-trip wire length) @suffix(ft)","label":"Round-trip wire length","prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"min wire area cmil = round((2 * resistivity * distance ft * amps) / (voltage * max voltage drop pct / 100)) // @hero @label(Min wire area (circular mils))","label":"Min wire area (circular mils)","prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":11556,"display":"11,556"},{"text":"# Voltage Drop","label":null,"prefix":null,"suffix":null,"section":"Voltage Drop","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage drop = round((2 * resistivity * distance ft * amps) / min wire area cmil * 100) / 100 // V","label":null,"prefix":null,"suffix":"V","section":"Voltage Drop","hidden":false,"hero":false,"slider":null,"value":3.6,"display":"3.6"},{"text":"voltage drop pct = round((voltage drop / voltage) * 100 * 100) / 100 // % @label(Voltage drop %)","label":"Voltage drop %","prefix":null,"suffix":"%","section":"Voltage Drop","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"power loss watts = round(voltage drop * amps * 10) / 10 // W @label(Power lost in wire)","label":"Power lost in wire","prefix":null,"suffix":"W","section":"Voltage Drop","hidden":false,"hero":false,"slider":null,"value":72,"display":"72"}]},{"id":"electricity-bill","title":"Electricity Bill","description":"Estimate your monthly electricity bill from appliance usage.","category":"everyday","icon":"zap","tags":["everyday"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Electricity Rate","label":null,"prefix":null,"suffix":null,"section":"Electricity Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"rate = 0.14 // $/kWh 0.05..0.5 by 0.01","label":null,"prefix":null,"suffix":"$/kWh","section":"Electricity Rate","hidden":false,"hero":false,"slider":{"min":0.05,"max":0.5,"step":0.01},"value":0.14,"display":"0.14"},{"text":"# Major Appliances (watts x hours/day)","label":null,"prefix":null,"suffix":null,"section":"Major Appliances (watts x hours/day)","hero":false,"slider":null,"value":null,"display":null},{"text":"ac watts = 1500 // W 0..5k by 100 @label(A/C or Heating)","label":"A/C or Heating","prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":100},"value":1500,"display":"1,500"},{"text":"ac hours = 6 // hrs/day 0..24","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":24,"step":1},"value":6,"display":"6"},{"text":"fridge watts = 150 // W 0..500 by 10","label":null,"prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":500,"step":10},"value":150,"display":"150"},{"text":"fridge hours = 24 // hrs/day","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"washer dryer watts = 3000 // W 0..5k by 100 @label(Washer + Dryer)","label":"Washer + Dryer","prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":100},"value":3000,"display":"3,000"},{"text":"washer dryer hours = 1 // hrs/day 0..4 by 0.5","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.5},"value":1,"display":"1"},{"text":"computer watts = 200 // W 0..1k @label(Computer / TV)","label":"Computer / TV","prefix":null,"suffix":"W","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":200,"display":"200"},{"text":"computer hours = 8 // hrs/day 0..24","label":null,"prefix":null,"suffix":"hrs/day","section":"Major Appliances (watts x hours/day)","hidden":false,"hero":false,"slider":{"min":0,"max":24,"step":1},"value":8,"display":"8"},{"text":"# Daily Usage","label":null,"prefix":null,"suffix":null,"section":"Daily Usage","hero":false,"slider":null,"value":null,"display":null},{"text":"daily kwh = round((ac watts * ac hours + fridge watts * fridge hours + washer dryer watts * washer dryer hours + computer watts * computer hours) / 1000 * 100) / 100","label":null,"prefix":null,"suffix":null,"section":"Daily Usage","hidden":false,"hero":false,"slider":null,"value":17.2,"display":"17.2"},{"text":"# Monthly Bill","label":null,"prefix":null,"suffix":null,"section":"Monthly Bill","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly kwh = round(daily kwh * 30.44 * 10) / 10 // kWh","label":null,"prefix":null,"suffix":"kWh","section":"Monthly Bill","hidden":false,"hero":false,"slider":null,"value":523.6,"display":"523.6"},{"text":"$monthly cost = round(monthly kwh * rate * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Monthly Bill","hidden":false,"hero":true,"slider":null,"value":73.3,"display":"$73.30"},{"text":"$annual cost = round(monthly cost * 12 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Monthly Bill","hidden":false,"hero":false,"slider":null,"value":879.6,"display":"$879.60"}]},{"id":"ellipse-area","title":"Ellipse Area","description":"Find the area of an ellipse from its two semi-axes: A = π × a × b.","category":"formulas","icon":"circle","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Semi-axes","label":null,"prefix":null,"suffix":null,"section":"Semi-axes","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 6 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Semi-axes","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":6,"display":"6"},{"text":"b = 4 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Semi-axes","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":4,"display":"4"},{"text":"# Area","label":null,"prefix":null,"suffix":null,"section":"Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = pi * a * b","label":null,"prefix":null,"suffix":null,"section":"Area","hidden":false,"hero":true,"slider":null,"value":75.39822368615503,"display":"75.4"}]},{"id":"email-marketing-roi","title":"Email Marketing Roi","description":"Calculate ROI of an email marketing campaign from open, click, and conversion rates.","category":"finance","icon":"dollar-sign","tags":["email","roi","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"total_emails_sent = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"open_rate_percentage = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"click_through_rate_percentage = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"conversion_rate_percentage = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"average_order_value = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"campaign_cost = 200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"total_clicks = total_emails_sent * (open_rate_percentage / 100) * (click_through_rate_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"total_conversions = total_clicks * (conversion_rate_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total_revenue = total_conversions * average_order_value","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"return_on_investment_percentage = ((total_revenue - campaign_cost) / campaign_cost) * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":-50,"display":"-50"}]},{"id":"email-open-rate-impact","title":"Email Open Rate Impact","description":"Calculate total clicks expected from email subscribers, open rate, and CTR.","category":"other","icon":"calculator","tags":["email"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"subscribers = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"open_rate = 0.20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"click_through_rate = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"total_opens = subscribers * open_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"total_clicks = total_opens * click_through_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"email-processing-time-batching","title":"Email Processing Time Batching","description":"Calculate daily and weekly hours spent processing email at a given pace.","category":"productivity","icon":"clock","tags":["email"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"emails_per_day = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"time_per_email_seconds = 120 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"_total_seconds = emails_per_day * time_per_email_seconds","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":6000,"display":"6,000"},{"text":"total_time_minutes = total_seconds / 60 // minutes @hero","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"},{"text":"weekly_email_hours = (total_time_minutes * 5) / 60 // hours @hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":8.333333333333334,"display":"8.333"}]},{"id":"emergency-fund-calculator","title":"Emergency Fund","description":"Calculate how much you need saved for a 3-6 month emergency cushion.","category":"finance","icon":"shield-check","tags":["fund","safety"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Monthly Expenses","label":null,"prefix":null,"suffix":null,"section":"Monthly Expenses","hero":false,"slider":null,"value":null,"display":null},{"text":"rent or mortgage = $1800 // 200..5k","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":200,"max":5000,"step":50},"value":1800,"display":"$1,800.00"},{"text":"groceries = $600 // 100..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":100,"max":2000,"step":25},"value":600,"display":"$600.00"},{"text":"utilities = $200 // 50..1k","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":50,"max":1000,"step":1},"value":200,"display":"$200.00"},{"text":"transportation = $300 // 0..1.5k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":1500,"step":25},"value":300,"display":"$300.00"},{"text":"insurance = $250 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":250,"display":"$250.00"},{"text":"other essentials = $400 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":400,"display":"$400.00"},{"text":"# Essential Monthly Total","label":null,"prefix":null,"suffix":null,"section":"Essential Monthly Total","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly essential expenses = $rent_or_mortgage + groceries + utilities + transportation + insurance + other_essentials","label":null,"prefix":"$","suffix":null,"section":"Essential Monthly Total","hidden":false,"hero":false,"slider":null,"value":3550,"display":"$3,550.00"},{"text":"# Emergency Fund Goals","label":null,"prefix":null,"suffix":null,"section":"Emergency Fund Goals","hero":false,"slider":null,"value":null,"display":null},{"text":"$six month fund conservative = monthly_essential_expenses * 6 // @hero @label(6-Month Fund (Conservative))","label":"6-Month Fund (Conservative)","prefix":"$","suffix":null,"section":"Emergency Fund Goals","hidden":false,"hero":true,"slider":null,"value":21300,"display":"$21,300.00"},{"text":"$four month fund moderate = monthly_essential_expenses * 4 // @label(4-Month Fund (Moderate))","label":"4-Month Fund (Moderate)","prefix":"$","suffix":null,"section":"Emergency Fund Goals","hidden":false,"hero":false,"slider":null,"value":14200,"display":"$14,200.00"},{"text":"$three month fund minimum = monthly_essential_expenses * 3 // @label(3-Month Fund (Minimum))","label":"3-Month Fund (Minimum)","prefix":"$","suffix":null,"section":"Emergency Fund Goals","hidden":false,"hero":false,"slider":null,"value":10650,"display":"$10,650.00"},{"text":"# Current Status","label":null,"prefix":null,"suffix":null,"section":"Current Status","hero":false,"slider":null,"value":null,"display":null},{"text":"current emergency savings = $8000 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Current Status","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":8000,"display":"$8,000.00"},{"text":"months currently covered = current_emergency_savings / monthly_essential_expenses","label":null,"prefix":null,"suffix":null,"section":"Current Status","hidden":false,"hero":false,"slider":null,"value":2.2535211267605635,"display":"2.254"},{"text":"# Progress","label":null,"prefix":null,"suffix":null,"section":"Progress","hero":false,"slider":null,"value":null,"display":null},{"text":"$remaining to 6 month goal = six_month_fund_conservative - current_emergency_savings","label":null,"prefix":"$","suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":13300,"display":"$13,300.00"},{"text":"monthly savings goal = $500 // 50..5k","label":null,"prefix":"$","suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":{"min":50,"max":5000,"step":50},"value":500,"display":"$500.00"},{"text":"months to reach goal = remaining_to_6_month_goal / monthly_savings_goal","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":26.6,"display":"26.6"}]},{"id":"emergency-fund-months-remaining","title":"Emergency Fund Months Remaining","description":"Calculate how many months your savings will cover at current monthly expenses.","category":"other","icon":"calculator","tags":["fund"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"current_savings = 12000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12000,"display":"12,000"},{"text":"monthly_expenses = 3000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"months_remaining = current_savings / monthly_expenses","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"empathy-quotient-approximation","title":"Empathy Quotient Approximation","description":"Estimate an empathy quotient score from social awareness and emotional reactivity.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"social_awareness_score = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"emotional_reactivity_score = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"empathy_quotient = (social_awareness_score + emotional_reactivity_score) * 2.5 // approximate score @hero","label":null,"prefix":null,"suffix":"approximate score","section":null,"hidden":false,"hero":true,"slider":null,"value":37.5,"display":"37.5"}]},{"id":"employee-cost","title":"Employee Cost","description":"Calculate the true annual cost of hiring an employee.","category":"business","icon":"users","tags":["salary"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Base Compensation","label":null,"prefix":null,"suffix":null,"section":"Base Compensation","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual salary = 75000 // 30k..300k by 1k","label":null,"prefix":"$","suffix":null,"section":"Base Compensation","hidden":false,"hero":false,"slider":{"min":30000,"max":300000,"step":1000},"value":75000,"display":"$75,000.00"},{"text":"benefits rate = 25 // % 0..50","label":null,"prefix":null,"suffix":"%","section":"Base Compensation","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":25,"display":"25"},{"text":"payroll tax rate = 7.65 // % 0..20","label":null,"prefix":null,"suffix":"%","section":"Base Compensation","hidden":false,"hero":false,"slider":{"min":0,"max":20,"step":1},"value":7.65,"display":"7.65"},{"text":"# Overhead","label":null,"prefix":null,"suffix":null,"section":"Overhead","hero":false,"slider":null,"value":null,"display":null},{"text":"$equipment and software = 3000 // 0..20k by 500","label":null,"prefix":"$","suffix":null,"section":"Overhead","hidden":false,"hero":false,"slider":{"min":0,"max":20000,"step":500},"value":3000,"display":"$3,000.00"},{"text":"$office and facilities = 6000 // 0..30k","label":null,"prefix":"$","suffix":null,"section":"Overhead","hidden":false,"hero":false,"slider":{"min":0,"max":30000,"step":500},"value":6000,"display":"$6,000.00"},{"text":"$training and development = 2000 // 0..10k by 500","label":null,"prefix":"$","suffix":null,"section":"Overhead","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":500},"value":2000,"display":"$2,000.00"},{"text":"# True Cost","label":null,"prefix":null,"suffix":null,"section":"True Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$benefits cost = round(annual salary * benefits rate / 100 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":18750,"display":"$18,750.00"},{"text":"$payroll taxes = round(annual salary * payroll tax rate / 100 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":5737.5,"display":"$5,737.50"},{"text":"$total overhead = equipment and software + office and facilities + training and development","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":11000,"display":"$11,000.00"},{"text":"$total annual cost = round((annual salary + benefits cost + payroll taxes + total overhead) * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"True Cost","hidden":false,"hero":true,"slider":null,"value":110487.5,"display":"$110,487.50"},{"text":"cost multiplier = round(total annual cost / annual salary * 100) / 100 // @label(Cost multiplier over salary)","label":"Cost multiplier over salary","prefix":null,"suffix":null,"section":"True Cost","hidden":false,"hero":false,"slider":null,"value":1.47,"display":"1.47"},{"text":"# Hourly Breakdown","label":null,"prefix":null,"suffix":null,"section":"Hourly Breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"working hours per year = 2080 // 1.5k..2.2k","label":null,"prefix":null,"suffix":null,"section":"Hourly Breakdown","hidden":false,"hero":false,"slider":{"min":1500,"max":2200,"step":1},"value":2080,"display":"2,080"},{"text":"$effective hourly rate = round(total annual cost / working hours per year * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Hourly Breakdown","hidden":false,"hero":false,"slider":null,"value":53.12,"display":"$53.12"}]},{"id":"employee-stock-option-valuation-eso","title":"Employee Stock Option Valuation Eso","description":"Estimate the intrinsic value of an employee stock option (ESO).","category":"finance","icon":"dollar-sign","tags":["stock","valuation","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"stock_price = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"strike_price = 80","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"years_to_expiry = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"volatility = 0.30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"risk_free_rate = 0.04","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"},{"text":"value = stock_price - strike_price","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"endangered-species-population-growth","title":"Endangered Species Growth","description":"Model population recovery using logistic growth.","category":"science","icon":"dog","tags":["science","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"initial_population = 500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"annual_growth_rate_percent = 5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"carrying_capacity = 2000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"years = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"population_after_years = carrying_capacity / (1 + ((carrying_capacity - initial_population) / initial_population) * exp(- (annual_growth_rate_percent / 100) * years)) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":709.3224887848869,"display":"709.32"}]},{"id":"energy-conversion","title":"Gas vs EV Energy","description":"Useful work from a gas tank versus an EV battery after efficiency losses.","category":"everyday","icon":"battery-charging","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.692Z"},"rows":[{"text":"# Gasoline Side","label":null,"prefix":null,"suffix":null,"section":"Gasoline Side","hero":false,"slider":null,"value":null,"display":null},{"text":"gallons = 8 // 0.1..50 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Gasoline Side","hidden":false,"hero":false,"slider":{"min":0.1,"max":50,"step":0.1},"value":8,"display":"8"},{"text":"_kwh_per_gallon = 33.7 // kWh","label":null,"prefix":null,"suffix":"kWh","section":"Gasoline Side","hidden":true,"hero":false,"slider":null,"value":33.7,"display":"33.7"},{"text":"ice efficiency = 25 // % 5..50","label":null,"prefix":null,"suffix":"%","section":"Gasoline Side","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":25,"display":"25"},{"text":"total gas kwh = gallons * kwh_per_gallon // kWh @label(Gas chemical energy)","label":"Gas chemical energy","prefix":null,"suffix":"kWh","section":"Gasoline Side","hidden":false,"hero":false,"slider":null,"value":269.6,"display":"269.6"},{"text":"useful gas kwh = total gas kwh * ice efficiency / 100 // kWh @label(Useful work from gas)","label":"Useful work from gas","prefix":null,"suffix":"kWh","section":"Gasoline 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Planning","label":null,"prefix":null,"suffix":null,"section":"Planning","hero":false,"slider":null,"value":null,"display":null},{"text":"weekends left = floor(days until event / 7)","label":null,"prefix":null,"suffix":null,"section":"Planning","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"months approx = round(days until event / 30.44 * 10) / 10 // @label(Approximately Months)","label":"Approximately Months","prefix":null,"suffix":null,"section":"Planning","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"work days = round(days until event * 5 / 7) // @label(Work Days (approx))","label":"Work Days (approx)","prefix":null,"suffix":null,"section":"Planning","hidden":false,"hero":false,"slider":null,"value":64,"display":"64"}]},{"id":"exam-algebra1","title":"Algebra I Final — Linear & Quadratic Equations","description":"Linear equations, systems, and quadratics worked with the `solve` verb — the engine returns every real 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-5","label":null,"prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":-5,"display":"-5"},{"text":"disc = b^2 - 4a*c // @formula @label(discriminant)","label":"discriminant","prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":49,"display":"49"},{"text":"x_plus = (-b + sqrt(disc)) / (2a) // @accent @formula @label($x_+$)","label":"$x_+$","prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"x_minus = (-b - sqrt(disc)) / (2a) // @accent @formula @label($x_-$)","label":"$x_-$","prefix":null,"suffix":null,"section":"Problem 6: The quadratic formula, spelled out","hidden":false,"hero":false,"slider":null,"value":-2.5,"display":"-2.5"},{"text":"# Problem 7: Vertex of a parabola","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Vertex of a parabola","hero":false,"slider":null,"value":null,"display":null},{"text":"x_vertex = -b / (2a) // @accent @formula @label($x$-vertex)","label":"$x$-vertex","prefix":null,"suffix":null,"section":"Problem 7: Vertex of a parabola","hidden":false,"hero":false,"slider":null,"value":-0.75,"display":"-0.75"},{"text":"y_vertex = a*x_vertex^2 + b*x_vertex + c // @accent @formula @label($y$-vertex)","label":"$y$-vertex","prefix":null,"suffix":null,"section":"Problem 7: Vertex of a parabola","hidden":false,"hero":false,"slider":null,"value":-6.125,"display":"-6.125"},{"text":"# Problem 8: Solve an inequality","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Solve an inequality","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: Exponential — solve for the exponent","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Exponential — solve for the exponent","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 10: Function notation and evaluation","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Function notation and evaluation","hero":false,"slider":null,"value":null,"display":null},{"text":"f(x) = x^2 - 3x + 2","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Function notation and evaluation","hidden":false,"hero":false,"slider":null,"value":{"type":"function","params":["x"],"body":["add",["sub",["power",["parenExpr",{"type":"id","value":"x","text":"x","offset":17,"lineBreaks":0,"line":1,"col":18}],{"type":"decimal","value":"2","text":"2","offset":20,"lineBreaks":0,"line":1,"col":21}],["parenMult",[{"type":"decimal","value":"3","text":"3","offset":24,"lineBreaks":0,"line":1,"col":25},[[{"type":"id","value":"x","text":"x","offset":26,"lineBreaks":0,"line":1,"col":27}]]]]],{"type":"decimal","value":"2","text":"2","offset":31,"lineBreaks":0,"line":1,"col":32}],"name":"f"},"display":null},{"text":"# Problem 11: Factor a quadratic (symbolic)","label":null,"prefix":null,"suffix":null,"section":"Problem 11: Factor a quadratic (symbolic)","hero":false,"slider":null,"value":null,"display":null},{"text":"factor x^2 - 5x + 6 // @hero @accent @label(factor x^2 - 5x + 6)","label":"factor x^2 - 5x + 6","prefix":null,"suffix":null,"section":"Problem 11: Factor a quadratic (symbolic)","hidden":false,"hero":true,"slider":null,"value":"(x - 2)*(x - 3)","display":"(x - 2)*(x - 3)"},{"text":"# Problem 12: Expand a binomial (symbolic)","label":null,"prefix":null,"suffix":null,"section":"Problem 12: Expand a binomial (symbolic)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 13: Simplify an expression (symbolic)","label":null,"prefix":null,"suffix":null,"section":"Problem 13: Simplify an expression (symbolic)","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-algebra2","title":"Algebra II Final — Functions, Logs & Complex Numbers","description":"Polynomials, exponentials and logarithms, complex numbers, and sequences — the second-year algebra core, every answer computed.","category":"education","icon":"book-open","tags":["algebra","algebra2","logarithms","complex","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Roots of a polynomial","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Roots of a polynomial","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: A quadratic with complex roots","label":null,"prefix":null,"suffix":null,"section":"Problem 2: A quadratic with complex roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Complex arithmetic","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Complex arithmetic","hero":false,"slider":null,"value":null,"display":null},{"text":"(2 + 3i) * (1 - i) // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Complex arithmetic","hidden":false,"hero":true,"slider":null,"value":{"r":5,"i":1},"display":"5 + i"},{"text":"# Problem 4: Magnitude of a complex number","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Magnitude of a complex number","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Laws of logarithms","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Laws of logarithms","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 6: Solve an exponential equation","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Solve an exponential equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Compound-growth (change of base)","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Compound-growth (change of base)","hero":false,"slider":null,"value":null,"display":null},{"text":"t_double = ln(2) / ln(1.05) // @accent @formula @label(years)","label":"years","prefix":null,"suffix":null,"section":"Problem 7: Compound-growth (change of base)","hidden":false,"hero":false,"slider":null,"value":14.20669908289046,"display":"14.21"},{"text":"# Problem 8: Arithmetic sequence — nth term","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Arithmetic sequence — nth 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III Final — Multivariable","description":"Gradients, partial derivatives, and vector magnitudes.","category":"education","icon":"book-open","tags":["calculus","multivariable","gradient","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Gradient of a paraboloid","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Gradient of a paraboloid","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Gradient of a mixed polynomial","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Gradient of a mixed polynomial","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Gradient of a triple product","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Gradient of a triple product","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: Gradient of a product of trig 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Each model is solved numerically (RK4) and cross-checked against its exact exponential solution. Sourced from MIT 18.03 and Boyce-DiPrima.","category":"education","icon":"activity","tags":["differential-equations","ode","circuits","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: RC circuit charging","label":null,"prefix":null,"suffix":null,"section":"Problem 1: RC circuit charging","hero":false,"slider":null,"value":null,"display":null},{"text":"_tau = 1000 * 0.001","label":null,"prefix":null,"suffix":null,"section":"Problem 1: RC circuit charging","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_exact = 0.001 * 10 * (1 - e^(-2/_tau))","label":null,"prefix":null,"suffix":null,"section":"Problem 1: RC circuit charging","hidden":true,"hero":false,"slider":null,"value":0.008646647167633872,"display":"0.008647"},{"text":"# Problem 2: RC circuit discharging","label":null,"prefix":null,"suffix":null,"section":"Problem 2: RC circuit discharging","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 0.01 * e^(-3/1)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: RC circuit discharging","hidden":true,"hero":false,"slider":null,"value":0.0004978706836786395,"display":"0.0004979"},{"text":"# Problem 3: RL circuit current","label":null,"prefix":null,"suffix":null,"section":"Problem 3: RL circuit current","hero":false,"slider":null,"value":null,"display":null},{"text":"_tau = 2 / 4","label":null,"prefix":null,"suffix":null,"section":"Problem 3: RL circuit current","hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_exact = (12/4) * (1 - e^(-1/_tau))","label":null,"prefix":null,"suffix":null,"section":"Problem 3: RL circuit current","hidden":true,"hero":false,"slider":null,"value":2.593994150290162,"display":"2.594"},{"text":"# Problem 4: Mixing tank filling with salt","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Mixing tank filling with salt","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 200 * (1 - e^(-30/20))","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Mixing tank filling with salt","hidden":true,"hero":false,"slider":null,"value":155.37396797031403,"display":"155.37"},{"text":"# Problem 5: Mixing tank flushed with pure water","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Mixing tank flushed with pure water","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 50 * e^(-40/50)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Mixing tank flushed with pure water","hidden":true,"hero":false,"slider":null,"value":22.466448205861077,"display":"22.47"},{"text":"# Problem 6: Newton's law of cooling","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Newton's law of cooling","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 20 + 70 * e^(-0.1 * 15)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Newton's law of cooling","hidden":true,"hero":false,"slider":null,"value":35.61911121039009,"display":"35.62"},{"text":"# Problem 7: Newton's law of warming","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Newton's law of warming","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 25 - 20 * e^(-0.05 * 20)","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Newton's law of warming","hidden":true,"hero":false,"slider":null,"value":17.642411176571155,"display":"17.64"},{"text":"plot T' = -0.05 * (T - 25), T(0) = 5, T(20) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Newton's law of warming","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-diffeq-first-order","title":"Differential Equations — First Order ODEs","description":"First-order initial-value problems solved numerically (RK4) with Instacalc, cross-checked against exact solutions. Sourced from MIT 18.03 and Paul's Online Notes.","category":"education","icon":"activity","tags":["differential-equations","ode","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Exponential growth","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Exponential growth","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = e^1","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Exponential growth","hidden":true,"hero":false,"slider":null,"value":2.718281828459045,"display":"2.718"},{"text":"# Problem 2: Exponential decay","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Exponential decay","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 3 * e^(-4)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Exponential decay","hidden":true,"hero":false,"slider":null,"value":0.05494691666620255,"display":"0.0549"},{"text":"# Problem 3: Linear relaxation to equilibrium","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Linear relaxation to equilibrium","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 - e^(-2)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Linear relaxation to equilibrium","hidden":true,"hero":false,"slider":null,"value":0.8646647167633873,"display":"0.8647"},{"text":"# Problem 4: Logistic growth","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Logistic growth","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Separable with variable coefficient","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Separable with variable coefficient","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = e^(2)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Separable with variable coefficient","hidden":true,"hero":false,"slider":null,"value":7.3890560989306495,"display":"7.389"},{"text":"# Problem 6: Bistable nonlinear ODE","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Bistable nonlinear ODE","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Nonautonomous linear ODE","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Nonautonomous linear ODE","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 3 - 1 + 2 * e^(-3)","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Nonautonomous linear ODE","hidden":true,"hero":false,"slider":null,"value":2.099574136735728,"display":"2.1"},{"text":"plot y' = x - y, y(0) = 1, y(3) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Nonautonomous linear ODE","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-diffeq-laplace","title":"Differential Equations — Laplace Transforms","description":"Laplace transforms L{f(t)} = F(s) of the standard table functions, computed symbolically by Instacalc. Each entry is a classic exam problem from the Laplace-transform table (MIT 18.03, Paul's Online Notes).","category":"education","icon":"activity","tags":["differential-equations","laplace","transforms","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Unit step / constant","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Unit step / constant","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace 1 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Unit step / constant","hidden":false,"hero":true,"slider":null,"value":"1/s","display":"1/s"},{"text":"# Problem 2: Ramp","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Ramp","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Ramp","hidden":false,"hero":true,"slider":null,"value":"1/s^2","display":"1/s^2"},{"text":"# Problem 3: Power t²","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Power t²","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t^2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Power t²","hidden":false,"hero":true,"slider":null,"value":"2/s^3","display":"2/s^3"},{"text":"# Problem 4: Power t³","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Power t³","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t^3 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Power t³","hidden":false,"hero":true,"slider":null,"value":"6/s^4","display":"6/s^4"},{"text":"# Problem 5: Power t⁴","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Power t⁴","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t^4 // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Power t⁴","hidden":false,"hero":true,"slider":null,"value":"24/s^5","display":"24/s^5"},{"text":"# Problem 6: Exponential","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exponential","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace e^t // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exponential","hidden":false,"hero":true,"slider":null,"value":"1/(s-1)","display":"1/(s-1)"},{"text":"# Problem 7: Shifted exponential","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Shifted exponential","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace e^(2*t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Shifted exponential","hidden":false,"hero":true,"slider":null,"value":"1/(s-2)","display":"1/(s-2)"},{"text":"# Problem 8: Sine","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Sine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace sin(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Sine","hidden":false,"hero":true,"slider":null,"value":"1/(s^2+1)","display":"1/(s^2+1)"},{"text":"# Problem 9: Sine with frequency","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Sine with frequency","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace sin(2*t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Sine with frequency","hidden":false,"hero":true,"slider":null,"value":"2/(s^2+4)","display":"2/(s^2+4)"},{"text":"# Problem 10: Cosine","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Cosine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace cos(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Cosine","hidden":false,"hero":true,"slider":null,"value":"s/(s^2+1)","display":"s/(s^2+1)"},{"text":"# Problem 11: Cosine with frequency","label":null,"prefix":null,"suffix":null,"section":"Problem 11: Cosine with frequency","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace cos(3*t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 11: Cosine with frequency","hidden":false,"hero":true,"slider":null,"value":"s/(s^2+9)","display":"s/(s^2+9)"},{"text":"# Problem 12: Hyperbolic sine","label":null,"prefix":null,"suffix":null,"section":"Problem 12: Hyperbolic sine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace sinh(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 12: Hyperbolic sine","hidden":false,"hero":true,"slider":null,"value":"1/(s^2-1)","display":"1/(s^2-1)"},{"text":"# Problem 13: Hyperbolic cosine","label":null,"prefix":null,"suffix":null,"section":"Problem 13: Hyperbolic cosine","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace cosh(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 13: Hyperbolic cosine","hidden":false,"hero":true,"slider":null,"value":"s/(s^2-1)","display":"s/(s^2-1)"},{"text":"# Problem 14: Resonance term","label":null,"prefix":null,"suffix":null,"section":"Problem 14: Resonance term","hero":false,"slider":null,"value":null,"display":null},{"text":"laplace t*sin(t) // @hero","label":null,"prefix":null,"suffix":null,"section":"Problem 14: Resonance term","hidden":false,"hero":true,"slider":null,"value":"2*s/(s^2+1)^2","display":"2*s/(s^2+1)^2"}]},{"id":"exam-diffeq-logistic-growth","title":"Differential Equations — Logistic Growth","description":"The logistic equation dP/dt = rP(1 - P/K) and its variants, solved numerically (RK4) and cross-checked against the closed-form logistic solution. Sourced from Paul's Online Notes and standard population-dynamics finals.","category":"education","icon":"activity","tags":["differential-equations","ode","logistic","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Normalized logistic, late time","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Normalized logistic, late time","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 / (1 + (0.7/0.3) * e^(-5))","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Normalized logistic, late time","hidden":true,"hero":false,"slider":null,"value":0.9845214751227109,"display":"0.9845"},{"text":"# Problem 2: Same logistic, mid-rise","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Same logistic, mid-rise","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 / (1 + (0.7/0.3) * e^(-2))","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Same logistic, mid-rise","hidden":true,"hero":false,"slider":null,"value":0.7600041276283265,"display":"0.76"},{"text":"# Problem 3: Slower growth rate (r = 0.5)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Slower growth rate (r = 0.5)","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 / (1 + (0.9/0.1) * e^(-0.5 * 10))","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Slower growth rate (r = 0.5)","hidden":true,"hero":false,"slider":null,"value":0.9428256185740148,"display":"0.9428"},{"text":"# Problem 4: Carrying capacity K = 100","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carrying capacity K = 100","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 100 / (1 + ((100 - 10)/10) * e^(-0.4 * 10))","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carrying capacity K = 100","hidden":true,"hero":false,"slider":null,"value":85.84864497582139,"display":"85.85"},{"text":"# Problem 5: Starting above capacity","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Starting above capacity","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 50 / (1 + ((50 - 80)/80) * e^(-0.3 * 8))","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Starting above capacity","hidden":true,"hero":false,"slider":null,"value":51.760864896461285,"display":"51.76"},{"text":"# Problem 6: Logistic with harvesting","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Logistic with harvesting","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Extinction below threshold","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Extinction below threshold","hero":false,"slider":null,"value":null,"display":null},{"text":"plot y' = y * (y - 0.2), y(0) = 0.1, y(3) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Extinction below threshold","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-diffeq-second-order","title":"Differential Equations — Second Order ODEs","description":"Second-order linear ODEs (oscillators, damping) solved numerically (RK4) with Instacalc, cross-checked against exact solutions. Provide both y(0) and y'(0). Sourced from MIT 18.03 and Boyce-DiPrima.","category":"education","icon":"activity","tags":["differential-equations","ode","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Simple harmonic oscillator","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Simple harmonic oscillator","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = cos(pi)","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Simple harmonic oscillator","hidden":true,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Problem 2: Faster oscillator (ω = 2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Faster oscillator (ω = 2)","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = cos(2 * pi/2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Faster oscillator (ω = 2)","hidden":true,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Problem 3: Oscillator started with velocity","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Oscillator started with velocity","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = sin(pi/2)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Oscillator started with velocity","hidden":true,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Problem 4: Underdamped oscillator","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Underdamped oscillator","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Critically damped","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Critically damped","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = (1 + 2) * e^(-2)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Critically damped","hidden":true,"hero":false,"slider":null,"value":0.4060058497098381,"display":"0.406"},{"text":"# Problem 6: Overdamped","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Overdamped","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 2 * e^(-2) - e^(-4)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Overdamped","hidden":true,"hero":false,"slider":null,"value":0.25235492758449124,"display":"0.2524"},{"text":"# Problem 7: Exponential-growth ODE","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Exponential-growth ODE","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = e^1","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Exponential-growth ODE","hidden":true,"hero":false,"slider":null,"value":2.718281828459045,"display":"2.718"},{"text":"# Problem 8: Undamped oscillator with constant drive","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Undamped oscillator with constant drive","hero":false,"slider":null,"value":null,"display":null},{"text":"_exact = 1 - cos(pi)","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Undamped oscillator with constant drive","hidden":true,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"plot y'' = -y + 1, y(0) = 0, y'(0) = 0, y(pi) // @formula","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Undamped oscillator with constant drive","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"exam-discrete-math","title":"Discrete Math Final — Logic, Sets, Sums & Recurrence","description":"The CS-math core: counting, finite sums in closed form, set sizes by inclusion–exclusion, and a recurrence — each result computed and cross-checked.","category":"education","icon":"grid","tags":["discrete-math","logic","recurrence","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Sum of the first n integers","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Sum of the first n integers","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 100","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Sum of the first n integers","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"gauss_sum = n*(n + 1) / 2 // @accent @formula @label(sum)","label":"sum","prefix":null,"suffix":null,"section":"Problem 1: Sum of the first n integers","hidden":false,"hero":false,"slider":null,"value":5050,"display":"5,050"},{"text":"# Problem 2: Cross-check the closed form","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Cross-check the closed form","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Sum of squares","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Sum of squares","hero":false,"slider":null,"value":null,"display":null},{"text":"n3 = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Sum of squares","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"sum_squares = n3*(n3 + 1)*(2*n3 + 1) / 6 // @accent @formula @label(formula)","label":"formula","prefix":null,"suffix":null,"section":"Problem 3: Sum of squares","hidden":false,"hero":false,"slider":null,"value":385,"display":"385"},{"text":"# Problem 4: Geometric sum (powers of two)","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Geometric sum (powers of two)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Counting subsets (the power set)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Counting subsets (the power set)","hero":false,"slider":null,"value":null,"display":null},{"text":"2^5 // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Counting subsets (the power set)","hidden":false,"hero":true,"slider":null,"value":32,"display":"32"},{"text":"# Problem 6: Counting subsets of a given size","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Counting subsets of a given size","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Inclusion–exclusion","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hero":false,"slider":null,"value":null,"display":null},{"text":"math_n = 18","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"physics_n = 15","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"both_n = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"at_least_one = math_n + physics_n - both_n // @accent @formula @label(at least one)","label":"at least one","prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"neither = 30 - at_least_one // @accent @formula @label(neither)","label":"neither","prefix":null,"suffix":null,"section":"Problem 7: Inclusion–exclusion","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"# Problem 8: The pigeonhole principle","label":null,"prefix":null,"suffix":null,"section":"Problem 8: The pigeonhole principle","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: A linear recurrence (Fibonacci)","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A linear recurrence (Fibonacci)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 10: Hamming distance (a bit of coding theory)","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Hamming distance (a bit of coding theory)","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-eng-dynamics","title":"Engineering Exam — Dynamics","description":"FE-style exam: kinematics, projectile motion, Newton's second law, work-energy, momentum, and circular motion. Launch angle in degrees — trig defaults to degrees.","category":"engineering","icon":"activity","tags":["engineering","mechanical","dynamics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Uniform acceleration kinematics","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hero":false,"slider":null,"value":null,"display":null},{"text":"acceleration = 3 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"time_s = 8 s","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"final_velocity = acceleration * time_s // @accent @formula @label(Final velocity)","label":"Final velocity","prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"_distance_m = 0.5 * acceleration * time_s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":true,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"_final_velocity_mph = final_velocity * 2.23694","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Uniform acceleration kinematics","hidden":true,"hero":false,"slider":null,"value":53.68656,"display":"53.6866"},{"text":"# Problem 2: Projectile motion","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hero":false,"slider":null,"value":null,"display":null},{"text":"launch_speed = 40 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"launch_angle = 35 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"g = 9.81 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"_vx = launch_speed * cos(launch_angle)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":32.766081771559676,"display":"32.7661"},{"text":"_vy = launch_speed * sin(launch_angle)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":22.94305745404184,"display":"22.9431"},{"text":"_time_of_flight = (2 * _vy) / g","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":4.6774836807424744,"display":"4.6775"},{"text":"range_m = _vx * _time_of_flight // @accent @formula @label(Range)","label":"Range","prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":false,"hero":false,"slider":null,"value":153.26281276834385,"display":"153.2628"},{"text":"_max_height_m = _vy^2 / (2 * g)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Projectile motion","hidden":true,"hero":false,"slider":null,"value":26.828944206904424,"display":"26.8289"},{"text":"# Problem 3: Newton's second law","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hero":false,"slider":null,"value":null,"display":null},{"text":"net_force_n = 120 N","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"mass_kg = 15 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"accel_ms2 = net_force_n / mass_kg in m/s^2 // @accent @formula @label(Acceleration)","label":"Acceleration","prefix":null,"suffix":null,"section":"Problem 3: Newton's second law","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Problem 4: Work–energy theorem","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hero":false,"slider":null,"value":null,"display":null},{"text":"car_mass = 1200 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"v_initial = 25 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"v_final = 10 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"_kinetic_initial_j = 0.5 * car_mass * v_initial^2","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":true,"hero":false,"slider":null,"value":375000,"display":"375,000"},{"text":"_kinetic_final_j = 0.5 * car_mass * v_final^2","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":true,"hero":false,"slider":null,"value":60000,"display":"60,000"},{"text":"work_done_j = _kinetic_final_j - _kinetic_initial_j // @accent @formula @label(Brake work)","label":"Brake work","prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":false,"hero":false,"slider":null,"value":-315000,"display":"-315,000"},{"text":"_work_done_kj = work_done_j / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Work–energy theorem","hidden":true,"hero":false,"slider":null,"value":-315,"display":"-315"},{"text":"# Problem 5: Conservation of momentum","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hero":false,"slider":null,"value":null,"display":null},{"text":"truck_mass = 2000 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"truck_v = 15 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"car_mass_p = 1000 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"common_velocity = (truck_mass * truck_v) / (truck_mass + car_mass_p) // @accent @formula @label(Common velocity)","label":"Common velocity","prefix":null,"suffix":null,"section":"Problem 5: Conservation of momentum","hidden":false,"hero":false,"slider":null,"value":9.999999999999998,"display":"10"},{"text":"# Problem 6: Centripetal acceleration and force","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hero":false,"slider":null,"value":null,"display":null},{"text":"speed_circ = 12 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"radius_m = 30 m","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"mass_circ = 5 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"centripetal_accel = speed_circ^2 / radius_m // @accent @formula @label(Centripetal a)","label":"Centripetal a","prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":false,"hero":false,"slider":null,"value":4.800000000000002,"display":"4.8"},{"text":"_centripetal_force_n = mass_circ * centripetal_accel","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Centripetal acceleration and force","hidden":true,"hero":false,"slider":null,"value":24.000000000000007,"display":"24"},{"text":"# Problem 7: Free-fall height from impact speed","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Free-fall height from impact speed","hero":false,"slider":null,"value":null,"display":null},{"text":"impact_speed = 20 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Free-fall height from impact speed","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"fall_height_m = impact_speed^2 / (2 * g) // @accent @formula @label(Fall height)","label":"Fall height","prefix":null,"suffix":null,"section":"Problem 7: Free-fall height from impact speed","hidden":false,"hero":true,"slider":null,"value":20.38735983690112,"display":"20.3874"}]},{"id":"exam-eng-ee-circuits","title":"Engineering Exam — DC & AC Circuits","description":"FE-style exam: Ohm's law, power, Kirchhoff, series/parallel, RC time constant, and RLC impedance.","category":"engineering","icon":"zap","tags":["engineering","electrical","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Current and power across a resistor","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage = 12 V","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"resistance = 4 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"current_amps = voltage / resistance // @accent @formula @label(Current)","label":"Current","prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_power_watts = voltage * current_amps","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Current and power across a resistor","hidden":true,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"# Problem 2: Three resistors in series","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hero":false,"slider":null,"value":null,"display":null},{"text":"r1 = 220 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":220,"display":"220"},{"text":"r2 = 330 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":330,"display":"330"},{"text":"r3 = 470 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":470,"display":"470"},{"text":"source_v = 9 V","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"r_series = r1 + r2 + r3 // @accent @formula @label(Total R)","label":"Total R","prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":false,"hero":false,"slider":null,"value":1020,"display":"1,020"},{"text":"_series_current_ma = (source_v / r_series) * 1000 // mA","label":null,"prefix":null,"suffix":"mA","section":"Problem 2: Three resistors in series","hidden":true,"hero":false,"slider":null,"value":8.823529411764707,"display":"8.8235"},{"text":"_v_across_r2 = (source_v / r_series) * r2","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Three resistors in series","hidden":true,"hero":false,"slider":null,"value":2.9117647058823533,"display":"2.9118"},{"text":"# Problem 3: Two resistors in parallel","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hero":false,"slider":null,"value":null,"display":null},{"text":"ra = 100 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"rb = 150 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"r_parallel = (ra * rb) / (ra + rb) // @accent @formula @label(Parallel R)","label":"Parallel R","prefix":null,"suffix":null,"section":"Problem 3: Two resistors in parallel","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"# Problem 4: Kirchhoff's current law at a node","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hero":false,"slider":null,"value":null,"display":null},{"text":"i_in_1 = 5 A","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"i_in_2 = 3 A","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"i_out_known = 2.5 A","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"i_out_remaining = i_in_1 + i_in_2 - i_out_known // @accent @formula @label(Branch I)","label":"Branch I","prefix":null,"suffix":null,"section":"Problem 4: Kirchhoff's current law at a node","hidden":false,"hero":false,"slider":null,"value":5.5,"display":"5.5"},{"text":"# Problem 5: RC charging circuit","label":null,"prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hero":false,"slider":null,"value":null,"display":null},{"text":"r_ohms = 10000 // ohms (typed ohm*F gives no \"second\" label; kept as note)","label":null,"prefix":null,"suffix":"ohms (typed ohm*F gives no \"second\" label; kept as note)","section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"c_farads = 0.0001 // F (100 uF)","label":null,"prefix":null,"suffix":"F (100 uF)","section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":0.0001,"display":"0.0001"},{"text":"v_step = 5 V","label":null,"prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"tau_seconds = r_ohms * c_farads // @accent @formula @label(Time const)","label":"Time const","prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"_v_after_one_tau = v_step * (1 - exp(-1))","label":null,"prefix":null,"suffix":null,"section":"Problem 5: RC charging circuit","hidden":true,"hero":false,"slider":null,"value":3.1606027941427883,"display":"3.1606"},{"text":"# Problem 6: Series RLC impedance and phase","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Series RLC impedance and phase","hero":false,"slider":null,"value":null,"display":null},{"text":"res_ohms = 100 // ohms","label":null,"prefix":null,"suffix":"ohms","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"inductance_h = 0.1 // H","label":null,"prefix":null,"suffix":"H","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"capacitance_f = 0.00001 // F (10 uF)","label":null,"prefix":null,"suffix":"F (10 uF)","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":0.00001,"display":"0.00001"},{"text":"freq_hz = 60 // Hz","label":null,"prefix":null,"suffix":"Hz","section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"_omega = 2 * pi * freq_hz // rad/s","label":null,"prefix":null,"suffix":"rad/s","section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":376.99111843077515,"display":"376.99"},{"text":"_x_l = _omega * inductance_h // inductive reactance","label":null,"prefix":null,"suffix":"inductive reactance","section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":37.69911184307751,"display":"37.7"},{"text":"_x_c = 1 / (_omega * capacitance_f) // capacitive reactance","label":null,"prefix":null,"suffix":"capacitive reactance","section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":265.2582384864923,"display":"265.26"},{"text":"impedance_ohms = sqrt(res_ohms^2 + (_x_l - _x_c)^2) // @accent @formula @label(Impedance)","label":"Impedance","prefix":null,"suffix":null,"section":"Problem 6: Series RLC impedance and phase","hidden":false,"hero":false,"slider":null,"value":248.5621775707513,"display":"248.56"},{"text":"_phase_angle_deg = atan((_x_l - _x_c) / res_ohms)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Series RLC impedance and phase","hidden":true,"hero":false,"slider":null,"value":-66.27709333961397,"display":"-66.2771"},{"text":"# Problem 7: AC real power with a power factor","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hero":false,"slider":null,"value":null,"display":null},{"text":"v_rms = 120 V","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"i_rms = 5 A","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"power_factor = 0.8","label":null,"prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"real_power_w = v_rms * i_rms * power_factor // @accent @formula @label(Real power)","label":"Real power","prefix":null,"suffix":null,"section":"Problem 7: AC real power with a power factor","hidden":false,"hero":true,"slider":null,"value":480,"display":"480"},{"text":"_real_power_kw = real_power_w / 1000 // kW","label":null,"prefix":null,"suffix":"kW","section":"Problem 7: AC real power with a power factor","hidden":true,"hero":false,"slider":null,"value":0.48,"display":"0.48"}]},{"id":"exam-eng-fluids","title":"Engineering Exam — Fluid Mechanics","description":"FE-style exam: continuity, Bernoulli, Reynolds number, hydrostatic pressure, flow rate, and head loss. Heavy on unit conversions (gpm, psi, m/s).","category":"engineering","icon":"wind","tags":["engineering","civil","fluids","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Volumetric flow rate from continuity","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hero":false,"slider":null,"value":null,"display":null},{"text":"diameter_m = 0.1 m","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"velocity_ms = 3 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_area_m2 = pi * (diameter_m / 2)^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":true,"hero":false,"slider":null,"value":0.007853981633974483,"display":"0.007854"},{"text":"flow_rate_m3s = _area_m2 * velocity_ms // @accent @formula @label(Flow rate)","label":"Flow rate","prefix":null,"suffix":null,"section":"Problem 1: Volumetric flow rate from continuity","hidden":false,"hero":false,"slider":null,"value":0.023561944901923447,"display":"0.0236"},{"text":"_flow_rate_gpm = (flow_rate_m3s) * 15850.3 // convert m^3/s to gpm","label":null,"prefix":null,"suffix":"convert","section":"Problem 1: Volumetric flow rate from continuity","hidden":true,"hero":false,"slider":null,"value":373.4638952789572,"display":"373.4639"},{"text":"# Problem 2: Velocity through a contraction","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Velocity through a contraction","hero":false,"slider":null,"value":null,"display":null},{"text":"diameter2_m = 0.05 m","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Velocity through a contraction","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"_area2_m2 = pi * (diameter2_m / 2)^2 // m^2","label":null,"prefix":null,"suffix":"m^2","section":"Problem 2: Velocity through a contraction","hidden":true,"hero":false,"slider":null,"value":0.001963495408493621,"display":"0.001963"},{"text":"velocity2_ms = flow_rate_m3s / _area2_m2 // @accent @formula @label(New velocity)","label":"New velocity","prefix":null,"suffix":null,"section":"Problem 2: Velocity through a contraction","hidden":false,"hero":false,"slider":null,"value":11.999999999999998,"display":"12"},{"text":"# Problem 3: Pressure drop from Bernoulli","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hero":false,"slider":null,"value":null,"display":null},{"text":"rho = 1000 kg/m^3","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"v_in = 2 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"v_out = 8 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"pressure_drop_pa = 0.5 * rho * (v_out^2 - v_in^2) // @accent @formula @label(Pressure drop)","label":"Pressure drop","prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":false,"hero":false,"slider":null,"value":30000,"display":"30,000"},{"text":"_pressure_drop_kpa = pressure_drop_pa / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":true,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"_pressure_drop_psi = (pressure_drop_pa) * 0.000145038","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Pressure drop from Bernoulli","hidden":true,"hero":false,"slider":null,"value":4.35114,"display":"4.3511"},{"text":"# Problem 4: Reynolds number and flow regime","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hero":false,"slider":null,"value":null,"display":null},{"text":"flow_velocity = 2 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"pipe_d = 0.05 m","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"kinematic_visc = 0.000001 m^2/s","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":0.000001,"display":"0.000001"},{"text":"reynolds_number = (flow_velocity * pipe_d) / kinematic_visc // @accent @formula @label(Reynolds)","label":"Reynolds","prefix":null,"suffix":null,"section":"Problem 4: Reynolds number and flow regime","hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"# Problem 5: Hydrostatic gauge pressure","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hero":false,"slider":null,"value":null,"display":null},{"text":"depth_m = 12 m","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"water_density = 1000 kg/m^3","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"g = 9.81 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"gauge_pressure_pa = water_density * g * depth_m // @accent @formula @label(Gauge p)","label":"Gauge p","prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":false,"hero":false,"slider":null,"value":117720,"display":"117,720"},{"text":"_gauge_pressure_kpa = gauge_pressure_pa / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Hydrostatic gauge pressure","hidden":true,"hero":false,"slider":null,"value":117.72,"display":"117.72"},{"text":"_absolute_pressure_kpa = _gauge_pressure_kpa + 101.325 // add 1 atm","label":null,"prefix":null,"suffix":"add 1 atm","section":"Problem 5: Hydrostatic gauge pressure","hidden":true,"hero":false,"slider":null,"value":219.045,"display":"219.045"},{"text":"# Problem 6: Exit velocity by Torricelli","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exit velocity by Torricelli","hero":false,"slider":null,"value":null,"display":null},{"text":"head_m = 5 m","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Exit velocity by Torricelli","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"exit_velocity_ms = sqrt(2 * g * head_m) // @accent @formula @label(Exit speed)","label":"Exit speed","prefix":null,"suffix":null,"section":"Problem 6: Exit velocity by Torricelli","hidden":false,"hero":false,"slider":null,"value":9.904544411531507,"display":"9.9045"},{"text":"# Problem 7: Head loss by Darcy–Weisbach","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hero":false,"slider":null,"value":null,"display":null},{"text":"friction_factor = 0.02","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":0.02,"display":"0.02"},{"text":"pipe_length_m = 100 m","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"pipe_diameter_m = 0.1 m","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"darcy_velocity = 3 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"head_loss_m = friction_factor * (pipe_length_m / pipe_diameter_m) * (darcy_velocity^2 / (2 * g)) // @accent @formula @label(Head loss)","label":"Head loss","prefix":null,"suffix":null,"section":"Problem 7: Head loss by Darcy–Weisbach","hidden":false,"hero":true,"slider":null,"value":9.174311926605505,"display":"9.1743"}]},{"id":"exam-eng-mechanics-materials","title":"Engineering Exam — Mechanics of Materials","description":"FE-style exam: axial stress/strain, Young's modulus, thermal stress, beam bending, deflection, and torsion. Stress in MPa with psi conversions.","category":"engineering","icon":"tool","tags":["engineering","mechanical","materials","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Axial normal stress","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Axial normal stress","hero":false,"slider":null,"value":null,"display":null},{"text":"load_n = 25000 N // (25 kN)","label":null,"prefix":null,"suffix":"(25 kN)","section":"Problem 1: Axial normal stress","hidden":false,"hero":false,"slider":null,"value":25000,"display":"25,000"},{"text":"area_mm2 = 200 mm^2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Axial normal stress","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"stress_mpa = load_n / area_mm2 in MPa // @accent @formula @label(Stress)","label":"Stress","prefix":null,"suffix":null,"section":"Problem 1: Axial normal stress","hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"_stress_psi = (stress_mpa * 1000000) * 0.000145038 // convert MPa to psi","label":null,"prefix":null,"suffix":"convert","section":"Problem 1: Axial normal stress","hidden":true,"hero":false,"slider":null,"value":18129.75,"display":"18,129.75"},{"text":"# Problem 2: Strain and elongation","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hero":false,"slider":null,"value":null,"display":null},{"text":"length_mm = 1500 mm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"youngs_modulus_mpa = 200000 MPa // (200 GPa)","label":null,"prefix":null,"suffix":"(200 GPa)","section":"Problem 2: Strain and elongation","hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"strain = stress_mpa / youngs_modulus_mpa // @accent @formula @label(Strain)","label":"Strain","prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hidden":false,"hero":false,"slider":null,"value":0.000625,"display":"0.000625"},{"text":"_elongation_mm = strain * length_mm","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Strain and elongation","hidden":true,"hero":false,"slider":null,"value":0.9375,"display":"0.9375"},{"text":"# Problem 3: Thermal stress in a restrained bar","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hero":false,"slider":null,"value":null,"display":null},{"text":"alpha = 0.000012 /kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":0.000012,"display":"0.000012"},{"text":"e_modulus_mpa = 200000 MPa","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"temp_rise = 60 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"thermal_stress_mpa = e_modulus_mpa * alpha * temp_rise // @accent @formula @label(Thermal stress)","label":"Thermal stress","prefix":null,"suffix":null,"section":"Problem 3: Thermal stress in a restrained bar","hidden":false,"hero":false,"slider":null,"value":144,"display":"144"},{"text":"# Problem 4: Bending stress in a beam","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Bending stress in a beam","hero":false,"slider":null,"value":null,"display":null},{"text":"moment_nmm = 5000000 // N*mm (5000 N*m)","label":null,"prefix":null,"suffix":"N*mm (5000 N*m)","section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":5000000,"display":"5,000,000"},{"text":"b_mm = 50 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"h_mm = 100 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"_moment_of_inertia = (b_mm * h_mm^3) / 12 // mm^4","label":null,"prefix":null,"suffix":"mm^4","section":"Problem 4: Bending stress in a beam","hidden":true,"hero":false,"slider":null,"value":4166666.6666666665,"display":"4,166,666.67"},{"text":"_c_mm = h_mm / 2 // distance to extreme fiber; 50 mm","label":null,"prefix":null,"suffix":"distance to extreme fiber; 50 mm","section":"Problem 4: Bending stress in a beam","hidden":true,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"bending_stress_mpa = (moment_nmm * _c_mm) / _moment_of_inertia // @accent @formula @label(Bending stress)","label":"Bending stress","prefix":null,"suffix":null,"section":"Problem 4: Bending stress in a beam","hidden":false,"hero":false,"slider":null,"value":60.00000000000001,"display":"60"},{"text":"# Problem 5: Maximum deflection of a beam","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Maximum deflection of a beam","hero":false,"slider":null,"value":null,"display":null},{"text":"p_load_n = 10000 // N","label":null,"prefix":null,"suffix":"N","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"span_mm = 3000 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"e_beam_mpa = 200000 // MPa","label":null,"prefix":null,"suffix":"MPa","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"inertia_mm4 = 4166667 // mm^4","label":null,"prefix":null,"suffix":"mm^4","section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":4166667,"display":"4,166,667"},{"text":"max_deflection_mm = (p_load_n * span_mm^3) / (48 * e_beam_mpa * inertia_mm4) // @accent @formula @label(Deflection)","label":"Deflection","prefix":null,"suffix":null,"section":"Problem 5: Maximum deflection of a beam","hidden":false,"hero":false,"slider":null,"value":6.749999460000043,"display":"6.75"},{"text":"# Problem 6: Torsional shear stress","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Torsional shear stress","hero":false,"slider":null,"value":null,"display":null},{"text":"torque_nmm = 800000 // N*mm (800 N*m)","label":null,"prefix":null,"suffix":"N*mm (800 N*m)","section":"Problem 6: Torsional shear stress","hidden":false,"hero":false,"slider":null,"value":800000,"display":"800,000"},{"text":"shaft_d_mm = 40 // mm","label":null,"prefix":null,"suffix":"mm","section":"Problem 6: Torsional shear stress","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"max_shear_stress_mpa = (16 * torque_nmm) / (pi * shaft_d_mm^3) // @accent @formula @label(Shear stress)","label":"Shear stress","prefix":null,"suffix":null,"section":"Problem 6: Torsional shear stress","hidden":false,"hero":false,"slider":null,"value":63.66197723675813,"display":"63.66"},{"text":"# Problem 7: Factor of safety","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hero":false,"slider":null,"value":null,"display":null},{"text":"yield_strength_mpa = 250 MPa","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"working_stress_mpa = 125 MPa","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"factor_of_safety = yield_strength_mpa / working_stress_mpa // @accent @formula @label(Safety factor)","label":"Safety factor","prefix":null,"suffix":null,"section":"Problem 7: Factor of safety","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"exam-eng-statics","title":"Engineering Exam — Statics","description":"FE-style exam: force resolution, resultants, moments, equilibrium, truss joints, and friction. Vectors done component-wise (no cross/dot in engine). Angles in degrees — trig defaults to degrees.","category":"engineering","icon":"move","tags":["engineering","mechanical","statics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Resolving a force into components","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hero":false,"slider":null,"value":null,"display":null},{"text":"force_n = 500 N","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"angle_deg = 35 // degrees from horizontal","label":null,"prefix":null,"suffix":"degrees from horizontal","section":"Problem 1: Resolving a force into components","hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"fx = force_n * cos(angle_deg) // @accent @formula @label(Fx)","label":"Fx","prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hidden":false,"hero":false,"slider":null,"value":409.57602214449594,"display":"409.576"},{"text":"_fy = force_n * sin(angle_deg)","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Resolving a force into components","hidden":true,"hero":false,"slider":null,"value":286.788218175523,"display":"286.7882"},{"text":"# Problem 2: Resultant of two concurrent forces","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hero":false,"slider":null,"value":null,"display":null},{"text":"f1 = 300 N","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"a1 = 20 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"f2 = 400 N","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"a2 = 110 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":110,"display":"110"},{"text":"_sum_x = f1 * cos(a1) + f2 * cos(a2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":true,"hero":false,"slider":null,"value":145.09972890550503,"display":"145.0997"},{"text":"_sum_y = f1 * sin(a1) + f2 * sin(a2)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":true,"hero":false,"slider":null,"value":478.48309131206395,"display":"478.4831"},{"text":"resultant_n = sqrt(_sum_x^2 + _sum_y^2) // @accent @formula @label(Resultant)","label":"Resultant","prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":false,"hero":false,"slider":null,"value":499.99999999999994,"display":"500"},{"text":"_resultant_dir_deg = atan2(_sum_y, _sum_x)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Resultant of two concurrent forces","hidden":true,"hero":false,"slider":null,"value":73.13010235415598,"display":"73.1301"},{"text":"# Problem 3: Moment of a force about a point","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hero":false,"slider":null,"value":null,"display":null},{"text":"load_n = 250 N","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"lever_arm_m = 0.4 m","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"moment_nm = load_n * lever_arm_m in N*m // @accent @formula @label(Moment)","label":"Moment","prefix":null,"suffix":null,"section":"Problem 3: Moment of a force about a point","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"# Problem 4: Beam reactions by equilibrium","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hero":false,"slider":null,"value":null,"display":null},{"text":"beam_len = 6 m","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"point_load = 800 N","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":800,"display":"800"},{"text":"load_pos = 2 m // from A","label":null,"prefix":null,"suffix":"from A","section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"_reaction_b = (point_load * load_pos) / beam_len // moment about A","label":null,"prefix":null,"suffix":"moment about A","section":"Problem 4: Beam reactions by equilibrium","hidden":true,"hero":false,"slider":null,"value":266.66666666666663,"display":"266.6667"},{"text":"reaction_a = point_load - _reaction_b // @accent @formula @label(Reaction A)","label":"Reaction A","prefix":null,"suffix":null,"section":"Problem 4: Beam reactions by equilibrium","hidden":false,"hero":false,"slider":null,"value":533.3333333333334,"display":"533.3333"},{"text":"# Problem 5: Truss joint by method of joints","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Truss joint by method of joints","hero":false,"slider":null,"value":null,"display":null},{"text":"horizontal_member_n = 600 N // (+x)","label":null,"prefix":null,"suffix":"(+x)","section":"Problem 5: Truss joint by method of joints","hidden":false,"hero":false,"slider":null,"value":600,"display":"600"},{"text":"diagonal_angle_deg = 40 // deg from horizontal","label":null,"prefix":null,"suffix":"deg from horizontal","section":"Problem 5: Truss joint by method of joints","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"diagonal_force_n = horizontal_member_n / cos(diagonal_angle_deg) // @accent @formula @label(Diagonal)","label":"Diagonal","prefix":null,"suffix":null,"section":"Problem 5: Truss joint by method of joints","hidden":false,"hero":false,"slider":null,"value":783.2443735993671,"display":"783.2444"},{"text":"_diagonal_vertical_comp = diagonal_force_n * sin(diagonal_angle_deg)","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Truss joint by method of joints","hidden":true,"hero":false,"slider":null,"value":503.459778706368,"display":"503.4598"},{"text":"# Problem 6: Block on a frictionless incline","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_kg = 200 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"ramp_deg = 25 // deg","label":null,"prefix":null,"suffix":"deg","section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"gravity = 9.81 m/s^2","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"_weight_n = mass_kg * gravity","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":true,"hero":false,"slider":null,"value":1962,"display":"1,962"},{"text":"holding_force_n = _weight_n * sin(ramp_deg) // @accent @formula @label(Hold force)","label":"Hold force","prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":829.1770295352524,"display":"829.177"},{"text":"_normal_force_n = _weight_n * cos(ramp_deg)","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Block on a frictionless incline","hidden":true,"hero":false,"slider":null,"value":1778.1758781659073,"display":"1,778.1759"},{"text":"# Problem 7: Maximum static friction","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hero":false,"slider":null,"value":null,"display":null},{"text":"block_weight_n = 400 N","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"mu_s = 0.35","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hidden":false,"hero":false,"slider":null,"value":0.35,"display":"0.35"},{"text":"max_static_friction_n = mu_s * block_weight_n // @accent @formula @label(Max friction)","label":"Max friction","prefix":null,"suffix":null,"section":"Problem 7: Maximum static friction","hidden":false,"hero":true,"slider":null,"value":140,"display":"140"}]},{"id":"exam-eng-thermo","title":"Engineering Exam — Thermodynamics & Heat Transfer","description":"FE-style exam: ideal gas law, sensible heat, conduction, Carnot efficiency, thermal expansion, and heat-engine work. Temperature unit conversions throughout.","category":"engineering","icon":"thermometer","tags":["engineering","mechanical","thermodynamics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Ideal gas pressure","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hero":false,"slider":null,"value":null,"display":null},{"text":"moles = 2 mol","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"temp_k = 300 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"volume_m3 = 0.05 m^3","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"r_gas = 8.314 J/(mol*kelvin)","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":8.314,"display":"8.314"},{"text":"pressure_pa = (moles * r_gas * temp_k) / volume_m3 in Pa // @accent @formula @label(Pressure)","label":"Pressure","prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":false,"hero":false,"slider":null,"value":99768,"display":"99,768"},{"text":"_pressure_kpa = pressure_pa / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":true,"hero":false,"slider":null,"value":99.768,"display":"99.768"},{"text":"_pressure_atm = _pressure_kpa / 101.325","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Ideal gas pressure","hidden":true,"hero":false,"slider":null,"value":0.9846336047372316,"display":"0.9846"},{"text":"# Problem 2: Sensible heat to warm water","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_water = 5 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"delta_t = (80 - 20) kelvin // same magnitude as deg C","label":null,"prefix":null,"suffix":"same magnitude as deg C","section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"specific_heat = 4186 J/(kg*kelvin)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":4186,"display":"4,186"},{"text":"heat_energy_j = mass_water * specific_heat * delta_t // @accent @formula @label(Heat)","label":"Heat","prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":false,"hero":false,"slider":null,"value":1255800,"display":"1,255,800"},{"text":"_heat_energy_kj = heat_energy_j / 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Sensible heat to warm water","hidden":true,"hero":false,"slider":null,"value":1255.8,"display":"1,255.8"},{"text":"# Problem 3: Steady conduction through a wall","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hero":false,"slider":null,"value":null,"display":null},{"text":"wall_area = 10 m^2","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"k_conduct = 0.8 W/(m*kelvin)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"thickness_m = 0.2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"temp_diff_k = 25 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"heat_rate_w = (k_conduct * wall_area * temp_diff_k) / thickness_m // @accent @formula @label(Heat rate)","label":"Heat rate","prefix":null,"suffix":null,"section":"Problem 3: Steady conduction through a wall","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"# Problem 4: Carnot efficiency","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hero":false,"slider":null,"value":null,"display":null},{"text":"t_hot = 500 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"t_cold = 300 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"carnot_efficiency = 1 - (t_cold / t_hot) // @accent @formula @label(Efficiency)","label":"Efficiency","prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"_carnot_efficiency_pct = carnot_efficiency * 100","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Carnot efficiency","hidden":true,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"# Problem 5: Heat-engine work and rejected heat","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hero":false,"slider":null,"value":null,"display":null},{"text":"heat_in_kj = 800 kJ","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":false,"hero":false,"slider":null,"value":800,"display":"800"},{"text":"efficiency = 0.4","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"work_out_kj = heat_in_kj * efficiency // @accent @formula @label(Work out)","label":"Work out","prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":false,"hero":false,"slider":null,"value":320,"display":"320"},{"text":"_heat_rejected_kj = heat_in_kj - work_out_kj","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Heat-engine work and rejected heat","hidden":true,"hero":false,"slider":null,"value":480,"display":"480"},{"text":"# Problem 6: Linear thermal expansion","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hero":false,"slider":null,"value":null,"display":null},{"text":"rod_length_m = 2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"alpha = 0.000012 /kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":0.000012,"display":"0.000012"},{"text":"temp_rise_k = 150 kelvin","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"delta_length_m = rod_length_m * alpha * temp_rise_k // @accent @formula @label(Expansion)","label":"Expansion","prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":false,"hero":false,"slider":null,"value":0.0036,"display":"0.0036"},{"text":"_delta_length_mm = delta_length_m * 1000","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Linear thermal expansion","hidden":true,"hero":false,"slider":null,"value":3.6,"display":"3.6"},{"text":"# Problem 7: Temperature unit conversion","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Temperature unit conversion","hero":false,"slider":null,"value":null,"display":null},{"text":"setpoint_c = 72 degF in degC // @accent @label(Setpoint C)","label":"Setpoint C","prefix":null,"suffix":null,"section":"Problem 7: Temperature unit conversion","hidden":false,"hero":true,"slider":null,"value":22.22222222222222,"display":"22.2222"},{"text":"_setpoint_k = 72 degF in K","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Temperature unit conversion","hidden":true,"hero":false,"slider":null,"value":295.3722222222222,"display":"295.3722"}]},{"id":"exam-geometry","title":"Geometry Final — Area, Volume & the Pythagorean Theorem","description":"Plane and solid geometry worked from the governing formula to the number — areas, volumes, the Pythagorean theorem, and coordinate distance.","category":"education","icon":"triangle","tags":["geometry","area","volume","pythagorean","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Area and circumference of a circle","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hero":false,"slider":null,"value":null,"display":null},{"text":"r = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"area_circle = pi * r^2 // @accent @formula @label(area)","label":"area","prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hidden":false,"hero":false,"slider":null,"value":78.53981633974483,"display":"78.54"},{"text":"circumference = 2 * pi * r // @accent @formula @label(circumference)","label":"circumference","prefix":null,"suffix":null,"section":"Problem 1: Area and circumference of a circle","hidden":false,"hero":false,"slider":null,"value":31.415926535897928,"display":"31.42"},{"text":"# Problem 2: The Pythagorean theorem","label":null,"prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hero":false,"slider":null,"value":null,"display":null},{"text":"leg_a = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"leg_b = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"hypotenuse = hypot(leg_a, leg_b) // @hero @accent @formula @label(hypotenuse)","label":"hypotenuse","prefix":null,"suffix":null,"section":"Problem 2: The Pythagorean theorem","hidden":false,"hero":true,"slider":null,"value":10,"display":"10"},{"text":"# Problem 3: Area of a triangle (Heron's formula)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hero":false,"slider":null,"value":null,"display":null},{"text":"sa = 7","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"sb = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"sc = 9","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"s = (sa + sb + sc) / 2 // @formula @label(semi-perimeter)","label":"semi-perimeter","prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"area_triangle = sqrt(s*(s - sa)*(s - sb)*(s - sc)) // @accent @formula @label(area)","label":"area","prefix":null,"suffix":null,"section":"Problem 3: Area of a triangle (Heron's formula)","hidden":false,"hero":false,"slider":null,"value":26.832815729997478,"display":"26.83"},{"text":"# Problem 4: Volume of a cylinder","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hero":false,"slider":null,"value":null,"display":null},{"text":"r_cyl = 3","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"h_cyl = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"vol_cylinder = pi * r_cyl^2 * h_cyl // @accent @formula @label(volume)","label":"volume","prefix":null,"suffix":null,"section":"Problem 4: Volume of a cylinder","hidden":false,"hero":false,"slider":null,"value":282.74333882308133,"display":"282.74"},{"text":"# Problem 5: Volume and surface area of a sphere","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hero":false,"slider":null,"value":null,"display":null},{"text":"r_sph = 4","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"vol_sphere = (4/3) * pi * r_sph^3 // @accent @formula @label(volume)","label":"volume","prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hidden":false,"hero":false,"slider":null,"value":268.082573106329,"display":"268.08"},{"text":"surf_sphere = 4 * pi * r_sph^2 // @accent @formula @label(surface area)","label":"surface area","prefix":null,"suffix":null,"section":"Problem 5: Volume and surface area of a sphere","hidden":false,"hero":false,"slider":null,"value":201.06192982974676,"display":"201.06"},{"text":"# Problem 6: Interior angles of a polygon","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Interior angles of a polygon","hero":false,"slider":null,"value":null,"display":null},{"text":"n_sides = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Interior angles of a polygon","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"interior_angle = (n_sides - 2) * 180 / n_sides // @accent @formula @label(angle °)","label":"angle °","prefix":null,"suffix":null,"section":"Problem 6: Interior angles of a polygon","hidden":false,"hero":false,"slider":null,"value":135,"display":"135"},{"text":"# Problem 7: Coordinate distance and midpoint","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hero":false,"slider":null,"value":null,"display":null},{"text":"dist_pts = hypot(8 - 2, 11 - 3) // @accent @formula @label(distance)","label":"distance","prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"mid_x = (2 + 8) / 2 // @formula @label($x_m$)","label":"$x_m$","prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"mid_y = (3 + 11) / 2 // @formula @label($y_m$)","label":"$y_m$","prefix":null,"suffix":null,"section":"Problem 7: Coordinate distance and midpoint","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"# Problem 8: A missing side by the Law of Cosines","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hero":false,"slider":null,"value":null,"display":null},{"text":"la = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"lb = 7","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"angle_C = 60","label":null,"prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"c_side = sqrt(la^2 + lb^2 - 2*la*lb*cos(angle_C deg)) // @accent @formula @label(c)","label":"c","prefix":null,"suffix":null,"section":"Problem 8: A missing side by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":6.244997998414912,"display":"6.245"},{"text":"# Problem 9: A missing angle by the Law of Cosines","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A missing angle by the Law of Cosines","hero":false,"slider":null,"value":null,"display":null},{"text":"angle_opposite = acos((3^2 + 4^2 - 6^2) / (2*3*4)) deg // @accent @formula @label(angle °)","label":"angle °","prefix":null,"suffix":null,"section":"Problem 9: A missing angle by the Law of Cosines","hidden":false,"hero":false,"slider":null,"value":117.279612736,"display":"117.2796"},{"text":"# Problem 10: Arc length and sector area","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hero":false,"slider":null,"value":null,"display":null},{"text":"r_arc = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"arc_length = (90/360) * 2 * pi * r_arc // @accent @formula @label(arc length)","label":"arc length","prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hidden":false,"hero":false,"slider":null,"value":15.707963267948964,"display":"15.71"},{"text":"sector_area = (90/360) * pi * r_arc^2 // @accent @formula @label(sector area)","label":"sector area","prefix":null,"suffix":null,"section":"Problem 10: Arc length and sector area","hidden":false,"hero":false,"slider":null,"value":78.53981633974483,"display":"78.54"}]},{"id":"exam-linalg-systems","title":"Linear Algebra — Systems","description":"Strang 18.06-style: 2×2 and 3×3 linear systems via determinants and Cramer's rule, every cofactor spelled out by formula.","category":"education","icon":"grid","tags":["linear-algebra","systems","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: A single linear equation","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single linear equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: A quadratic with two roots","label":null,"prefix":null,"suffix":null,"section":"Problem 2: A quadratic with two roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: A 2×2 determinant","label":null,"prefix":null,"suffix":null,"section":"Problem 3: A 2×2 determinant","hero":false,"slider":null,"value":null,"display":null},{"text":"# Matrix entries (row-major) @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hero":false,"slider":null,"value":null,"display":null},{"text":"a11 = 2","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"a12 = 1","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"a21 = 3","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"a22 = 4","label":null,"prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"det_2x2 = a11*a22 - a12*a21 // @accent @formula @label(det)","label":"det","prefix":null,"suffix":null,"section":"Matrix entries (row-major)","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"# Problem 4: A 2×2 system by Cramer's rule","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hero":false,"slider":null,"value":null,"display":null},{"text":"b1 = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"b2 = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"_det_main = a11*a22 - a12*a21","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"_det_x = b1*a22 - a12*b2","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":true,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"_det_y = a11*b2 - b1*a21","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"x_sol = _det_x / _det_main // @accent @formula @label(x)","label":"x","prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":2.8,"display":"2.8"},{"text":"y_sol = _det_y / _det_main // @accent @formula @label(y)","label":"y","prefix":null,"suffix":null,"section":"Problem 4: A 2×2 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":-0.6,"display":"-0.6"},{"text":"# Problem 5: A 3×3 determinant by cofactor expansion","label":null,"prefix":null,"suffix":null,"section":"Problem 5: A 3×3 determinant by cofactor expansion","hero":false,"slider":null,"value":null,"display":null},{"text":"# Row 1 @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Row 1","hero":false,"slider":null,"value":null,"display":null},{"text":"m11 = 1","label":null,"prefix":null,"suffix":null,"section":"Row 1","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"m12 = 2","label":null,"prefix":null,"suffix":null,"section":"Row 1","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"m13 = 3","label":null,"prefix":null,"suffix":null,"section":"Row 1","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Row 2 @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Row 2","hero":false,"slider":null,"value":null,"display":null},{"text":"m21 = 4","label":null,"prefix":null,"suffix":null,"section":"Row 2","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"m22 = 5","label":null,"prefix":null,"suffix":null,"section":"Row 2","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"m23 = 6","label":null,"prefix":null,"suffix":null,"section":"Row 2","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"# Row 3 @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Row 3","hero":false,"slider":null,"value":null,"display":null},{"text":"m31 = 7","label":null,"prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"m32 = 8","label":null,"prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"m33 = 10","label":null,"prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"det_3x3 = m11*(m22*m33 - m23*m32) - m12*(m21*m33 - m23*m31) + m13*(m21*m32 - m22*m31) // @accent @formula @label(det)","label":"det","prefix":null,"suffix":null,"section":"Row 3","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"# Problem 6: A 3×3 system by Cramer's rule","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hero":false,"slider":null,"value":null,"display":null},{"text":"c1 = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"c2 = 15","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"c3 = 25","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A 3×3 system by Cramer's rule","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"# Replace column 1 with constants → det_x3","label":null,"prefix":null,"suffix":null,"section":"Replace column 1 with constants → det_x3","hero":false,"slider":null,"value":null,"display":null},{"text":"_det_x3 = c1*(m22*m33 - m23*m32) - m12*(c2*m33 - m23*c3) + m13*(c2*m32 - m22*c3)","label":null,"prefix":null,"suffix":null,"section":"Replace column 1 with constants → det_x3","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"# Replace column 2 with constants → det_y3","label":null,"prefix":null,"suffix":null,"section":"Replace column 2 with constants → det_y3","hero":false,"slider":null,"value":null,"display":null},{"text":"_det_y3 = m11*(c2*m33 - m23*c3) - c1*(m21*m33 - m23*m31) + m13*(m21*c3 - c2*m31)","label":null,"prefix":null,"suffix":null,"section":"Replace column 2 with constants → det_y3","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"# Replace column 3 with constants → det_z3","label":null,"prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hero":false,"slider":null,"value":null,"display":null},{"text":"_det_z3 = m11*(m22*c3 - c2*m32) - m12*(m21*c3 - c2*m31) + c1*(m21*m32 - m22*m31)","label":null,"prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":true,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"x3 = _det_x3 / det_3x3 // @accent @formula @label(x)","label":"x","prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"y3 = _det_y3 / det_3x3 // @accent @formula @label(y)","label":"y","prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"z3 = _det_z3 / det_3x3 // @accent @formula @label(z)","label":"z","prefix":null,"suffix":null,"section":"Replace column 3 with constants → det_z3","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Problem 7: Solve by substitution","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Solve by substitution","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Singular matrix test","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hero":false,"slider":null,"value":null,"display":null},{"text":"s11 = 2","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"s12 = 4","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"s21 = 1","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"s22 = 2","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"det_singular = s11*s22 - s12*s21 // @accent @formula @label($0 \\Rightarrow$ singular)","label":"$0 \\Rightarrow$ singular","prefix":null,"suffix":null,"section":"Problem 8: Singular matrix test","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"exam-linalg-vectors","title":"Linear Algebra — Vectors","description":"MIT 18.06-style: dot product, cross product, magnitude, angle, and projection — every operation spelled out 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@layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Vector b","hero":false,"slider":null,"value":null,"display":null},{"text":"bx = 4","label":null,"prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"by = 5","label":null,"prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"bz = 6","label":null,"prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"dot_ab = ax*bx + ay*by + az*bz // @accent @formula @label($\\vec a\\cdot\\vec b$)","label":"$\\vec a\\cdot\\vec b$","prefix":null,"suffix":null,"section":"Vector b","hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"# Problem 2: Magnitudes","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Magnitudes","hero":false,"slider":null,"value":null,"display":null},{"text":"mag_a = sqrt(ax^2 + ay^2 + az^2) // @formula @label($\\lvert\\vec a\\rvert$)","label":"$\\lvert\\vec a\\rvert$","prefix":null,"suffix":null,"section":"Problem 2: Magnitudes","hidden":false,"hero":false,"slider":null,"value":3.7416573867739413,"display":"3.742"},{"text":"mag_b = sqrt(bx^2 + by^2 + bz^2) // @accent @formula @label($\\lvert\\vec b\\rvert$)","label":"$\\lvert\\vec b\\rvert$","prefix":null,"suffix":null,"section":"Problem 2: Magnitudes","hidden":false,"hero":false,"slider":null,"value":8.774964387392123,"display":"8.775"},{"text":"# Problem 3: Angle between the vectors","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Angle between the vectors","hero":false,"slider":null,"value":null,"display":null},{"text":"_cos_theta = dot_ab / (mag_a * mag_b)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Angle between the vectors","hidden":true,"hero":false,"slider":null,"value":0.974631846197076,"display":"0.9746"},{"text":"angle_ab_deg = acos(_cos_theta) // @accent @formula @label($\\theta$) degrees","label":"$\\theta$","prefix":null,"suffix":"degrees","section":"Problem 3: Angle between the vectors","hidden":false,"hero":false,"slider":null,"value":12.933154491899192,"display":"12.9332"},{"text":"# Problem 4: Cross product","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Cross product","hero":false,"slider":null,"value":null,"display":null},{"text":"# Components @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Components","hero":false,"slider":null,"value":null,"display":null},{"text":"cross_x = ay*bz - az*by // @formula @label($(\\vec a\\times\\vec b)_x$)","label":"$(\\vec a\\times\\vec b)_x$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"cross_y = az*bx - ax*bz // @formula @label($(\\vec a\\times\\vec b)_y$)","label":"$(\\vec a\\times\\vec b)_y$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"cross_z = ax*by - ay*bx // @formula @label($(\\vec a\\times\\vec b)_z$)","label":"$(\\vec a\\times\\vec b)_z$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"cross_mag = sqrt(cross_x^2 + cross_y^2 + cross_z^2) // @accent @formula @label($\\lvert\\vec a\\times\\vec b\\rvert$)","label":"$\\lvert\\vec a\\times\\vec b\\rvert$","prefix":null,"suffix":null,"section":"Components","hidden":false,"hero":false,"slider":null,"value":7.3484692283495345,"display":"7.348"},{"text":"# Problem 5: Right-hand rule check","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Right-hand rule check","hero":false,"slider":null,"value":null,"display":null},{"text":"# Vector u @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Vector 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0","label":null,"prefix":null,"suffix":null,"section":"Vector v","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# u × v should be (0,0,1) @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hero":false,"slider":null,"value":null,"display":null},{"text":"uv_x = uy*vz - uz*vy","label":null,"prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"uv_y = uz*vx - ux*vz","label":null,"prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"uv_z = ux*vy - uy*vx // @accent @formula @label($(\\vec u\\times\\vec v)_z$)","label":"$(\\vec u\\times\\vec v)_z$","prefix":null,"suffix":null,"section":"u × v should be (0,0,1)","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Problem 6: Scalar projection","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Scalar projection","hero":false,"slider":null,"value":null,"display":null},{"text":"scalar_proj = dot_ab / mag_b // @accent @formula @label(comp_b a)","label":"comp_b a","prefix":null,"suffix":null,"section":"Problem 6: Scalar projection","hidden":false,"hero":false,"slider":null,"value":3.646738446708414,"display":"3.647"},{"text":"# Problem 7: Vector projection","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Vector projection","hero":false,"slider":null,"value":null,"display":null},{"text":"_proj_scale = dot_ab / mag_b^2","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Vector projection","hidden":true,"hero":false,"slider":null,"value":0.41558441558441556,"display":"0.4156"},{"text":"# Projection vector @layout(grid-3)","label":null,"prefix":null,"suffix":null,"section":"Projection vector","hero":false,"slider":null,"value":null,"display":null},{"text":"proj_x = _proj_scale * bx","label":null,"prefix":null,"suffix":null,"section":"Projection vector","hidden":false,"hero":false,"slider":null,"value":1.662337662337662,"display":"1.662"},{"text":"proj_y = _proj_scale * by","label":null,"prefix":null,"suffix":null,"section":"Projection vector","hidden":false,"hero":false,"slider":null,"value":2.0779220779220773,"display":"2.078"},{"text":"proj_z = _proj_scale * bz // @accent @formula @label(proj_b a, z)","label":"proj_b a, z","prefix":null,"suffix":null,"section":"Projection vector","hidden":false,"hero":false,"slider":null,"value":2.493506493506493,"display":"2.494"},{"text":"# Problem 8: Orthogonality test","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Orthogonality test","hero":false,"slider":null,"value":null,"display":null},{"text":"is_orthogonal = dot_ab // @accent @formula @label($0 \\Rightarrow$ orthogonal)","label":"$0 \\Rightarrow$ orthogonal","prefix":null,"suffix":null,"section":"Problem 8: Orthogonality test","hidden":false,"hero":true,"slider":null,"value":32,"display":"32"}]},{"id":"exam-number-theory","title":"Number Theory Final — Divisibility, Modular Arithmetic & GCD","description":"The integers up close: divisibility, the GCD/LCM identity, modular arithmetic, Fibonacci, and base conversion — every result computed.","category":"education","icon":"book-open","tags":["number-theory","modular","gcd","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.053Z"},"rows":[{"text":"# Problem 1: Divisibility by remainder","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Divisibility by remainder","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Greatest common divisor (Euclid)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Greatest common divisor (Euclid)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Least common 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numbers","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Fibonacci numbers","hero":false,"slider":null,"value":null,"display":null},{"text":"fib(10) // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Fibonacci numbers","hidden":false,"hero":true,"slider":null,"value":55,"display":"55"},{"text":"# Problem 9: The golden ratio from Fibonacci","label":null,"prefix":null,"suffix":null,"section":"Problem 9: The golden ratio from Fibonacci","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 10: Base conversion","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Base conversion","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-physics-em-waves","title":"Physics Final — E&M and Waves","description":"MIT 8.02-style final: Coulomb's law, fields, DC circuits, and wave optics — each from the governing law to the 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m","label":null,"prefix":null,"suffix":"m","section":"Problem 1: Coulomb force","hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"coulomb_force = k_e * abs(q1 * q2) / r1^2 // @accent @formula @label(F) N","label":"F","prefix":null,"suffix":"N","section":"Problem 1: Coulomb force","hidden":false,"hero":false,"slider":null,"value":21.575999999999997,"display":"21.58"},{"text":"# Problem 2: Field of a point charge","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Field of a point charge","hero":false,"slider":null,"value":null,"display":null},{"text":"charge_q = 5e-9 // C","label":null,"prefix":null,"suffix":"C","section":"Problem 2: Field of a point charge","hidden":false,"hero":false,"slider":null,"value":5e-9,"display":"5e-9"},{"text":"r2 = 0.1 // m","label":null,"prefix":null,"suffix":"m","section":"Problem 2: Field of a point charge","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"e_field = k_e * charge_q / r2^2 // @accent @formula @label(E) N/C","label":"E","prefix":null,"suffix":"N/C","section":"Problem 2: Field of a point charge","hidden":false,"hero":false,"slider":null,"value":4494.999999999999,"display":"4,495"},{"text":"# Problem 3: Parallel-plate capacitance","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Parallel-plate capacitance","hero":false,"slider":null,"value":null,"display":null},{"text":"eps0 = 8.854e-12 // F/m","label":null,"prefix":null,"suffix":"F/m","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":8.854e-12,"display":"8.854e-12"},{"text":"area = 0.02 // m^2","label":null,"prefix":null,"suffix":"m^2","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":0.02,"display":"0.02"},{"text":"d3 = 0.001 // m","label":null,"prefix":null,"suffix":"m","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":0.001,"display":"0.001"},{"text":"capacitance = eps0 * area / d3 // @accent @formula @label(C) F","label":"C","prefix":null,"suffix":"F","section":"Problem 3: Parallel-plate capacitance","hidden":false,"hero":false,"slider":null,"value":1.7708e-10,"display":"1.7708e-10"},{"text":"# Problem 4: Ohm's law — current and power","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage = 12 V","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"resistance = 4 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"_current = voltage / resistance","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"power = voltage * _current // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 4: Ohm's law — current and power","hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"# Problem 5: Resistors in parallel","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hero":false,"slider":null,"value":null,"display":null},{"text":"ra = 6 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"rb = 3 ohm","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"r_parallel = (ra * rb) / (ra + rb) // @accent @formula @label(R_eq)","label":"R_eq","prefix":null,"suffix":null,"section":"Problem 5: Resistors in parallel","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"# Problem 6: RC time constant","label":null,"prefix":null,"suffix":null,"section":"Problem 6: RC time constant","hero":false,"slider":null,"value":null,"display":null},{"text":"r6 = 1000 // ohm","label":null,"prefix":null,"suffix":"ohm","section":"Problem 6: RC time constant","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"c6 = 100e-6 // F","label":null,"prefix":null,"suffix":"F","section":"Problem 6: RC time constant","hidden":false,"hero":false,"slider":null,"value":0.0001,"display":"0.0001"},{"text":"time_constant = r6 * c6 // @accent @formula @label($\\tau$) s","label":"$\\tau$","prefix":null,"suffix":"s","section":"Problem 6: RC time constant","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"# Problem 7: Wavelength of light","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Wavelength of light","hero":false,"slider":null,"value":null,"display":null},{"text":"c_light = 3e8 // m/s","label":null,"prefix":null,"suffix":"m/s","section":"Problem 7: Wavelength of light","hidden":false,"hero":false,"slider":null,"value":300000000,"display":"300,000,000"},{"text":"freq = 5e14 // Hz","label":null,"prefix":null,"suffix":"Hz","section":"Problem 7: Wavelength of light","hidden":false,"hero":false,"slider":null,"value":500000000000000,"display":"500,000,000,000,000"},{"text":"wavelength = c_light / freq // @accent @formula @label($\\lambda$) m","label":"$\\lambda$","prefix":null,"suffix":"m","section":"Problem 7: Wavelength of light","hidden":false,"hero":false,"slider":null,"value":6e-7,"display":"0.0000006"},{"text":"# Problem 8: Snell's law refraction","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hero":false,"slider":null,"value":null,"display":null},{"text":"n_air = 1","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"n_glass = 1.5","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"theta_i_deg = 40","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"_theta_i = theta_i_deg * pi / 180","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":true,"hero":false,"slider":null,"value":0.6981317007977318,"display":"0.6981"},{"text":"_sin_refract = n_air * sin(_theta_i) / n_glass","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Snell's law refraction","hidden":true,"hero":false,"slider":null,"value":0.42852507312435956,"display":"0.4285"},{"text":"theta_refract_deg = asin(_sin_refract) // @accent @formula @label($\\theta_2$) degrees","label":"$\\theta_2$","prefix":null,"suffix":"degrees","section":"Problem 8: Snell's law refraction","hidden":false,"hero":false,"slider":null,"value":25.37399393917941,"display":"25.374"},{"text":"# Problem 9: Double-slit fringe spacing","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hero":false,"slider":null,"value":null,"display":null},{"text":"slit_d = 0.0001 m","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":false,"slider":null,"value":0.0001,"display":"0.0001"},{"text":"screen_L = 2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"lambda9 = 600e-9 m","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":false,"slider":null,"value":6e-7,"display":"0.0000006"},{"text":"fringe_spacing = lambda9 * screen_L / slit_d // @accent @formula @label($\\Delta y$)","label":"$\\Delta y$","prefix":null,"suffix":null,"section":"Problem 9: Double-slit fringe spacing","hidden":false,"hero":true,"slider":null,"value":0.012,"display":"0.012"}]},{"id":"exam-physics-mechanics","title":"Physics Final — Mechanics","description":"MIT 8.01-style final: kinematics, Newton's laws, energy, and momentum — each worked from the governing law to the number.","category":"physics","icon":"activity","tags":["physics","mechanics","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.057Z"},"rows":[{"text":"# Problem 1: Projectile range","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Projectile 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Constant acceleration from rest","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"_v_final = a2 * t2","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Constant acceleration from rest","hidden":true,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"dist = 0.5 * a2 * t2^2 // @accent @formula @label(distance)","label":"distance","prefix":null,"suffix":null,"section":"Problem 2: Constant acceleration from rest","hidden":false,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"# Problem 3: Block on a frictionless incline","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_block = 5 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"incline_deg = 25","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"_incline = incline_deg * pi / 180","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":true,"hero":false,"slider":null,"value":0.4363323129985824,"display":"0.4363"},{"text":"a_slope = g * sin(_incline) // @accent @formula @label(a)","label":"a","prefix":null,"suffix":null,"section":"Problem 3: Block on a frictionless incline","hidden":false,"hero":false,"slider":null,"value":4.145885147676261,"display":"4.1459"},{"text":"# Problem 3b: Normal force","label":null,"prefix":null,"suffix":null,"section":"Problem 3b: Normal force","hero":false,"slider":null,"value":null,"display":null},{"text":"normal_force = mass_block * g * cos(_incline) // @accent @formula @label(N)","label":"N","prefix":null,"suffix":null,"section":"Problem 3b: Normal force","hidden":false,"hero":false,"slider":null,"value":44.45439695414769,"display":"44.4544"},{"text":"# Problem 4: Elastic potential energy","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Elastic potential energy","hero":false,"slider":null,"value":null,"display":null},{"text":"k4 = 200 N/m","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Elastic potential energy","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"x4 = 0.15 m","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Elastic potential energy","hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"spring_pe = 0.5 * k4 * x4^2 // @accent @formula @label(U)","label":"U","prefix":null,"suffix":null,"section":"Problem 4: Elastic potential energy","hidden":false,"hero":false,"slider":null,"value":2.25,"display":"2.25"},{"text":"# Problem 5: Kinetic energy","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Kinetic energy","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_car = 1200 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Kinetic energy","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"v5 = 25 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Kinetic energy","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"kinetic_energy = 0.5 * mass_car * v5^2 in J // @accent @formula @label(KE)","label":"KE","prefix":null,"suffix":null,"section":"Problem 5: Kinetic energy","hidden":false,"hero":false,"slider":null,"value":375000,"display":"375,000"},{"text":"# Problem 6: Perfectly inelastic collision","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic collision","hero":false,"slider":null,"value":null,"display":null},{"text":"m6a = 2 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic collision","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"v6a = 4 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic collision","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"m6b = 3 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic collision","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"v6b = 0 m/s","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic collision","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"v_combined = (m6a*v6a + m6b*v6b) / (m6a + m6b) // @accent @formula @label(v_f)","label":"v_f","prefix":null,"suffix":null,"section":"Problem 6: Perfectly inelastic collision","hidden":false,"hero":false,"slider":null,"value":1.6,"display":"1.6"},{"text":"# Problem 7: Pendulum period","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Pendulum period","hero":false,"slider":null,"value":null,"display":null},{"text":"L7 = 2 m","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Pendulum period","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"period = 2 * pi * sqrt(L7 / g) // @accent @formula @label(T)","label":"T","prefix":null,"suffix":null,"section":"Problem 7: Pendulum period","hidden":false,"hero":false,"slider":null,"value":2.8370067068857745,"display":"2.837"},{"text":"# Problem 8: Work against gravity","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hero":false,"slider":null,"value":null,"display":null},{"text":"mass_lift = 10 kg","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"h8 = 3 m","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"work = mass_lift * g * h8 in J // @accent @formula @label(W)","label":"W","prefix":null,"suffix":null,"section":"Problem 8: Work against gravity","hidden":false,"hero":true,"slider":null,"value":294.3,"display":"294.3"}]},{"id":"exam-prealgebra","title":"Pre-Algebra Final — Integers, Expressions & Equations","description":"The bridge from arithmetic to algebra: signed numbers, exponents, one-variable equations, and the coordinate plane — each step computed.","category":"education","icon":"book-open","tags":["prealgebra","integers","equations","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.057Z"},"rows":[{"text":"# Problem 1: Signed-number arithmetic","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Signed-number arithmetic","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Absolute value","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Absolute value","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Exponents and the laws of exponents","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Exponents and the laws of exponents","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: Negative and zero exponents","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Negative and zero exponents","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 5: Evaluating an algebraic expression","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Evaluating an algebraic expression","hero":false,"slider":null,"value":null,"display":null},{"text":"x = 4","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Evaluating an algebraic expression","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"# Problem 6: Solve a one-step equation","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Solve a one-step equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: Solve a two-step equation","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Solve a two-step equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Distance between two points","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hero":false,"slider":null,"value":null,"display":null},{"text":"dx = 4 - 1","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"dy = 6 - 2","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"distance = hypot(dx, dy) // @hero @accent @formula @label(distance)","label":"distance","prefix":null,"suffix":null,"section":"Problem 8: Distance between two points","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"# Problem 9: Slope of a line","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Slope of a line","hero":false,"slider":null,"value":null,"display":null},{"text":"slope = dy / dx // @accent @formula @label(slope)","label":"slope","prefix":null,"suffix":null,"section":"Problem 9: Slope of a line","hidden":false,"hero":false,"slider":null,"value":1.3333333333333333,"display":"1.333"},{"text":"# Problem 10: Mean of a data set","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Mean of a data set","hero":false,"slider":null,"value":null,"display":null}]},{"id":"exam-probability","title":"Probability Final — Counting, Conditional & Distributions","description":"Classical probability worked end to end: equally-likely outcomes, complements, conditional probability, and the binomial distribution — every number computed.","category":"education","icon":"book-open","tags":["probability","binomial","conditional","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.057Z"},"rows":[{"text":"# Problem 1: A single fair die","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hero":false,"slider":null,"value":null,"display":null},{"text":"favorable = 2","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total = 6","label":null,"prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"p_gt4 = favorable / total // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 1: A single fair die","hidden":false,"hero":false,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"# Problem 2: Two independent events (AND)","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Two independent events (AND)","hero":false,"slider":null,"value":null,"display":null},{"text":"p_two_heads = 0.5 * 0.5 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 2: Two independent events (AND)","hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"# Problem 3: Complement (at least one)","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Complement (at least one)","hero":false,"slider":null,"value":null,"display":null},{"text":"p_at_least_one_six = 1 - (5/6)^2 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 3: Complement (at least one)","hidden":false,"hero":false,"slider":null,"value":0.3055555555555555,"display":"0.3056"},{"text":"# Problem 4: Mutually exclusive events (OR)","label":null,"prefix":null,"suffix":null,"section":"Problem 4: Mutually exclusive events (OR)","hero":false,"slider":null,"value":null,"display":null},{"text":"p_king_or_queen = 4/52 + 4/52 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 4: Mutually exclusive events (OR)","hidden":false,"hero":false,"slider":null,"value":0.15384615384615385,"display":"0.1538"},{"text":"# Problem 5: Conditional probability","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Conditional probability","hero":false,"slider":null,"value":null,"display":null},{"text":"p_both_red = (5/8) * (4/7) // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 5: Conditional probability","hidden":false,"hero":false,"slider":null,"value":0.3571428571428571,"display":"0.3571"},{"text":"# Problem 6: A binomial probability","label":null,"prefix":null,"suffix":null,"section":"Problem 6: A binomial probability","hero":false,"slider":null,"value":null,"display":null},{"text":"p_exactly_3 = C(10, 3) * 0.5^3 * 0.5^7 // @hero @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 6: A binomial probability","hidden":false,"hero":true,"slider":null,"value":0.1171875,"display":"0.1172"},{"text":"# Problem 7: Binomial — at least k successes","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Binomial — at least k successes","hero":false,"slider":null,"value":null,"display":null},{"text":"p_all_five = 0.8^5 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 7: Binomial — at least k successes","hidden":false,"hero":false,"slider":null,"value":0.3276800000000001,"display":"0.3277"},{"text":"# Problem 8: Expected value","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Expected value","hero":false,"slider":null,"value":null,"display":null},{"text":"expected_value = 10 * 0.2 + 0 * 0.8 - 3 // @accent @formula @label(E net)","label":"E net","prefix":null,"suffix":null,"section":"Problem 8: Expected value","hidden":false,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Problem 9: Odds vs. probability","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Odds vs. probability","hero":false,"slider":null,"value":null,"display":null},{"text":"p_event = 0.75","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Odds vs. probability","hidden":false,"hero":false,"slider":null,"value":0.75,"display":"0.75"},{"text":"odds_in_favor = p_event / (1 - p_event) // @accent @formula @label(odds)","label":"odds","prefix":null,"suffix":null,"section":"Problem 9: Odds vs. probability","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Problem 10: Birthday-style collision","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Birthday-style collision","hero":false,"slider":null,"value":null,"display":null},{"text":"p_distinct = P(365, 5) / 365^5 // @accent @formula @label(P)","label":"P","prefix":null,"suffix":null,"section":"Problem 10: Birthday-style collision","hidden":false,"hero":false,"slider":null,"value":0.9728644263002064,"display":"0.9729"}]},{"id":"exam-statistics","title":"Statistics Final — Descriptive & Inferential","description":"Intro statistics worked from raw data: center, spread, z-scores, correlation, and a confidence interval — each computed with the engine's built-in stats functions.","category":"education","icon":"activity","tags":["statistics","data","z-score","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.057Z"},"rows":[{"text":"# Problem 1: Measures of center","label":null,"prefix":null,"suffix":null,"section":"Problem 1: Measures of center","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 2: Spread — variance and standard deviation","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Spread — variance and standard deviation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 3: Range","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Range","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 4: A z-score","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hero":false,"slider":null,"value":null,"display":null},{"text":"mu = 75","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":false,"slider":null,"value":75,"display":"75"},{"text":"sigma = 8","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"score = 91","label":null,"prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":false,"slider":null,"value":91,"display":"91"},{"text":"z_score = (score - mu) / sigma // @hero @accent @formula @label(z)","label":"z","prefix":null,"suffix":null,"section":"Problem 4: A z-score","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"},{"text":"# Problem 5: Converting a z-score back to a value","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Converting a z-score back to a value","hero":false,"slider":null,"value":null,"display":null},{"text":"raw_score = mu + (-1.5) * sigma // @accent @formula @label(score)","label":"score","prefix":null,"suffix":null,"section":"Problem 5: Converting a z-score back to a value","hidden":false,"hero":false,"slider":null,"value":63,"display":"63"},{"text":"# Problem 6: Correlation coefficient","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Correlation coefficient","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 7: A perfect linear relationship","label":null,"prefix":null,"suffix":null,"section":"Problem 7: A perfect linear relationship","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 8: Standard error of the mean","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hero":false,"slider":null,"value":null,"display":null},{"text":"s_sample = 12","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"n_sample = 36","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"std_error = s_sample / sqrt(n_sample) // @accent @formula @label(SE)","label":"SE","prefix":null,"suffix":null,"section":"Problem 8: Standard error of the mean","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"# Problem 9: A 95% confidence interval for the mean","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hero":false,"slider":null,"value":null,"display":null},{"text":"x_bar = 50","label":null,"prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"ci_low = x_bar - 1.96 * std_error // @accent @formula @label(lower)","label":"lower","prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hidden":false,"hero":false,"slider":null,"value":46.08,"display":"46.08"},{"text":"ci_high = x_bar + 1.96 * std_error // @accent @formula @label(upper)","label":"upper","prefix":null,"suffix":null,"section":"Problem 9: A 95% confidence interval for the mean","hidden":false,"hero":false,"slider":null,"value":53.92,"display":"53.92"},{"text":"# Problem 10: Empirical rule (68–95–99.7)","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hero":false,"slider":null,"value":null,"display":null},{"text":"mu_iq = 100","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"sigma_iq = 15","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"band_low = mu_iq - 2 * sigma_iq // @accent @formula @label(lower)","label":"lower","prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"band_high = mu_iq + 2 * sigma_iq // @accent @formula @label(upper)","label":"upper","prefix":null,"suffix":null,"section":"Problem 10: Empirical rule (68–95–99.7)","hidden":false,"hero":false,"slider":null,"value":130,"display":"130"}]},{"id":"exam-trig-precalc","title":"Trigonometry & Precalculus Final","description":"Right-triangle and unit-circle trig, identities, the laws of sines and cosines, and polar form — every value computed.","category":"education","icon":"triangle","tags":["trigonometry","precalculus","unit-circle","exam"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.057Z"},"rows":[{"text":"# Problem 1: The basic trig ratios","label":null,"prefix":null,"suffix":null,"section":"Problem 1: The basic trig ratios","hero":false,"slider":null,"value":null,"display":null},{"text":"sin(30 deg) // @hero @accent","label":null,"prefix":null,"suffix":null,"section":"Problem 1: The basic trig ratios","hidden":false,"hero":true,"slider":null,"value":0.4999999999997412,"display":"0.5"},{"text":"# Problem 2: Solve a right triangle","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hero":false,"slider":null,"value":null,"display":null},{"text":"h = 10","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"theta = 35","label":null,"prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"opposite = h * sin(theta deg) // @accent @formula @label(opposite)","label":"opposite","prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":5.735764363510335,"display":"5.736"},{"text":"adjacent = h * cos(theta deg) // @accent @formula @label(adjacent)","label":"adjacent","prefix":null,"suffix":null,"section":"Problem 2: Solve a right triangle","hidden":false,"hero":false,"slider":null,"value":8.191520442890006,"display":"8.192"},{"text":"# Problem 3: Inverse trig — find the angle","label":null,"prefix":null,"suffix":null,"section":"Problem 3: Inverse trig — find the angle","hero":false,"slider":null,"value":null,"display":null},{"text":"ramp_angle = atan(3 / 12) deg // @accent @formula @label(angle °)","label":"angle °","prefix":null,"suffix":null,"section":"Problem 3: Inverse trig — find the angle","hidden":false,"hero":false,"slider":null,"value":14.0362434679,"display":"14.0362"},{"text":"# Problem 4: The Pythagorean identity","label":null,"prefix":null,"suffix":null,"section":"Problem 4: The Pythagorean identity","hero":false,"slider":null,"value":null,"display":null},{"text":"ang = 50","label":null,"prefix":null,"suffix":null,"section":"Problem 4: The Pythagorean identity","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"# Problem 5: Law of Sines","label":null,"prefix":null,"suffix":null,"section":"Problem 5: Law of Sines","hero":false,"slider":null,"value":null,"display":null},{"text":"side_b = 8 * sin(60 deg) / sin(40 deg) // @accent @formula @label(b)","label":"b","prefix":null,"suffix":null,"section":"Problem 5: Law of Sines","hidden":false,"hero":false,"slider":null,"value":10.778370842688613,"display":"10.78"},{"text":"# Problem 6: Law of Cosines","label":null,"prefix":null,"suffix":null,"section":"Problem 6: Law of Cosines","hero":false,"slider":null,"value":null,"display":null},{"text":"side_c = sqrt(5^2 + 7^2 - 2*5*7*cos(60 deg)) // @accent @formula @label(c)","label":"c","prefix":null,"suffix":null,"section":"Problem 6: Law of Cosines","hidden":false,"hero":false,"slider":null,"value":6.244997998414912,"display":"6.245"},{"text":"# Problem 7: Radians and degrees","label":null,"prefix":null,"suffix":null,"section":"Problem 7: Radians and degrees","hero":false,"slider":null,"value":null,"display":null},{"text":"deg_value = (5*pi/6) * 180 / pi // @accent @formula @label(degrees)","label":"degrees","prefix":null,"suffix":null,"section":"Problem 7: Radians and degrees","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"rad_value = 120 * pi / 180 // @accent @formula @label(radians)","label":"radians","prefix":null,"suffix":null,"section":"Problem 7: Radians and degrees","hidden":false,"hero":false,"slider":null,"value":2.0943951023931953,"display":"2.094"},{"text":"# Problem 8: Solve a trig equation (general solution)","label":null,"prefix":null,"suffix":null,"section":"Problem 8: Solve a trig equation (general solution)","hero":false,"slider":null,"value":null,"display":null},{"text":"# Problem 9: Polar to rectangular (complex form)","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hero":false,"slider":null,"value":null,"display":null},{"text":"r_polar = 5","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"theta_polar = 53.13","label":null,"prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":53.13,"display":"53.13"},{"text":"x_rect = r_polar * cos(theta_polar deg) // @accent @formula @label(x)","label":"x","prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":3.0000071456616615,"display":"3"},{"text":"y_rect = r_polar * sin(theta_polar deg) // @accent @formula @label(y)","label":"y","prefix":null,"suffix":null,"section":"Problem 9: Polar to rectangular (complex form)","hidden":false,"hero":false,"slider":null,"value":3.9999946407437807,"display":"4"},{"text":"# Problem 10: Rectangular to polar","label":null,"prefix":null,"suffix":null,"section":"Problem 10: Rectangular to polar","hero":false,"slider":null,"value":null,"display":null},{"text":"r_back = hypot(3, 4) // @accent @formula @label(r)","label":"r","prefix":null,"suffix":null,"section":"Problem 10: Rectangular to polar","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"theta_back = atan2(4, 3) deg // @accent @formula @label(θ °)","label":"θ °","prefix":null,"suffix":null,"section":"Problem 10: Rectangular to polar","hidden":false,"hero":false,"slider":null,"value":53.1301023542,"display":"53.1301"}]},{"id":"exhaust-pipe-sizing","title":"Exhaust Pipe Sizing","description":"Estimate recommended exhaust pipe diameter.","category":"engineering","icon":"settings","tags":["automotive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Engine Power","label":null,"prefix":null,"suffix":null,"section":"Engine Power","hero":false,"slider":null,"value":null,"display":null},{"text":"horsepower = 400","label":null,"prefix":null,"suffix":null,"section":"Engine Power","hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"diameter inches = (horsepower ^ 0.5) * 0.125","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"exoplanet-habitability","title":"Exoplanet Habitability","description":"Calculate the habitable zone boundaries around a star from its luminosity.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"star_luminosity_relative_to_sun = 1.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"inner_boundary_astronomical_units = sqrt(star_luminosity_relative_to_sun / 1.1) // Inner (AU) @hero","label":null,"prefix":null,"suffix":"Inner (AU)","section":null,"hidden":false,"hero":true,"slider":null,"value":0.9534625892455924,"display":"0.9535"},{"text":"outer_boundary_astronomical_units = sqrt(star_luminosity_relative_to_sun / 0.53) // Outer (AU) @hero","label":null,"prefix":null,"suffix":"Outer (AU)","section":null,"hidden":false,"hero":true,"slider":null,"value":1.3736056394868903,"display":"1.374"}]},{"id":"expected-value","title":"Expected Value","description":"E[X] = Σ xᵢ · P(xᵢ) for a discrete distribution (up to 4 outcomes).","category":"formulas","icon":"percent","tags":["probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Outcomes and their probabilities","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 0 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their 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0..1","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.15,"display":"0.15"},{"text":"x4 = 10 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":10,"display":"10"},{"text":"p4 = 0.05 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Outcomes and their probabilities","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.05,"display":"0.05"},{"text":"# Expected value","label":null,"prefix":null,"suffix":null,"section":"Expected value","hero":false,"slider":null,"value":null,"display":null},{"text":"expected = x1 * p1 + x2 * p2 + x3 * p3 + x4 * p4 // @label(E[X])","label":"E[X]","prefix":null,"suffix":null,"section":"Expected 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Parameters","label":null,"prefix":null,"suffix":null,"section":"Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"initial_amount = 100 // 0..1M","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"decay_constant = 0.1 // 0..1","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1,"step":0.01},"value":0.1,"display":"0.1"},{"text":"time = 10 // 0..1k","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Amount remaining at time t","label":null,"prefix":null,"suffix":null,"section":"Amount remaining at time t","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = initial_amount * exp(-decay_constant * time) // @label(N(t))","label":"N(t)","prefix":null,"suffix":null,"section":"Amount remaining at time t","hidden":false,"hero":true,"slider":null,"value":36.787944117144235,"display":"36.79"}]},{"id":"exponential-growth","title":"Exponential Growth","description":"N(t) = N₀ · e^(k·t) — continuous exponential growth.","category":"formulas","icon":"trending-up","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Parameters","label":null,"prefix":null,"suffix":null,"section":"Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"initial_amount = 100 // 0..1M","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"rate = 0.05 // -1..1","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":-1,"max":1,"step":0.02},"value":0.05,"display":"0.05"},{"text":"time = 10 // 0..1k","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Amount at time t","label":null,"prefix":null,"suffix":null,"section":"Amount at time t","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = initial_amount * exp(rate * time) // @label(N(t))","label":"N(t)","prefix":null,"suffix":null,"section":"Amount at time t","hidden":false,"hero":true,"slider":null,"value":164.87212707001282,"display":"164.87"}]},{"id":"exposure-value-compensation","title":"Exposure Value Compensation","description":"Calculate adjusted shutter speed from a base speed and exposure compensation stops.","category":"math","icon":"infinity","tags":["exposure","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"base_shutter_speed_seconds = 0.01 // 1/100","label":null,"prefix":null,"suffix":"1/100","section":null,"hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"ev_compensation = 1 // +1 stop","label":null,"prefix":null,"suffix":"+1 stop","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"adjusted_shutter_speed_seconds = base_shutter_speed_seconds * (2^ev_compensation) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.02,"display":"0.02"}]},{"id":"extrinsic-reward-decay","title":"Extrinsic Reward Decay","description":"Estimate the diminishing effective value of repeated extrinsic rewards.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"number_of_rewards = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"satiation_factor = 0.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"effective_reward_value = 1 / (1 + satiation_factor * number_of_rewards) // relative value @hero","label":null,"prefix":null,"suffix":"relative value","section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"factor-by-grouping","title":"Factor by Grouping Check","description":"Given ax² + bx + c, find the two numbers that multiply to a·c and sum to b.","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Quadratic ax² + bx + c","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 2 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":2,"display":"2"},{"text":"b = 7 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":7,"display":"7"},{"text":"c = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Quadratic ax² + bx + c","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"# Product and sum to find","label":null,"prefix":null,"suffix":null,"section":"Product and sum to find","hero":false,"slider":null,"value":null,"display":null},{"text":"target_product = a * c // @label(a·c)","label":"a·c","prefix":null,"suffix":null,"section":"Product and sum to find","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"target_sum = b // @label(b)","label":"b","prefix":null,"suffix":null,"section":"Product and sum to find","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"# Find m and n where m + n = b and m · n = a · c","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hero":false,"slider":null,"value":null,"display":null},{"text":"discriminant = b^2 - 4 * target_product","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"m = (b + sqrt(abs(discriminant))) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hidden":false,"hero":true,"slider":null,"value":6,"display":"6"},{"text":"n = (b - sqrt(abs(discriminant))) / 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Find m and n where m + n = b and m · n = a · c","hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"factorial-calculator","title":"Factorial Calculator","description":"Calculate the factorial (n!) of a number.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"number = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"result = factorial(number)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":120,"display":"120"}]},{"id":"fair-trade-coffee-premium","title":"Fair Trade Coffee Premium","description":"Calculate the total cost including social and organic premiums.","category":"finance","icon":"coffee","tags":["finance","eco","coffee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"coffee_price_per_lb = 15 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"fair_trade_social_premium_per_lb = 0.20 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":0.2,"display":"0.2"},{"text":"organic_premium_per_lb = 0.30 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"total_fair_trade_organic_price = coffee_price_per_lb + fair_trade_social_premium_per_lb + organic_premium_per_lb // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":15.5,"display":"15.5"},{"text":"percentage_premium = (fair_trade_social_premium_per_lb + organic_premium_per_lb) / coffee_price_per_lb * 100 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":3.333333333333334,"display":"3.333"}]},{"id":"fan-laws-performance-scaling","title":"Fan Laws Performance Scaling","description":"Predict fan performance changes with RPM shifts.","category":"engineering","icon":"fan","tags":["engineering","mechanical","fluids"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"initial_rpm = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"new_rpm = 1500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"initial_cfm = 100 // cubic feet per minute","label":null,"prefix":null,"suffix":"cubic feet per minute","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"new_cfm = initial_cfm * (new_rpm / initial_rpm) // cfm @hero","label":null,"prefix":null,"suffix":"cfm","section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"},{"text":"initial_static_pressure = 1 // in H2O","label":null,"prefix":null,"suffix":"in H2O","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"new_static_pressure = initial_static_pressure * ((new_rpm / initial_rpm)^2) // in H2O","label":null,"prefix":null,"suffix":"in H2O","section":null,"hidden":false,"hero":false,"slider":null,"value":2.25,"display":"2.25"},{"text":"initial_power_watts = 10 // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"new_power_watts = initial_power_watts * ((new_rpm / initial_rpm)^3) // Watts","label":null,"prefix":null,"suffix":"Watts","section":null,"hidden":false,"hero":false,"slider":null,"value":33.75,"display":"33.75"}]},{"id":"fantasy-football-expected-points","title":"Fantasy Football Expected Points","description":"Calculate fantasy football points for a player from passing, rushing, and receiving stats.","category":"math","icon":"infinity","tags":["football","points","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Passing","label":null,"prefix":null,"suffix":null,"section":"Passing","hero":false,"slider":null,"value":null,"display":null},{"text":"passing yards = 250","label":null,"prefix":null,"suffix":null,"section":"Passing","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"passing touchdowns = 2","label":null,"prefix":null,"suffix":null,"section":"Passing","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"interceptions = 1","label":null,"prefix":null,"suffix":null,"section":"Passing","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Rushing/Receiving","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hero":false,"slider":null,"value":null,"display":null},{"text":"rushing yards = 40","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"receiving yards = 20","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"receptions = 5 // PPR league","label":null,"prefix":null,"suffix":"PPR league","section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"total touchdowns = 1","label":null,"prefix":null,"suffix":null,"section":"Rushing/Receiving","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"points = (passing yards * 0.04) + (passing touchdowns * 4) - (interceptions * 2) + (rushing yards * 0.1) + (receiving yards * 0.1) + (receptions * 1) + (total touchdowns * 6)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":33,"display":"33"}]},{"id":"fcpa-compliance-risk-score","title":"FCPA Risk Score","description":"Measure risk levels related to the Foreign Corrupt Practices Act.","category":"other","icon":"globe","tags":["compliance","risk"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"foreignOfficialInteractionFrequency = 8 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"thirdPartyAgentUsage = 6 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"localCorruptionIndex = 5 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"fcpaRisk = (foreignOfficialInteractionFrequency + thirdPartyAgentUsage + localCorruptionIndex) / 3 // scale 1-10 @hero","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":true,"slider":null,"value":6.333333333333333,"display":"6.333"}]},{"id":"fence-calculator","title":"Fence Calculator","description":"Estimate posts, pickets, and material costs for your fence project.","category":"construction","icon":"fence","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Project","label":null,"prefix":null,"suffix":null,"section":"Project","hero":false,"slider":null,"value":null,"display":null},{"text":"total fence length = 150 // ft 10..1k by 5","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":10,"max":1000,"step":5},"value":150,"display":"150"},{"text":"fence height = 6 // ft 3..10","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":3,"max":10,"step":0.1},"value":6,"display":"6"},{"text":"post spacing = 8 // ft 4..12","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":4,"max":12,"step":0.1},"value":8,"display":"8"},{"text":"number of gates = 1 // 0..5","label":null,"prefix":null,"suffix":null,"section":"Project","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.05},"value":1,"display":"1"},{"text":"gate width = 4 // ft 3..16","label":null,"prefix":null,"suffix":"ft","section":"Project","hidden":false,"hero":false,"slider":{"min":3,"max":16,"step":0.2},"value":4,"display":"4"},{"text":"# Posts","label":null,"prefix":null,"suffix":null,"section":"Posts","hero":false,"slider":null,"value":null,"display":null},{"text":"fence run = total_fence_length - (number_of_gates * gate_width)","label":null,"prefix":null,"suffix":null,"section":"Posts","hidden":false,"hero":false,"slider":null,"value":146,"display":"146"},{"text":"posts needed = roundup(fence_run / post_spacing) + 1 + (number_of_gates * 2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Posts","hidden":false,"hero":true,"slider":null,"value":22,"display":"22"},{"text":"post depth = 2 // ft 1..4 by 0.5","label":null,"prefix":null,"suffix":"ft","section":"Posts","hidden":false,"hero":false,"slider":{"min":1,"max":4,"step":0.5},"value":2,"display":"2"},{"text":"total post length = fence_height + post_depth // ft","label":null,"prefix":null,"suffix":"ft","section":"Posts","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Pickets","label":null,"prefix":null,"suffix":null,"section":"Pickets","hero":false,"slider":null,"value":null,"display":null},{"text":"picket width = 3.5 // in 1..8 by 0.5","label":null,"prefix":null,"suffix":"in","section":"Pickets","hidden":false,"hero":false,"slider":{"min":1,"max":8,"step":0.5},"value":3.5,"display":"3.5"},{"text":"gap between pickets = 0 // in 0..4 by 0.25","label":null,"prefix":null,"suffix":"in","section":"Pickets","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.25},"value":0,"display":"0"},{"text":"pickets per foot = 12 / (picket_width + gap_between_pickets)","label":null,"prefix":null,"suffix":null,"section":"Pickets","hidden":false,"hero":false,"slider":null,"value":3.4285714285714284,"display":"3.429"},{"text":"total pickets = roundup(fence_run * pickets_per_foot)","label":null,"prefix":null,"suffix":null,"section":"Pickets","hidden":false,"hero":false,"slider":null,"value":501,"display":"501"},{"text":"# Cost 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10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"phosphorus_percentage = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"potassium_percentage = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"nitrogen_weight = fertilizer_weight_pounds * (nitrogen_percentage / 100) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"phosphorus_weight = fertilizer_weight_pounds * (phosphorus_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7.5,"display":"7.5"},{"text":"potassium_weight = fertilizer_weight_pounds * (potassium_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"}]},{"id":"fibonacci-nth-term","title":"Fibonacci nth Term","description":"Find the nth Fibonacci number (F₁=1, F₂=1, Fₙ=Fₙ₋₁+Fₙ₋₂).","category":"formulas","icon":"infinity","tags":["number-theory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Index","label":null,"prefix":null,"suffix":null,"section":"Index","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 10 // 0..50","label":null,"prefix":null,"suffix":null,"section":"Index","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":10,"display":"10"},{"text":"# Fibonacci number","label":null,"prefix":null,"suffix":null,"section":"Fibonacci number","hero":false,"slider":null,"value":null,"display":null},{"text":"result = fibonacci(n) // @label(Fₙ)","label":"Fₙ","prefix":null,"suffix":null,"section":"Fibonacci 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0.5","label":null,"prefix":null,"suffix":"%","section":"Assumptions","hidden":false,"hero":false,"slider":{"min":0,"max":10,"step":0.5},"value":2.5,"display":"2.5"},{"text":"# Analysis","label":null,"prefix":null,"suffix":null,"section":"Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"_savings_rate = ((annual_income - annual_expenses) / annual_income) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Analysis","hidden":true,"hero":false,"slider":null,"value":43.75,"display":"43.75"},{"text":"$_annual_savings = annual_income - annual_expenses","label":null,"prefix":"$","suffix":null,"section":"Analysis","hidden":true,"hero":false,"slider":null,"value":35000,"display":"$35,000.00"},{"text":"_real_return = (expected_return - inflation_rate) / 100","label":null,"prefix":null,"suffix":null,"section":"Analysis","hidden":true,"hero":false,"slider":null,"value":0.045,"display":"0.045"},{"text":"$FIRE number = annual_expenses / (safe_withdrawal_rate / 100) // @hero @label(FIRE Number (25x Expenses))","label":"FIRE Number (25x Expenses)","prefix":"$","suffix":null,"section":"Analysis","hidden":false,"hero":true,"slider":null,"value":1125000,"display":"$1,125,000.00"},{"text":"# Timeline","label":null,"prefix":null,"suffix":null,"section":"Timeline","hero":false,"slider":null,"value":null,"display":null},{"text":"years until FIRE = round(ln((FIRE_number * real_return + annual_savings) / (current_savings * real_return + annual_savings)) / ln(1 + real_return), 1) // years","label":null,"prefix":null,"suffix":"years","section":"Timeline","hidden":false,"hero":false,"slider":null,"value":17.6,"display":"17.6"},{"text":"FIRE age = round(35 + years_until_FIRE, 1) // years old","label":null,"prefix":null,"suffix":"years old","section":"Timeline","hidden":false,"hero":false,"slider":null,"value":52.6,"display":"52.6"},{"text":"# Monthly Breakdown","label":null,"prefix":null,"suffix":null,"section":"Monthly 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mph","label":null,"prefix":null,"suffix":"mph","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"recommended_clearance_feet = 10 + (flame_height_feet * 2) + (wind_speed_mph / 2) // feet @hero","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":true,"slider":null,"value":19,"display":"19"}]},{"id":"fireplace-efficiency-loss","title":"Fireplace Efficiency Loss","description":"Estimate heat loss in BTU/hour from a fireplace chimney drawing room air.","category":"finance","icon":"dollar-sign","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"room_temperature_fahrenheit = 70","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"outside_temperature_fahrenheit = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"chimney_flow_rate_cubic_feet_per_minute = 200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"temperature_difference = room_temperature_fahrenheit - outside_temperature_fahrenheit","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"heat_loss_btu_per_hour = chimney_flow_rate_cubic_feet_per_minute * 60 * 0.018 * temperature_difference","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8640,"display":"8,640"}]},{"id":"firewood-cord-volume","title":"Firewood Cord Volume","description":"Calculate how many standard cords a stacked firewood pile 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cubic feet","section":null,"hidden":false,"hero":false,"slider":null,"value":128,"display":"128"},{"text":"number_of_cords = volume_cubic_feet / cord_volume_cubic_feet // cords","label":null,"prefix":null,"suffix":"cords","section":null,"hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"firework-burst-radius","title":"Firework Burst Radius","description":"Estimate firework burst radius in feet from shell diameter in inches.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"shell_diameter_inches = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"burst_radius_feet = shell_diameter_inches * 45 // feet @hero","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":true,"slider":null,"value":180,"display":"180"}]},{"id":"fish-tank-heater-watts","title":"Fish Tank Heater Watts","description":"Calculate required heater wattage for a fish tank from volume and temperature rise.","category":"science","icon":"fish","tags":["heater","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"tank_volume_gallons = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"desired_temperature_increase_fahrenheit = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"watts_per_gallon_per_degree = 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"total_heater_wattage_required = tank_volume_gallons * desired_temperature_increase_fahrenheit * watts_per_gallon_per_degree","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"}]},{"id":"fishing-line-capacity-monofill","title":"Fishing Line Capacity Monofill","description":"Estimate fishing line yardage on a spool when changing line test weight.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"spool_capacity_yards_at_12lb = 200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"target_line_test_lb = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"estimated_capacity_yards = spool_capacity_yards_at_12lb * (12 / target_line_test_lb) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":120,"display":"120"}]},{"id":"flash-guide-number-distance","title":"Flash Guide Number Distance","description":"Calculate maximum flash distance from guide number and aperture f-stop.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"guide_number_feet = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"aperture_f_stop = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"max_flash_distance_feet = guide_number_feet / aperture_f_stop // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12.5,"display":"12.5"}]},{"id":"fleet-utilization-rate","title":"Fleet Utilization Rate","description":"Monitor the percentage of your fleet currently in active service.","category":"business","icon":"truck","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"activeVehicles = 45 // vehicles","label":null,"prefix":null,"suffix":"vehicles","section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"totalVehiclesInFleet = 50 // vehicles","label":null,"prefix":null,"suffix":"vehicles","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"utilizationRatePercent = (activeVehicles / totalVehiclesInFleet) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":90,"display":"90"}]},{"id":"flexible-spending-account-fsa-savings","title":"Flexible Spending Account Fsa Savings","description":"Calculate total FSA tax savings from federal, Social Security, and Medicare withholding.","category":"finance","icon":"dollar-sign","tags":["account","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"annual_contribution = 3050","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3050,"display":"3,050"},{"text":"tax_rate = 0.22","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.22,"display":"0.22"},{"text":"social_security_rate = 0.062","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.062,"display":"0.062"},{"text":"medicare_rate = 0.0145","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.0145,"display":"0.0145"},{"text":"total_tax_savings = annual_contribution * (tax_rate + social_security_rate + medicare_rate)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":904.325,"display":"904.33"}]},{"id":"flight-carbon-footprint","title":"Flight Carbon Footprint","description":"Estimate CO2 emissions for your air 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overtimeThreshold","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"_overtimePay = overtimeHours * (hourlyRate * 1.5)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"totalPay = regularPay + overtimePay // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1100,"display":"1,100"}]},{"id":"fluid-density-buoyancy","title":"Fluid Density Buoyancy","description":"Calculate buoyant force from submerged volume and fluid density.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"volume_submerged = 0.5 // cubic meters","label":null,"prefix":null,"suffix":"cubic 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250","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"touchdowns = 2","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"interceptions = 1","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_a = ((completions / attempts) - 0.3) * 5","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.8333333333333328,"display":"1.833"},{"text":"_b = ((yards / attempts) - 3) * 0.25","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.3333333333333335,"display":"1.333"},{"text":"_c 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1.225","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.225,"display":"1.225"},{"text":"gravity = 9.81","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"time_seconds = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"terminal_velocity = ( (2 * object_mass_kilograms * gravity) / (air_density * projected_area_square_meters * drag_coefficient) ) ** 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40.02040295975572,"display":"40.02"},{"text":"exponent_value = (2 * gravity * time_seconds) / terminal_velocity","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.451249681285038,"display":"2.451"},{"text":"e_val = 2.71828 ** 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dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"business_expenses_annual = 20000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":20000,"display":"20,000"},{"text":"billable_hours_per_week = 20 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"weeks_per_year = 48 // weeks","label":null,"prefix":null,"suffix":"weeks","section":null,"hidden":false,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"_total_target_revenue = target_annual_income + business_expenses_annual","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":120000,"display":"120,000"},{"text":"_total_billable_hours = billable_hours_per_week * 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40..52","label":null,"prefix":null,"suffix":null,"section":"Availability","hidden":false,"hero":false,"slider":{"min":40,"max":52,"step":0.2},"value":48,"display":"48"},{"text":"# Required Rate","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_needed = desired annual income + annual business expenses","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hidden":true,"hero":false,"slider":null,"value":92000,"display":"92,000"},{"text":"_tax_adjusted = total_needed / (1 - self employment tax rate / 100)","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hidden":true,"hero":false,"slider":null,"value":108618.65407319953,"display":"108,618.65"},{"text":"total billable hours = billable hours per week * weeks per year","label":null,"prefix":null,"suffix":null,"section":"Required Rate","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"$required hourly rate = round(tax_adjusted / total billable hours * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Required Rate","hidden":false,"hero":true,"slider":null,"value":90.52,"display":"$90.52"},{"text":"$required day rate = round(required hourly rate * 8 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Required Rate","hidden":false,"hero":false,"slider":null,"value":724.16,"display":"$724.16"},{"text":"$effective monthly income = round(desired annual income / 12 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Required Rate","hidden":false,"hero":false,"slider":null,"value":6666.67,"display":"$6,666.67"}]},{"id":"freezing-point-depression-colligative","title":"Freezing Point Depression Colligative","description":"Calculate freezing point depression of a solution from molality and solvent 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1728","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":53.333333333333336,"display":"53.33"},{"text":"density = weightInPounds / volumeInCubicFeet // pounds per cubic foot @hero","label":null,"prefix":null,"suffix":"pounds per cubic foot","section":null,"hidden":false,"hero":true,"slider":null,"value":9.375,"display":"9.375"}]},{"id":"frequency","title":"Musical Frequency","description":"Frequency from a reference pitch using 12-tone equal temperament.","category":"science","icon":"music","tags":["acoustics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Reference Note","label":null,"prefix":null,"suffix":null,"section":"Reference Note","hero":false,"slider":null,"value":null,"display":null},{"text":"base frequency = 440 // Hz 20..20k","label":null,"prefix":null,"suffix":"Hz","section":"Reference Note","hidden":false,"hero":false,"slider":{"min":20,"max":20000,"step":200},"value":440,"display":"440"},{"text":"semitones from base = 12 // -48..48","label":null,"prefix":null,"suffix":null,"section":"Reference Note","hidden":false,"hero":false,"slider":{"min":-48,"max":48,"step":1},"value":12,"display":"12"},{"text":"# Equal Temperament","label":null,"prefix":null,"suffix":null,"section":"Equal Temperament","hero":false,"slider":null,"value":null,"display":null},{"text":"frequency = base frequency * 2^(semitones from base / 12) // Hz @hero @label(Frequency) @suffix(Hz)","label":"Frequency","prefix":null,"suffix":"Hz","section":"Equal Temperament","hidden":false,"hero":true,"slider":null,"value":880,"display":"880"},{"text":"# Octave + Cents Breakdown","label":null,"prefix":null,"suffix":null,"section":"Octave + Cents Breakdown","hero":false,"slider":null,"value":null,"display":null},{"text":"octaves up = semitones from base / 12 // @label(Octaves from base)","label":"Octaves from base","prefix":null,"suffix":null,"section":"Octave + Cents Breakdown","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"cents from base = semitones from base * 100 // ¢","label":null,"prefix":null,"suffix":"¢","section":"Octave + Cents Breakdown","hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"# Period + Wavelength","label":null,"prefix":null,"suffix":null,"section":"Period + Wavelength","hero":false,"slider":null,"value":null,"display":null},{"text":"period ms = 1000 / frequency // ms @label(Period) @suffix(ms)","label":"Period","prefix":null,"suffix":"ms","section":"Period + Wavelength","hidden":false,"hero":false,"slider":null,"value":1.1363636363636365,"display":"1.136"},{"text":"wavelength m = 343 / frequency // m @label(Wavelength in air) @suffix(m)","label":"Wavelength in air","prefix":null,"suffix":"m","section":"Period + Wavelength","hidden":false,"hero":false,"slider":null,"value":0.38977272727272727,"display":"0.3898"}]},{"id":"friction-coefficient","title":"Friction Coefficient","description":"Calculate the coefficient of friction from friction force and normal force.","category":"other","icon":"calculator","tags":["coefficient"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Force Details","label":null,"prefix":null,"suffix":null,"section":"Force Details","hero":false,"slider":null,"value":null,"display":null},{"text":"friction force = 25 // newtons 0..1k","label":null,"prefix":null,"suffix":"newtons","section":"Force Details","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":25,"display":"25"},{"text":"normal force = 100 // newtons 1..2k","label":null,"prefix":null,"suffix":"newtons","section":"Force Details","hidden":false,"hero":false,"slider":{"min":1,"max":2000,"step":20},"value":100,"display":"100"},{"text":"# Formula: mu = Ff / Fn","label":null,"prefix":null,"suffix":null,"section":"Formula: mu = Ff / Fn","hero":false,"slider":null,"value":null,"display":null},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"coefficient of friction = friction force / normal force // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":0.25,"display":"0.25"},{"text":"# Common Values","label":null,"prefix":null,"suffix":null,"section":"Common Values","hero":false,"slider":null,"value":null,"display":null},{"text":"ice on ice = 0.1","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"rubber on concrete = 0.7","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.7,"display":"0.7"},{"text":"wood on wood = 0.4","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"steel on steel = 0.6","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"teflon on steel = 0.04","label":null,"prefix":null,"suffix":null,"section":"Common Values","hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"}]},{"id":"frictional-force-coefficient-static","title":"Frictional Force Coefficient Static","description":"Calculate maximum static friction force from normal force and friction 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investment.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"investment_amount = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"front_end_load = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"annual_growth = 0.07","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.07,"display":"0.07"},{"text":"years = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"net_investment = investment_amount * (1 - front_end_load)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9500,"display":"9,500"},{"text":"future_value = net_investment * (1 + annual_growth) ** years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":18687.93789425088,"display":"18,687.94"}]},{"id":"fuel-burn-aviation-gph","title":"Fuel Burn Aviation Gph","description":"Calculate aviation fuel burn rate in gallons per hour from total fuel and time.","category":"other","icon":"flame","tags":["fuel","burn"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"total_fuel_burned_gallons = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"flight_duration_hours = 3.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.5,"display":"3.5"},{"text":"fuel_burn_rate_gallons_per_hour = total_fuel_burned_gallons / flight_duration_hours // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12.857142857142858,"display":"12.86"}]},{"id":"fuel-consumption-l-100km-to-mpg","title":"Fuel Consumption L 100km To MPG","description":"Convert liters per 100km to miles per gallon.","category":"conversion","icon":"settings","tags":["automotive","fuel"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Fuel Consumption","label":null,"prefix":null,"suffix":null,"section":"Fuel Consumption","hero":false,"slider":null,"value":null,"display":null},{"text":"liters per 100km = 10","label":null,"prefix":null,"suffix":null,"section":"Fuel 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Consumption","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"liters per 100km = 235.215 / miles per gallon","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":9.4086,"display":"9.409"}]},{"id":"fuel-cost","title":"Fuel Cost","description":"Calculate fuel costs for trips and estimate your monthly/yearly gas budget.","category":"everyday","icon":"fuel","tags":["fuel","gas"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.696Z"},"rows":[{"text":"# Your Car","label":null,"prefix":null,"suffix":null,"section":"Your Car","hero":false,"slider":null,"value":null,"display":null},{"text":"tank size = 14 // gallons 5..40","label":null,"prefix":null,"suffix":"gallons","section":"Your 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30..100","label":null,"prefix":null,"suffix":"mph","section":"Cruise Speed","hidden":false,"hero":false,"slider":{"min":30,"max":100,"step":1},"value":70,"display":"70"},{"text":"# Drag-Dominated Loss (above_peak)","label":null,"prefix":null,"suffix":null,"section":"Drag-Dominated Loss (above_peak)","hero":false,"slider":null,"value":null,"display":null},{"text":"_above_peak = max(cruise speed - peak speed, 0)","label":null,"prefix":null,"suffix":null,"section":"Drag-Dominated Loss (above_peak)","hidden":true,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"_loss_exponent = 1.05","label":null,"prefix":null,"suffix":null,"section":"Drag-Dominated Loss (above_peak)","hidden":true,"hero":false,"slider":null,"value":1.05,"display":"1.05"},{"text":"mpg now = round(peak mpg * (peak speed / max(cruise speed, peak speed))^loss_exponent, 1) // mpg @hero @label(MPG at cruise speed)","label":"MPG at cruise speed","prefix":null,"suffix":"mpg","section":"Drag-Dominated Loss 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W","label":null,"prefix":null,"suffix":"W","section":"Power","hidden":false,"hero":false,"slider":null,"value":9424.77796076938,"display":"9,424.78"},{"text":"output power = input_power * efficiency / 100 // W","label":null,"prefix":null,"suffix":"W","section":"Power","hidden":false,"hero":false,"slider":null,"value":8953.539062730912,"display":"8,953.54"}]},{"id":"gear-tooth-bending-stress-lewis","title":"Gear Tooth Bending Stress","description":"Estimate gear tooth stress using the Lewis formula.","category":"engineering","icon":"settings","tags":["engineering","mechanical"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"tangential_force_lbs = 500 // lbs","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"diametral_pitch = 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r^(n−1).","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Sequence parameters","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"r = 3 // -10..10 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":0.1},"value":3,"display":"3"},{"text":"n = 6 // 1..50","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":6,"display":"6"},{"text":"# nth term","label":null,"prefix":null,"suffix":null,"section":"nth term","hero":false,"slider":null,"value":null,"display":null},{"text":"an = a1 * r^(n - 1) // @label(aₙ)","label":"aₙ","prefix":null,"suffix":null,"section":"nth term","hidden":false,"hero":true,"slider":null,"value":486,"display":"486"}]},{"id":"geometric-series-sum","title":"Geometric Series Sum","description":"Sum the first n terms of a geometric sequence: Sₙ = a₁·(1−rⁿ)/(1−r).","category":"formulas","icon":"sigma","tags":["algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Sequence parameters","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Sequence parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"r = 3 // -10..10 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Sequence 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systems.","category":"engineering","icon":"thermometer","tags":["engineering"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"heat_energy_output_kwh = 400 // kWh","label":null,"prefix":null,"suffix":"kWh","section":null,"hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"electrical_energy_input_kwh = 100 // kWh","label":null,"prefix":null,"suffix":"kWh","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"coefficient_of_performance = heat_energy_output_kwh / electrical_energy_input_kwh // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"gift-exchange-pairing-odds","title":"Gift Exchange Pairing Odds","description":"Calculate probabilities for picking specific people in a Secret Santa exchange.","category":"other","icon":"gift","tags":["gift","odds"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Group Size","label":null,"prefix":null,"suffix":null,"section":"Group Size","hero":false,"slider":null,"value":null,"display":null},{"text":"number of people = 10 // n","label":null,"prefix":null,"suffix":"n","section":"Group Size","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"prob of picking self = (1 / number of people) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":10,"display":"10"},{"text":"prob of picking specific person = (1 / (number of people - 1)) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":11.11111111111111,"display":"11.11"},{"text":"prob of no one picking self = exp(-1) * 100 // @hero @suffix(%) @note(approx for large n)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":36.787944117144235,"display":"36.79"}]},{"id":"gift-tax-calculator","title":"Gift Tax Calculator","description":"Estimate gift tax owed after annual exclusion and lifetime exclusion remaining.","category":"finance","icon":"gift","tags":["gift","tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Gift Details","label":null,"prefix":null,"suffix":null,"section":"Gift Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$gift amount = 25000 // 1k..1M","label":null,"prefix":"$","suffix":null,"section":"Gift Details","hidden":false,"hero":false,"slider":{"min":1000,"max":1000000,"step":10000},"value":25000,"display":"$25,000.00"},{"text":"$annual exclusion per person = 18000 // 2024 limit 0..25000 by 1000","label":null,"prefix":"$","suffix":"2024 limit","section":"Gift Details","hidden":false,"hero":false,"slider":{"min":0,"max":25000,"step":1000},"value":18000,"display":"$18,000.00"},{"text":"$lifetime exclusion remaining = 13610000 // 0..13610k","label":null,"prefix":"$","suffix":null,"section":"Gift Details","hidden":false,"hero":false,"slider":{"min":0,"max":13610000,"step":200000},"value":13610000,"display":"$13,610,000.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_taxable_gift_amount = if(gift amount > annual exclusion per person, gift amount - annual exclusion per person, 0)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":7000,"display":"$7,000.00"},{"text":"$_impact_on_lifetime_exclusion = if(taxable_gift_amount > lifetime exclusion remaining, lifetime exclusion remaining, taxable_gift_amount)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":7000,"display":"$7,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated gift tax out of pocket = if(taxable_gift_amount > lifetime exclusion remaining, (taxable_gift_amount - lifetime exclusion remaining) * 0.40, 0) // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":0,"display":"$0.00"},{"text":"$remaining lifetime exclusion = if(lifetime exclusion remaining > taxable_gift_amount, lifetime exclusion remaining - taxable_gift_amount, 0)","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":13603000,"display":"$13,603,000.00"},{"text":"$non taxable portion = gift amount - estimated gift tax out of pocket","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":25000,"display":"$25,000.00"}]},{"id":"gift-tax-lifetime-exclusion","title":"Gift Tax Lifetime Exclusion","description":"Calculate remaining lifetime gift tax exclusion from gifts already given.","category":"finance","icon":"gift","tags":["gift","tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"total_gifts_given = 500000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500000,"display":"500,000"},{"text":"lifetime_exclusion_limit = 12920000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12920000,"display":"12,920,000"},{"text":"remaining_exclusion = lifetime_exclusion_limit - total_gifts_given","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12420000,"display":"12,420,000"}]},{"id":"glicko-2-rating-step","title":"Glicko 2 Rating Step","description":"Calculate a single Glicko-2 rating update step after a chess or game result.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Current Stats","label":null,"prefix":null,"suffix":null,"section":"Current Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"rating = 1500","label":null,"prefix":null,"suffix":null,"section":"Current Stats","hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"rating deviation = 200 // RD","label":null,"prefix":null,"suffix":"RD","section":"Current Stats","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"volatility = 0.06","label":null,"prefix":null,"suffix":null,"section":"Current Stats","hidden":false,"hero":false,"slider":null,"value":0.06,"display":"0.06"},{"text":"# Game Result","label":null,"prefix":null,"suffix":null,"section":"Game Result","hero":false,"slider":null,"value":null,"display":null},{"text":"opponent rating = 1500","label":null,"prefix":null,"suffix":null,"section":"Game Result","hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"opponent rd = 30","label":null,"prefix":null,"suffix":null,"section":"Game Result","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"outcome = 1 // win","label":null,"prefix":null,"suffix":"win","section":"Game Result","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Simplified Step","label":null,"prefix":null,"suffix":null,"section":"Simplified Step","hero":false,"slider":null,"value":null,"display":null},{"text":"_g = 1 / sqrt(1 + 3 * (opponent rd / pi)^2)","label":null,"prefix":null,"suffix":null,"section":"Simplified Step","hidden":true,"hero":false,"slider":null,"value":0.0603497778616256,"display":"0.0603"},{"text":"_e = 1 / (1 + exp(-g * (rating - opponent rating)))","label":null,"prefix":null,"suffix":null,"section":"Simplified Step","hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"new rating = rating + (1 / (1/rating deviation^2 + 1/(1/(g^2 * e * (1-e))))) * g * (outcome - e)","label":null,"prefix":null,"suffix":null,"section":"Simplified Step","hidden":false,"hero":true,"slider":null,"value":1532.2545348351184,"display":"1,532.25"}]},{"id":"glide-ratio-aircraft","title":"Glide Ratio Aircraft","description":"Calculate an aircraft's glide ratio from altitude lost and distance traveled.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"altitude_lost_feet = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"distance_traveled_feet = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"glide_ratio = distance_traveled_feet / altitude_lost_feet // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"global-time-zone-offset","title":"Global Time Zone Offset","description":"Convert UTC time to local time using a timezone offset.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"current_hour_utc = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"offset_hours = -5 // EST","label":null,"prefix":null,"suffix":"EST","section":null,"hidden":false,"hero":false,"slider":null,"value":-5,"display":"-5"},{"text":"local_hour = mod(current_hour_utc + offset_hours, 24) // 24-hour clock @hero","label":null,"prefix":null,"suffix":"24-hour clock","section":null,"hidden":false,"hero":true,"slider":null,"value":7,"display":"7"}]},{"id":"goal-achievement-probability-estimate","title":"Goal Achievement Probability Estimate","description":"Estimate goal success probability from resources, time, and complexity penalty.","category":"productivity","icon":"clock","tags":["probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"resources_available_percent = 80 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"time_allocated_percent = 70 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"complexity_penalty_percent = 30 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"success_probability = (resources_available_percent * 0.4 + time_allocated_percent * 0.4 - complexity_penalty_percent * 0.2) // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":54,"display":"54"}]},{"id":"goat-milk-yield-estimate","title":"Goat Milk Yield Estimate","description":"Estimate total goat milk yield in gallons over a lactation period.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"number_of_goats = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"days_in_lactation = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"average_daily_yield_quarts = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"total_yield_gallons = (number_of_goats * average_daily_yield_quarts * days_in_lactation) / 4 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":150,"display":"150"}]},{"id":"gold-gain-multiplier","title":"Gold Gain Multiplier","description":"Calculate total gold gain with bonuses.","category":"math","icon":"dollar-sign","tags":["gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Gold Settings","label":null,"prefix":null,"suffix":null,"section":"Gold Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base gold = 200","label":null,"prefix":null,"suffix":null,"section":"Gold Settings","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"gold find percent = 120 // %","label":null,"prefix":null,"suffix":"%","section":"Gold Settings","hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"final gold = base gold * (1 + (gold find percent / 100))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":440,"display":"440"}]},{"id":"gold-price-by-weight","title":"Gold Price By Weight","description":"Calculate the value of gold from weight in grams and price per ounce.","category":"finance","icon":"tag","tags":["price","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"current_gold_price_per_ounce = 2000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"gold_weight_grams = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"grams_per_ounce = 31.1035","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":31.1035,"display":"31.1"},{"text":"total_gold_value = (gold_weight_grams / grams_per_ounce) * current_gold_price_per_ounce","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":643.0144517498031,"display":"643.01"}]},{"id":"golden-ratio-ui-layout","title":"Golden Ratio Ui Layout","description":"Split a UI width into main content and sidebar using the golden ratio.","category":"design","icon":"palette","tags":["layout"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"total_width = 1200 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"phi = 1.618","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.618,"display":"1.618"},{"text":"main_content_width = total_width / phi // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":741.6563658838072,"display":"741.66"},{"text":"sidebar_width = total_width - main_content_width // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":458.3436341161928,"display":"458.34"}]},{"id":"golden-ratio","title":"Golden Ratio","description":"Compute φ, Fibonacci ratios, and compare against the rule of thirds.","category":"design","icon":"function","tags":["math","design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# The Number","label":null,"prefix":null,"suffix":null,"section":"The Number","hero":false,"slider":null,"value":null,"display":null},{"text":"phi = (1 + sqrt(5)) / 2 // @hero @label(φ = (1+√5)/2)","label":"φ = (1+√5)/2","prefix":null,"suffix":null,"section":"The Number","hidden":false,"hero":true,"slider":null,"value":1.618033988749895,"display":"1.618"},{"text":"one over phi = 1 / phi // @label(1/φ (≈ 0.618))","label":"1/φ (≈ 0.618)","prefix":null,"suffix":null,"section":"The Number","hidden":false,"hero":false,"slider":null,"value":0.6180339887498948,"display":"0.618"},{"text":"phi squared = phi^2 // @label(φ² (≈ 2.618))","label":"φ² (≈ 2.618)","prefix":null,"suffix":null,"section":"The Number","hidden":false,"hero":false,"slider":null,"value":2.618033988749895,"display":"2.618"},{"text":"# Fibonacci Approximation","label":null,"prefix":null,"suffix":null,"section":"Fibonacci Approximation","hero":false,"slider":null,"value":null,"display":null},{"text":"fib n minus 1 = 89 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":89,"display":"89"},{"text":"fib n = 144 // 1..1k","label":null,"prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":144,"display":"144"},{"text":"ratio = fib n / fib n minus 1 // @label(Fib ratio (144/89))","label":"Fib ratio (144/89)","prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":null,"value":1.6179775280898876,"display":"1.618"},{"text":"error from phi = round((ratio - phi) * 1000000) / 1000000 // @label(Error vs φ)","label":"Error vs φ","prefix":null,"suffix":null,"section":"Fibonacci Approximation","hidden":false,"hero":false,"slider":null,"value":-0.000056,"display":"-0.000056"},{"text":"# Rule of Thirds vs Golden Section","label":null,"prefix":null,"suffix":null,"section":"Rule of Thirds vs Golden Section","hero":false,"slider":null,"value":null,"display":null},{"text":"thirds split = 1 / 3 // @label(Rule of thirds (1/3 ≈ 0.333))","label":"Rule of thirds (1/3 ≈ 0.333)","prefix":null,"suffix":null,"section":"Rule of Thirds vs Golden Section","hidden":false,"hero":false,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"golden split = 1 / phi^2 // @label(Golden section (1/φ² ≈ 0.382))","label":"Golden section (1/φ² ≈ 0.382)","prefix":null,"suffix":null,"section":"Rule of Thirds vs Golden Section","hidden":false,"hero":false,"slider":null,"value":0.38196601125010515,"display":"0.382"},{"text":"percent difference = round(abs(thirds split - golden split) / golden split * 100, 1) // % @label(Rule-of-thirds error vs golden section)","label":"Rule-of-thirds error vs golden section","prefix":null,"suffix":"%","section":"Rule of Thirds vs Golden Section","hidden":false,"hero":false,"slider":null,"value":12.7,"display":"12.7"}]},{"id":"golf-handicap-differential","title":"Golf Handicap Differential","description":"Calculate golf handicap differential for a round.","category":"health","icon":"activity","tags":["sports"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Round Settings","label":null,"prefix":null,"suffix":null,"section":"Round Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"score = 85","label":null,"prefix":null,"suffix":null,"section":"Round Settings","hidden":false,"hero":false,"slider":null,"value":85,"display":"85"},{"text":"course rating = 72.0","label":null,"prefix":null,"suffix":null,"section":"Round Settings","hidden":false,"hero":false,"slider":null,"value":72,"display":"72"},{"text":"slope rating = 113","label":null,"prefix":null,"suffix":null,"section":"Round 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4","label":null,"prefix":null,"suffix":null,"section":"Course 4","hero":false,"slider":null,"value":null,"display":null},{"text":"course4_credits = 3 // 1..6","label":null,"prefix":null,"suffix":null,"section":"Course 4","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":3,"display":"3"},{"text":"course4_grade = 2.7 // 0..4 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Course 4","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.1},"value":2.7,"display":"2.7"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"total_credits = course1_credits + course2_credits + course3_credits + course4_credits","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":13,"display":"13"},{"text":"total_grade_points = course1_credits * course1_grade + course2_credits * course2_grade + course3_credits * 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100)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":59.5,"display":"59.5"},{"text":"needed_from_final = target_grade - coursework_contribution","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":30.5,"display":"30.5"},{"text":"needed_final_score = round(needed_from_final / (final_weight / 100) * 10) / 10 // %","label":null,"prefix":null,"suffix":"%","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":101.7,"display":"101.7"}]},{"id":"grass-seed-coverage","title":"Grass Seed Coverage","description":"Calculate weight of grass seed needed for your lawn area.","category":"everyday","icon":"sprout","tags":["garden","seed"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"area_square_meters = 250 // square meters","label":null,"prefix":null,"suffix":"square 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// 0.5..100 by 0.5","label":null,"prefix":null,"suffix":null,"section":"Gravel Volume","hidden":false,"hero":false,"slider":{"min":0.5,"max":100,"step":0.5},"value":5,"display":"5"},{"text":"# Weight Calculations","label":null,"prefix":null,"suffix":null,"section":"Weight Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"# Average density is approx 2800 lbs per cubic yard","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hero":false,"slider":null,"value":null,"display":null},{"text":"pounds per cubic yard = 2800 // 2.4k..3.2k","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hidden":false,"hero":false,"slider":{"min":2400,"max":3200,"step":1},"value":2800,"display":"2,800"},{"text":"_total_weight_pounds = volume cubic yards * pounds per cubic yard","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hidden":true,"hero":false,"slider":null,"value":14000,"display":"14,000"},{"text":"total weight tons = round(total_weight_pounds / 2000, 2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Average density is approx 2800 lbs per cubic yard","hidden":false,"hero":true,"slider":null,"value":7,"display":"7"},{"text":"# Delivery","label":null,"prefix":null,"suffix":null,"section":"Delivery","hero":false,"slider":null,"value":null,"display":null},{"text":"# Typical small dump truck capacity is 5 tons","label":null,"prefix":null,"suffix":null,"section":"Typical small dump truck capacity is 5 tons","hero":false,"slider":null,"value":null,"display":null},{"text":"truck loads = roundup(total weight tons / 5)","label":null,"prefix":null,"suffix":null,"section":"Typical small dump truck capacity is 5 tons","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"}]},{"id":"gravitational-potential-energy-orbital","title":"Gravitational Potential Energy 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mass_planet * mass_object / radius_orbit // Joules @hero","label":null,"prefix":null,"suffix":"Joules","section":null,"hidden":false,"hero":true,"slider":null,"value":-5886446315.167628,"display":"-5,886,446,315.17"}]},{"id":"great-circle-distance-advanced","title":"Great Circle Distance Advanced","description":"Calculate great-circle distance between two coordinates using the haversine formula.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"radius_of_earth_kilometers = 6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"lat1_degrees = 40.71","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40.71,"display":"40.71"},{"text":"lon1_degrees = -74.00","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-74,"display":"-74"},{"text":"lat2_degrees = 34.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":34.05,"display":"34.05"},{"text":"lon2_degrees = -118.24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-118.24,"display":"-118.24"},{"text":"dlat = lat2_degrees - lat1_degrees","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-6.66,"display":"-6.66"},{"text":"dlon = lon2_degrees - lon1_degrees","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-44.24,"display":"-44.24"},{"text":"a = (sin(dlat/2))^2 + cos(lat1_degrees) * cos(lat2_degrees) * (sin(dlon/2))^2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.09242515272053431,"display":"0.0924"},{"text":"c = 2 * atan2(sqrt(a), sqrt(1-a)) * pi / 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.6178087507443442,"display":"0.6178"},{"text":"distance_kilometers = radius_of_earth_kilometers * c // kilometers @hero","label":null,"prefix":null,"suffix":"kilometers","section":null,"hidden":false,"hero":true,"slider":null,"value":3936.059550992217,"display":"3,936.0596"}]},{"id":"great-circle-distance-haversine","title":"Great Circle Distance Haversine","description":"Calculate great-circle distance between two latitude/longitude points.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"lat1 = 40.7128","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40.7128,"display":"40.71"},{"text":"lon1 = -74.0060","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-74.006,"display":"-74.01"},{"text":"lat2 = 34.0522","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":34.0522,"display":"34.05"},{"text":"lon2 = -118.2437","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-118.2437,"display":"-118.24"},{"text":"r = 6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"dlat = lat2 - lat1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-6.6606,"display":"-6.661"},{"text":"dlon = lon2 - lon1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-44.2377,"display":"-44.24"},{"text":"a = sin(dlat / 2)**2 + cos(lat1) * cos(lat2) * sin(dlon / 2)**2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.09241091078348553,"display":"0.0924"},{"text":"c = 2 * atan2(a**0.5, (1 - a)**0.5) * pi / 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.6177595753586126,"display":"0.6178"},{"text":"distance = r * c","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3935.746254609721,"display":"3,935.7463"}]},{"id":"greenhouse-ventilation-requirement","title":"Greenhouse Ventilation","description":"Calculate required airflow for greenhouse 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Calculator","description":"Calculate CSS grid column widths from container and gap.","category":"design","icon":"grid","tags":["layout"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Container","label":null,"prefix":null,"suffix":null,"section":"Container","hero":false,"slider":null,"value":null,"display":null},{"text":"container width = 1200 // px 320..2560 by 10","label":null,"prefix":null,"suffix":"px","section":"Container","hidden":false,"hero":false,"slider":{"min":320,"max":2560,"step":10},"value":1200,"display":"1,200"},{"text":"columns = 12 // 1..24","label":null,"prefix":null,"suffix":null,"section":"Container","hidden":false,"hero":false,"slider":{"min":1,"max":24,"step":1},"value":12,"display":"12"},{"text":"gap = 24 // px 0..80 by 2","label":null,"prefix":null,"suffix":"px","section":"Container","hidden":false,"hero":false,"slider":{"min":0,"max":80,"step":2},"value":24,"display":"24"},{"text":"# Grid Calculations","label":null,"prefix":null,"suffix":null,"section":"Grid Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"total gap space = gap * (columns - 1) // px","label":null,"prefix":null,"suffix":"px","section":"Grid Calculations","hidden":false,"hero":false,"slider":null,"value":264,"display":"264"},{"text":"column width = round((container width - total gap space) / columns * 100) / 100 // px @hero","label":null,"prefix":null,"suffix":"px","section":"Grid Calculations","hidden":false,"hero":true,"slider":null,"value":78,"display":"78"},{"text":"# Span Widths","label":null,"prefix":null,"suffix":null,"section":"Span Widths","hero":false,"slider":null,"value":null,"display":null},{"text":"span 2 = round((column width * 2 + gap * 1) * 100) / 100 // px @label(2-column span)","label":"2-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"span 3 = round((column width * 3 + gap * 2) * 100) / 100 // px @label(3-column span)","label":"3-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":282,"display":"282"},{"text":"span 4 = round((column width * 4 + gap * 3) * 100) / 100 // px @label(4-column span)","label":"4-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":384,"display":"384"},{"text":"span 6 = round((column width * 6 + gap * 5) * 100) / 100 // px @label(6-column span)","label":"6-column span","prefix":null,"suffix":"px","section":"Span Widths","hidden":false,"hero":false,"slider":null,"value":588,"display":"588"},{"text":"# Percentages","label":null,"prefix":null,"suffix":null,"section":"Percentages","hero":false,"slider":null,"value":null,"display":null},{"text":"col width pct = round((column width / container width) * 100 * 100) / 100 // % @label(Column width %)","label":"Column width %","prefix":null,"suffix":"%","section":"Percentages","hidden":false,"hero":false,"slider":null,"value":6.5,"display":"6.5"},{"text":"gap pct = round((total gap space / container width) * 100 * 100) / 100 // % @label(Total gap %)","label":"Total gap %","prefix":null,"suffix":"%","section":"Percentages","hidden":false,"hero":false,"slider":null,"value":22,"display":"22"}]},{"id":"grit-score-estimator","title":"Grit Score Estimator","description":"Estimate a grit score from perseverance and passion ratings.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"perseverance_score = 4.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4.5,"display":"4.5"},{"text":"passion_score = 4.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"grit_score = (perseverance_score + passion_score) / 2 // score 1-5 @hero","label":null,"prefix":null,"suffix":"score 1-5","section":null,"hidden":false,"hero":true,"slider":null,"value":4.25,"display":"4.25"}]},{"id":"gross-rent-multiplier","title":"Gross Rent Multiplier","description":"Quick valuation tool for comparing rental properties in an area.","category":"real-estate","icon":"ratio","tags":["rent"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"propertyPrice = 350000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":350000,"display":"350,000"},{"text":"grossAnnualRent = 42000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":42000,"display":"42,000"},{"text":"grm = propertyPrice / grossAnnualRent // ratio @hero","label":null,"prefix":null,"suffix":"ratio","section":null,"hidden":false,"hero":true,"slider":null,"value":8.333333333333334,"display":"8.333"}]},{"id":"groupthink-risk-indicator","title":"Groupthink Risk Indicator","description":"Estimate groupthink risk from group size, homogeneity, and isolation factors.","category":"health","icon":"brain","tags":["risk"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"group_size = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"homogeneity_factor_1_to_10 = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"isolation_factor_1_to_10 = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"risk_index = (group_size * homogeneity_factor_1_to_10 * isolation_factor_1_to_10) / 100 // risk factor @hero","label":null,"prefix":null,"suffix":"risk factor","section":null,"hidden":false,"hero":true,"slider":null,"value":5.6,"display":"5.6"}]},{"id":"guild-contribution-point-ratio","title":"Guild Contribution Point Ratio","description":"Calculate contribution points earned from donations.","category":"math","icon":"users","tags":["gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Donation Settings","label":null,"prefix":null,"suffix":null,"section":"Donation Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"gold donated = 50000","label":null,"prefix":null,"suffix":null,"section":"Donation Settings","hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"gold to point ratio = 1000","label":null,"prefix":null,"suffix":null,"section":"Donation Settings","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"contribution points = gold donated / gold to point ratio","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"}]},{"id":"gutter-capacity-slope","title":"Gutter Capacity and Slope","description":"Calculate required gutter size based on roof area and rainfall.","category":"construction","icon":"cloud-rain","tags":["construction","home"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"roof_area_square_meters = 200 // square meters","label":null,"prefix":null,"suffix":"square meters","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"rainfall_intensity_mm_per_hour = 50 // mm/hr","label":null,"prefix":null,"suffix":"mm/hr","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"total_flow_liters_per_second = (roof_area_square_meters * rainfall_intensity_mm_per_hour) / 3600 // L/s","label":null,"prefix":null,"suffix":"L/s","section":null,"hidden":false,"hero":false,"slider":null,"value":2.7777777777777777,"display":"2.778"},{"text":"gutter_slope_percent = 0.5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"required_gutter_cross_section_sq_cm = (total_flow_liters_per_second * 10) / (gutter_slope_percent^0.5) // sq cm @hero","label":null,"prefix":null,"suffix":"sq cm","section":null,"hidden":false,"hero":true,"slider":null,"value":39.2837100659193,"display":"39.28"}]},{"id":"habit-cue-reward-timing","title":"Habit Cue Reward Timing","description":"Calculate habit reinforcement strength based on cue-to-reward 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remaining radioactive material after time elapsed using half-life.","category":"science","icon":"flask-conical","tags":["life","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Decay Stats","label":null,"prefix":null,"suffix":null,"section":"Decay Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"initial amount = 100 // grams 0.1..10k","label":null,"prefix":null,"suffix":"grams","section":"Decay Stats","hidden":false,"hero":false,"slider":{"min":0.1,"max":10000,"step":100},"value":100,"display":"100"},{"text":"half life = 5730 // years 0.1..1e9","label":null,"prefix":null,"suffix":"years","section":"Decay Stats","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000000000,"step":10000000},"value":5730,"display":"5,730"},{"text":"time elapsed = 1000 // years 0..1e9","label":null,"prefix":null,"suffix":"years","section":"Decay 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life","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":0.00012096806282722514,"display":"0.000121"},{"text":"percent remaining = (remaining amount / initial amount) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Progress","hidden":false,"hero":false,"slider":null,"value":88.60622295433987,"display":"88.61"},{"text":"amount lost = initial amount - remaining amount","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":11.39377704566013,"display":"11.39"},{"text":"fractional remaining = remaining amount / initial amount","label":null,"prefix":null,"suffix":null,"section":"Progress","hidden":false,"hero":false,"slider":null,"value":0.8860622295433987,"display":"0.8861"}]},{"id":"half-life-radioactive-atoms-remaining","title":"Half Life Radioactive Atoms Remaining","description":"Calculate radioactive atoms remaining after a number of half-lives.","category":"education","icon":"book-open","tags":["life","radioactive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"initial_atoms = 1000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"half_life_seconds = 60 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"time_elapsed_seconds = 180 // seconds","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"_number_of_half_lives = time_elapsed_seconds / half_life_seconds","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"atoms_remaining = initial_atoms * (0.5)^number_of_half_lives // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":125000,"display":"125,000"}]},{"id":"half-life","title":"Half-Life","description":"Remaining amount after time t given half-life: N(t) = N₀ · (1/2)^(t/T½).","category":"formulas","icon":"timer","tags":["half-life"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"initial_amount = 100 // 0..1M","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"half_life = 5 // 0.01..10k","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.01,"max":10000,"step":100},"value":5,"display":"5"},{"text":"time = 10 // 0..100k","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":1000},"value":10,"display":"10"},{"text":"# Remaining amount","label":null,"prefix":null,"suffix":null,"section":"Remaining amount","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = initial_amount * (1 / 2)^(time / half_life) // @hero @label(N(t))","label":"N(t)","prefix":null,"suffix":null,"section":"Remaining amount","hidden":false,"hero":true,"slider":null,"value":25,"display":"25"},{"text":"decay_constant = log(2) / half_life // @label(Decay constant λ)","label":"Decay constant λ","prefix":null,"suffix":null,"section":"Remaining amount","hidden":false,"hero":false,"slider":null,"value":0.060205999132796235,"display":"0.0602"}]},{"id":"halo-effect-bias-estimate","title":"Halo Effect Bias Estimate","description":"Estimate perceived intelligence boost from the halo effect of attractiveness.","category":"health","icon":"brain","tags":["effect"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.700Z"},"rows":[{"text":"attractiveness_rating = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"perceived_intelligence_boost = attractiveness_rating * 0.5 // bias points @hero","label":null,"prefix":null,"suffix":"bias points","section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"hammock-hang-angle-tension","title":"Hammock Hang Angle Tension","description":"Calculate cord tension based on body weight and hang angle.","category":"everyday","icon":"anchor","tags":["everyday","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"body_weight_lbs = 180 // lbs","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"hang_angle_degrees = 30 // degrees (30 is ideal)","label":null,"prefix":null,"suffix":"degrees (30 is ideal)","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"cord_tension_lbs = (body_weight_lbs / 2) / sin(hang_angle_degrees) // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":true,"slider":null,"value":180.00000000000003,"display":"180"}]},{"id":"hamster-life-stage","title":"Hamster Life Stage","description":"Calculate a hamster's equivalent human age from months lived vs average lifespan.","category":"health","icon":"activity","tags":["life","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"hamster_age_months = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"average_lifespan_months = 24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"life_percentage = (hamster_age_months / average_lifespan_months) * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"equivalent_human_age = life_percentage * 0.8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":40,"display":"40"}]},{"id":"happiness-set-point-adjuster","title":"Happiness Set Point Adjuster","description":"Calculate a total happiness score from baseline, circumstances, and intentional 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loans.","category":"real-estate","icon":"dollar-sign","tags":["loan"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"loanAmount = 150000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":150000,"display":"150,000"},{"text":"interestRateAnnual = 12 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"loanPoints = 2 // points","label":null,"prefix":null,"suffix":"points","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"loanTermMonths = 6 // months","label":null,"prefix":null,"suffix":"months","section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"_interestCost = (loanAmount * (interestRateAnnual / 100) / 12) * loanTermMonths","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":9000,"display":"9,000"},{"text":"_pointsCost = loanAmount * (loanPoints / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"totalLoanCost = interestCost + pointsCost // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12000,"display":"12,000"}]},{"id":"hash-collision","title":"Hash Collision Probability","description":"Calculate collision probability using the birthday problem for any hash size.","category":"programming","icon":"fingerprint-pattern","tags":["birthday","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Hash Parameters","label":null,"prefix":null,"suffix":null,"section":"Hash 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total_hash_space)","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":1.4693679385278594e-27,"display":"1.4694e-27"},{"text":"# Birthday Problem","label":null,"prefix":null,"suffix":null,"section":"Birthday Problem","hero":false,"slider":null,"value":null,"display":null},{"text":"prob no collision = E^(-(number_of_items_hashed * (number_of_items_hashed - 1)) / (2 * total_hash_space)) // @label(P(no collision))","label":"P(no collision)","prefix":null,"suffix":null,"section":"Birthday Problem","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"prob at least one collision = 1 - prob_no_collision // @hero @label(P(at least one collision))","label":"P(at least one collision)","prefix":null,"suffix":null,"section":"Birthday Problem","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"},{"text":"# 50% Collision Threshold","label":null,"prefix":null,"suffix":null,"section":"50% Collision Threshold","hero":false,"slider":null,"value":null,"display":null},{"text":"items needed for 50 pct collision chance = sqrt(2 * total_hash_space * ln(2))","label":null,"prefix":null,"suffix":null,"section":"50% Collision Threshold","hidden":false,"hero":false,"slider":null,"value":21719381355163560000,"display":"2.1719e19"}]},{"id":"health-savings-account-hsa-growth","title":"Health Savings Account Hsa Growth","description":"Calculate the future value of HSA contributions invested over 20 years.","category":"finance","icon":"heart","tags":["health","account","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"annual_contribution = 3850","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3850,"display":"3,850"},{"text":"years = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"expected_return = 0.07","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.07,"display":"0.07"},{"text":"future_value = annual_contribution * (((1 + expected_return) ** years - 1) / expected_return)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":157832.64543674007,"display":"157,832.65"}]},{"id":"heart-rate-zones","title":"Heart Rate Zones","description":"Find your training heart rate zones using the Karvonen method.","category":"health","icon":"heart-pulse","tags":["training"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Your Info","label":null,"prefix":null,"suffix":null,"section":"Your Info","hero":false,"slider":null,"value":null,"display":null},{"text":"age = 30 // years 15..85","label":null,"prefix":null,"suffix":"years","section":"Your Info","hidden":false,"hero":false,"slider":{"min":15,"max":85,"step":1},"value":30,"display":"30"},{"text":"resting heart rate = 65 // bpm 40..100","label":null,"prefix":null,"suffix":"bpm","section":"Your Info","hidden":false,"hero":false,"slider":{"min":40,"max":100,"step":1},"value":65,"display":"65"},{"text":"# Max Heart Rate","label":null,"prefix":null,"suffix":null,"section":"Max Heart Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"estimated max heart rate = 220 - age // bpm @hero","label":null,"prefix":null,"suffix":"bpm","section":"Max Heart Rate","hidden":false,"hero":true,"slider":null,"value":190,"display":"190"},{"text":"heart rate reserve = estimated_max_heart_rate - resting_heart_rate // bpm","label":null,"prefix":null,"suffix":"bpm","section":"Max Heart Rate","hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"# Training Zones (Karvonen Method)","label":null,"prefix":null,"suffix":null,"section":"Training Zones (Karvonen Method)","hero":false,"slider":null,"value":null,"display":null},{"text":"zone 1 recovery low = resting_heart_rate + heart_rate_reserve * 0.50 // bpm @label(Zone 1: Recovery (50%))","label":"Zone 1: Recovery (50%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":127.5,"display":"127.5"},{"text":"zone 1 recovery high = resting_heart_rate + heart_rate_reserve * 0.60 // bpm @label(Zone 1: Recovery (60%))","label":"Zone 1: Recovery (60%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":140,"display":"140"},{"text":"zone 2 aerobic low = resting_heart_rate + heart_rate_reserve * 0.60 // bpm @label(Zone 2: Aerobic (60%))","label":"Zone 2: Aerobic (60%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":140,"display":"140"},{"text":"zone 2 aerobic high = resting_heart_rate + heart_rate_reserve * 0.70 // bpm @label(Zone 2: Aerobic (70%))","label":"Zone 2: Aerobic (70%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":152.5,"display":"152.5"},{"text":"zone 3 tempo low = resting_heart_rate + heart_rate_reserve * 0.70 // bpm @label(Zone 3: Tempo (70%))","label":"Zone 3: Tempo (70%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":152.5,"display":"152.5"},{"text":"zone 3 tempo high = resting_heart_rate + heart_rate_reserve * 0.80 // bpm @label(Zone 3: Tempo (80%))","label":"Zone 3: Tempo (80%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":165,"display":"165"},{"text":"zone 4 threshold low = resting_heart_rate + heart_rate_reserve * 0.80 // bpm @label(Zone 4: Threshold (80%))","label":"Zone 4: Threshold (80%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":165,"display":"165"},{"text":"zone 4 threshold high = resting_heart_rate + heart_rate_reserve * 0.90 // bpm @label(Zone 4: Threshold (90%))","label":"Zone 4: Threshold (90%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":177.5,"display":"177.5"},{"text":"zone 5 max low = resting_heart_rate + heart_rate_reserve * 0.90 // bpm @label(Zone 5: Max (90%))","label":"Zone 5: Max (90%)","prefix":null,"suffix":"bpm","section":"Training Zones (Karvonen Method)","hidden":false,"hero":false,"slider":null,"value":177.5,"display":"177.5"},{"text":"zone 5 max high = estimated_max_heart_rate // bpm @label(Zone 5: Max (100%))","label":"Zone 5: Max 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Daily","label":null,"prefix":null,"suffix":null,"section":"Daily","hero":false,"slider":null,"value":null,"display":null},{"text":"beats per hour = resting bpm * 60","label":null,"prefix":null,"suffix":null,"section":"Daily","hidden":false,"hero":false,"slider":null,"value":4200,"display":"4,200"},{"text":"beats per day = resting bpm * 60 * 24 // @hero","label":null,"prefix":null,"suffix":null,"section":"Daily","hidden":false,"hero":true,"slider":null,"value":100800,"display":"100,800"},{"text":"# Longer","label":null,"prefix":null,"suffix":null,"section":"Longer","hero":false,"slider":null,"value":null,"display":null},{"text":"beats per year = beats per day * 365","label":null,"prefix":null,"suffix":null,"section":"Longer","hidden":false,"hero":false,"slider":null,"value":36792000,"display":"36,792,000"},{"text":"lifetime years = 80 // years 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Only: 1, Principal and Interest: 2})","label":null,"prefix":null,"suffix":null,"section":"HELOC Terms","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_monthly_interest_payment = heloc balance * (interest rate / 100 / 12)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":354.16666666666663,"display":"$354.17"},{"text":"$_monthly_principal_and_interest = heloc balance * (interest rate/1200 * (1+interest rate/1200)^240) / ((1+interest rate/1200)^240 - 1) // assumes 20yr","label":null,"prefix":"$","suffix":"assumes 20yr","section":"Calculations","hidden":true,"hero":false,"slider":null,"value":433.91161668276703,"display":"$433.91"},{"text":"# 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0..50","label":null,"prefix":null,"suffix":"miles","section":"Route Details","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":5,"display":"5"},{"text":"elevation gain = 2000 // feet 0..10k","label":null,"prefix":null,"suffix":"feet","section":"Route Details","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":2000,"display":"2,000"},{"text":"# Naismith's Rule","label":null,"prefix":null,"suffix":null,"section":"Naismith's Rule","hero":false,"slider":null,"value":null,"display":null},{"text":"distance km = horizontal distance * 1.60934","label":null,"prefix":null,"suffix":null,"section":"Naismith's Rule","hidden":false,"hero":false,"slider":null,"value":8.0467,"display":"8.047"},{"text":"ascent meters = elevation gain * 0.3048","label":null,"prefix":null,"suffix":null,"section":"Naismith's Rule","hidden":false,"hero":false,"slider":null,"value":609.6,"display":"609.6"},{"text":"# 1 hour per 5km + 1 hour per 600m 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total hiking time / 60","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":2.62534,"display":"2.625"},{"text":"walking speed = horizontal distance / (total hiking time / 60) // mph","label":null,"prefix":null,"suffix":"mph","section":"Result","hidden":false,"hero":false,"slider":null,"value":1.9045152246947061,"display":"1.905"}]},{"id":"hipaa-violation-penalty-hypothetical","title":"HIPAA Penalty Estimator","description":"Estimate hypothetical HIPAA penalties for data violations.","category":"other","icon":"activity","tags":["penalty"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"numberOfViolations = 10 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"penaltyPerViolation = 1000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"totalPenalty = numberOfViolations * penaltyPerViolation // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":10000,"display":"10,000"}]},{"id":"hockey-save-percentage","title":"Hockey Save Percentage","description":"Calculate hockey goalie save percentage.","category":"health","icon":"activity","tags":["sports"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Stats","label":null,"prefix":null,"suffix":null,"section":"Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"saves = 28","label":null,"prefix":null,"suffix":null,"section":"Stats","hidden":false,"hero":false,"slider":null,"value":28,"display":"28"},{"text":"shots on goal = 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%","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"status = if(requested loan amount <= max_equity_loan_available, \"Approved\", \"Exceeds LTV limit\")","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Approved","display":"Approved"}]},{"id":"home-inspection-cost-estimate","title":"Home Inspection Cost","description":"Estimate the cost of a professional home inspection by size.","category":"real-estate","icon":"search","tags":["home"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"squareFootage = 2000 // square feet","label":null,"prefix":null,"suffix":"square feet","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"baseFee = 300 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"feePerSquareFoot = 0.05 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"estimatedInspectionCost = baseFee + (squareFootage * feePerSquareFoot) // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":400,"display":"400"}]},{"id":"home-insulation-roi","title":"Home Insulation ROI","description":"Calculate savings and break-even point for home insulation.","category":"finance","icon":"home","tags":["finance","insulation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"insulation_cost = 2000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"annual_energy_savings_dollars = 400 // dollars per year","label":null,"prefix":null,"suffix":"dollars per year","section":null,"hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"years_to_break_even = insulation_cost / annual_energy_savings_dollars // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"twenty_year_total_savings = (annual_energy_savings_dollars * 20) - insulation_cost // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":6000,"display":"6,000"}]},{"id":"homebrew-og-fg-abv","title":"Homebrew Og Fg Abv","description":"Calculate beer ABV, attenuation, and calories from original and final gravity.","category":"everyday","icon":"home","tags":["abv","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Brewing Stats","label":null,"prefix":null,"suffix":null,"section":"Brewing Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"original gravity = 1.050 // 1..1.12","label":null,"prefix":null,"suffix":null,"section":"Brewing Stats","hidden":false,"hero":false,"slider":{"min":1,"max":1.12,"step":0.002},"value":1.05,"display":"1.05"},{"text":"final gravity = 1.010 // 1..1.04","label":null,"prefix":null,"suffix":null,"section":"Brewing Stats","hidden":false,"hero":false,"slider":{"min":1,"max":1.04,"step":0.0005},"value":1.01,"display":"1.01"},{"text":"# ABV Formula","label":null,"prefix":null,"suffix":null,"section":"ABV Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"abv = (original gravity - final gravity) * 131.25","label":null,"prefix":null,"suffix":null,"section":"ABV Formula","hidden":false,"hero":false,"slider":null,"value":5.25,"display":"5.25"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"alcohol by volume = abv // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":5.25,"display":"5.25"},{"text":"# Details","label":null,"prefix":null,"suffix":null,"section":"Details","hero":false,"slider":null,"value":null,"display":null},{"text":"apparent attenuation = (original gravity - final gravity) / (original gravity - 1) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Details","hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"calories per twelve oz = (6.9 * abv) + 355 * (original gravity - 1) * (0.1808 * original gravity + 0.8192) // kcal","label":null,"prefix":null,"suffix":"kcal","section":"Details","hidden":false,"hero":false,"slider":null,"value":54.13546,"display":"54.14"},{"text":"total calories = round(calories per twelve oz)","label":null,"prefix":null,"suffix":null,"section":"Details","hidden":false,"hero":false,"slider":null,"value":54,"display":"54"}]},{"id":"honey-bee-colony-growth","title":"Honey Bee Colony Growth","description":"Estimate honey bee colony growth from queen laying rate and worker lifespan.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"starting_bees = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"days_passed = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"queen_laying_rate_per_day = 1500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"worker_lifespan_days = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"bees_born = days_passed * queen_laying_rate_per_day","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45000,"display":"45,000"},{"text":"bees_died = (starting_bees / worker_lifespan_days) * days_passed","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6666.666666666668,"display":"6,666.67"},{"text":"estimated_colony_size = starting_bees + bees_born - bees_died // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":48333.33333333333,"display":"48,333.33"}]},{"id":"hookes-law-spring-constant","title":"Hookes Law Spring Constant","description":"Calculate a spring constant and elastic potential energy using Hooke's Law.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"force = 10 // Newtons","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"displacement = 0.05 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"spring_constant_k = force / displacement // Newtons per meter @hero","label":null,"prefix":null,"suffix":"Newtons per meter","section":null,"hidden":false,"hero":true,"slider":null,"value":200,"display":"200"},{"text":"elastic_potential_energy = 0.5 * spring_constant_k * displacement^2 // Joules @hero","label":null,"prefix":null,"suffix":"Joules","section":null,"hidden":false,"hero":true,"slider":null,"value":0.25000000000000006,"display":"0.25"}]},{"id":"hop-bitterness-ibus","title":"Hop Bitterness Ibus","description":"Calculate beer IBUs from hop weight, alpha acid percent, and boil time.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"hop_weight_ounces = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"alpha_acid_percent = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"boil_time_minutes = 60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"batch_size_gallons = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"utilization = 0.25 // Estimate for 60 min boil","label":null,"prefix":null,"suffix":"Estimate for 60 min boil","section":null,"hidden":false,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"ibu = (hop_weight_ounces * alpha_acid_percent * utilization * 74.89) / batch_size_gallons // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":37.445,"display":"37.45"}]},{"id":"horse-height-hands-to-cm","title":"Horse Height Hands To Cm","description":"Convert a horse's height in hands to centimeters.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"height_in_hands = 15.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15.2,"display":"15.2"},{"text":"whole_hands = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"inches_remainder = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total_inches = (whole_hands * 4) + inches_remainder","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":62,"display":"62"},{"text":"height_in_centimeters = total_inches * 2.54","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":157.48,"display":"157.48"}]},{"id":"horsepower-to-torque-converter","title":"Horsepower To Torque Converter","description":"Convert horsepower to torque at a given RPM.","category":"engineering","icon":"settings","tags":["automotive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Specs","label":null,"prefix":null,"suffix":null,"section":"Specs","hero":false,"slider":null,"value":null,"display":null},{"text":"horsepower = 300","label":null,"prefix":null,"suffix":null,"section":"Specs","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"rpm = 5252","label":null,"prefix":null,"suffix":null,"section":"Specs","hidden":false,"hero":false,"slider":null,"value":5252,"display":"5,252"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"torque foot pounds = (horsepower * 5252) / rpm","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":300,"display":"300"}]},{"id":"hot-tub-heating-time","title":"Hot Tub Heating Time","description":"Calculate hours needed to heat a hot tub based on volume.","category":"everyday","icon":"thermometer","tags":["everyday","pool"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"volume_liters = 1500 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"heater_kilowatts = 4 // kW","label":null,"prefix":null,"suffix":"kW","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"initial_temp_celsius = 15 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"target_temp_celsius = 38 // C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":38,"display":"38"},{"text":"energy_needed_kwh = volume_liters * (target_temp_celsius - initial_temp_celsius) * 0.00116 // kWh","label":null,"prefix":null,"suffix":"kWh","section":null,"hidden":false,"hero":false,"slider":null,"value":40.02,"display":"40.02"},{"text":"heating_time_hours = energy_needed_kwh / heater_kilowatts // hours @hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":10.005,"display":"10.01"}]},{"id":"hourly-to-salary","title":"Hourly to Salary","description":"Convert hourly rates to annual salary with tax deductions and overtime.","category":"business","icon":"briefcase","tags":["salary"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Hourly Input","label":null,"prefix":null,"suffix":null,"section":"Hourly Input","hero":false,"slider":null,"value":null,"display":null},{"text":"hourly rate = $35 // 7..200 by 0.5","label":null,"prefix":"$","suffix":null,"section":"Hourly Input","hidden":false,"hero":false,"slider":{"min":7,"max":200,"step":0.5},"value":35,"display":"$35.00"},{"text":"hours per week = 40 // 10..80","label":null,"prefix":null,"suffix":null,"section":"Hourly Input","hidden":false,"hero":false,"slider":{"min":10,"max":80,"step":1},"value":40,"display":"40"},{"text":"weeks per year = 52 // 40..52","label":null,"prefix":null,"suffix":null,"section":"Hourly Input","hidden":false,"hero":false,"slider":{"min":40,"max":52,"step":0.2},"value":52,"display":"52"},{"text":"# Annual Salary","label":null,"prefix":null,"suffix":null,"section":"Annual Salary","hero":false,"slider":null,"value":null,"display":null},{"text":"$annual gross salary = hourly_rate * hours_per_week * weeks_per_year // @hero","label":null,"prefix":"$","suffix":null,"section":"Annual Salary","hidden":false,"hero":true,"slider":null,"value":72800,"display":"$72,800.00"},{"text":"$monthly gross = annual_gross_salary / 12","label":null,"prefix":"$","suffix":null,"section":"Annual Salary","hidden":false,"hero":false,"slider":null,"value":6066.666666666667,"display":"$6,066.67"},{"text":"$biweekly gross = annual_gross_salary / 26","label":null,"prefix":"$","suffix":null,"section":"Annual Salary","hidden":false,"hero":false,"slider":null,"value":2800,"display":"$2,800.00"},{"text":"# After Deductions","label":null,"prefix":null,"suffix":null,"section":"After Deductions","hero":false,"slider":null,"value":null,"display":null},{"text":"effective tax rate = 25 // % 0..50","label":null,"prefix":null,"suffix":"%","section":"After Deductions","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":25,"display":"25"},{"text":"$annual take home = annual_gross_salary * (1 - effective_tax_rate / 100)","label":null,"prefix":"$","suffix":null,"section":"After Deductions","hidden":false,"hero":false,"slider":null,"value":54600,"display":"$54,600.00"},{"text":"$monthly take home = annual_take_home / 12","label":null,"prefix":"$","suffix":null,"section":"After Deductions","hidden":false,"hero":false,"slider":null,"value":4550,"display":"$4,550.00"},{"text":"$effective hourly after tax = annual_take_home / (hours_per_week * weeks_per_year)","label":null,"prefix":"$","suffix":null,"section":"After Deductions","hidden":false,"hero":false,"slider":null,"value":26.25,"display":"$26.25"},{"text":"# Overtime","label":null,"prefix":null,"suffix":null,"section":"Overtime","hero":false,"slider":null,"value":null,"display":null},{"text":"$overtime rate = hourly rate * 1.5","label":null,"prefix":"$","suffix":null,"section":"Overtime","hidden":false,"hero":false,"slider":null,"value":52.5,"display":"$52.50"},{"text":"overtime hours per week = 5 // 0..30","label":null,"prefix":null,"suffix":null,"section":"Overtime","hidden":false,"hero":false,"slider":{"min":0,"max":30,"step":1},"value":5,"display":"5"},{"text":"$weekly overtime pay = overtime hours per week * overtime rate","label":null,"prefix":"$","suffix":null,"section":"Overtime","hidden":false,"hero":false,"slider":null,"value":262.5,"display":"$262.50"}]},{"id":"hsl-to-rgb-color-converter","title":"Hsl To Rgb Color Converter","description":"Convert HSL color values to RGB components.","category":"design","icon":"palette","tags":["rgb","color"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"hue = 180 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"saturation_percent = 50 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"lightness_percent = 50 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"_s = saturation_percent / 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_l = lightness_percent / 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_c = (1 - abs(2 * l - 1)) * s","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_x = c * (1 - abs(mod(hue / 60, 2) - 1))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_m = l - c / 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"_sextant = floor(hue / 60)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_r1 = if(sextant == 0, c, if(sextant == 1, x, if(sextant == 2, 0, if(sextant == 3, 0, if(sextant == 4, x, c)))))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"_g1 = if(sextant == 0, x, if(sextant == 1, c, if(sextant == 2, c, if(sextant == 3, x, if(sextant == 4, 0, 0)))))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_b1 = if(sextant == 0, 0, if(sextant == 1, 0, if(sextant == 2, x, if(sextant == 3, c, if(sextant == 4, c, x)))))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"red_rgb = round((r1 + m) * 255) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":64,"display":"64"},{"text":"green_rgb = round((g1 + m) * 255) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":191,"display":"191"},{"text":"blue_rgb = round((b1 + m) * 255) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":191,"display":"191"}]},{"id":"hubble-law-distance","title":"Hubble Law Distance","description":"Calculate distance to a galaxy in megaparsecs using Hubble's Law.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"velocity_km_s = 7000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7000,"display":"7,000"},{"text":"hubble_constant = 70 // km/s/Mpc","label":null,"prefix":null,"suffix":"km/s/Mpc","section":null,"hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"distance_megaparsecs = velocity_km_s / hubble_constant // Megaparsecs @hero","label":null,"prefix":null,"suffix":"Megaparsecs","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"hue-rotation-degree-shift","title":"Hue Rotation Degree Shift","description":"Calculate a new HSL hue after rotating by a degree amount.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"original_hue = 100 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"rotation_degrees = 45 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"new_hue = mod(original_hue + rotation_degrees, 360) // degrees @hero","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":true,"slider":null,"value":145,"display":"145"}]},{"id":"hula-hoop-rotations","title":"Hula Hoop Rotations","description":"Calculate total hula hoop rotations from rpm and duration.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"rotations_per_minute = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"time_minutes = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"total_rotations = rotations_per_minute * time_minutes // rotations @hero","label":null,"prefix":null,"suffix":"rotations","section":null,"hidden":false,"hero":true,"slider":null,"value":500,"display":"500"}]},{"id":"humidity-adjustment-for-bread","title":"Humidity Adjustment For Bread","description":"Adjust bread recipe water grams based on ambient humidity.","category":"science","icon":"flask-conical","tags":["humidity","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"standard_water_grams = 350","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"relative_humidity_percent = 80","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"humidity_factor = (relative_humidity_percent - 50) / 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"water_adjustment_grams = -5 * humidity_factor","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":-1.5,"display":"-1.5"},{"text":"adjusted_water_grams = standard_water_grams + water_adjustment_grams // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":348.5,"display":"348.5"}]},{"id":"humidity-dew-point","title":"Humidity Dew Point","description":"Calculate dew point and humidity comfort level using the Magnus-Tetens formula.","category":"science","icon":"flask-conical","tags":["humidity","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Environment","label":null,"prefix":null,"suffix":null,"section":"Environment","hero":false,"slider":null,"value":null,"display":null},{"text":"air temperature = 75 // fahrenheit 32..110","label":null,"prefix":null,"suffix":"fahrenheit","section":"Environment","hidden":false,"hero":false,"slider":{"min":32,"max":110,"step":1},"value":75,"display":"75"},{"text":"relative humidity = 50 // % 1..100","label":null,"prefix":null,"suffix":"%","section":"Environment","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":50,"display":"50"},{"text":"# Magnus-Tetens Formula","label":null,"prefix":null,"suffix":null,"section":"Magnus-Tetens Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"temp celsius = (air temperature - 32) * 5 / 9","label":null,"prefix":null,"suffix":null,"section":"Magnus-Tetens Formula","hidden":false,"hero":false,"slider":null,"value":23.88888888888889,"display":"23.89"},{"text":"gamma = (17.27 * temp celsius / (237.7 + temp celsius)) + ln(relative humidity / 100)","label":null,"prefix":null,"suffix":null,"section":"Magnus-Tetens Formula","hidden":false,"hero":false,"slider":null,"value":0.8839882737152105,"display":"0.884"},{"text":"dew point celsius = (237.7 * gamma) / (17.27 - gamma)","label":null,"prefix":null,"suffix":null,"section":"Magnus-Tetens Formula","hidden":false,"hero":false,"slider":null,"value":12.823377413128894,"display":"12.82"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"dew point = (dew point celsius * 9 / 5) + 32 // fahrenheit @hero","label":null,"prefix":null,"suffix":"fahrenheit","section":"Result","hidden":false,"hero":true,"slider":null,"value":55.08207934363201,"display":"55.08"},{"text":"# Spread","label":null,"prefix":null,"suffix":null,"section":"Spread","hero":false,"slider":null,"value":null,"display":null},{"text":"temperature dew point spread = air temperature - dew point","label":null,"prefix":null,"suffix":null,"section":"Spread","hidden":false,"hero":false,"slider":null,"value":19.91792065636799,"display":"19.92"},{"text":"condensation risk = relative humidity > 90","label":null,"prefix":null,"suffix":null,"section":"Spread","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"is comfortable = dew point < 60","label":null,"prefix":null,"suffix":null,"section":"Spread","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"},{"text":"is humid = dew point > 65","label":null,"prefix":null,"suffix":null,"section":"Spread","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"is oppressive = dew point > 75","label":null,"prefix":null,"suffix":null,"section":"Spread","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"}]},{"id":"hunting-zero-distance-drop","title":"Hunting Zero Distance Drop","description":"Calculate hunting rifle bullet drop adjustment 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Environment","hidden":false,"hero":false,"slider":{"min":0,"max":300,"step":1},"value":60,"display":"60"},{"text":"sweat loss rate = exercise duration * 0.4 // ounces","label":null,"prefix":null,"suffix":"ounces","section":"Activity and Environment","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"temperature = 85 // fahrenheit 60..110","label":null,"prefix":null,"suffix":"fahrenheit","section":"Activity and Environment","hidden":false,"hero":false,"slider":{"min":60,"max":110,"step":1},"value":85,"display":"85"},{"text":"heat adjustment = max(0, (temperature - 80) * 2) // ounces","label":null,"prefix":null,"suffix":"ounces","section":"Activity and Environment","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"total daily water goal = base hydration + sweat loss rate + heat adjustment // ounces @hero","label":null,"prefix":null,"suffix":"ounces","section":"Result","hidden":false,"hero":true,"slider":null,"value":124,"display":"124"},{"text":"water in liters = total daily water goal * 0.0295735","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":3.667114,"display":"3.667"}]},{"id":"hydraulic-cylinder-force","title":"Hydraulic Cylinder Force","description":"Calculate extension and retraction force for hydraulics.","category":"engineering","icon":"settings-2","tags":["engineering"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"bore_diameter_inches = 3 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"system_pressure_psi = 2000 // psi","label":null,"prefix":null,"suffix":"psi","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"piston_area = 3.14159 * ((bore_diameter_inches / 2)^2) // sq inches","label":null,"prefix":null,"suffix":"sq inches","section":null,"hidden":false,"hero":false,"slider":null,"value":7.0685775,"display":"7.069"},{"text":"extension_force_lbs = system_pressure_psi * piston_area // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":null,"hidden":false,"hero":true,"slider":null,"value":14137.155,"display":"14,137.16"},{"text":"retraction_force_lbs = extension_force_lbs * 0.8 // assuming rod takes 20% area","label":null,"prefix":null,"suffix":"assuming rod takes 20% area","section":null,"hidden":false,"hero":false,"slider":null,"value":11309.724,"display":"11,309.72"}]},{"id":"hyperfocal-distance","title":"Hyperfocal Distance","description":"Calculate hyperfocal distance for a lens from focal length, aperture, and crop 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35mm)","label":null,"prefix":null,"suffix":null,"section":"Circle of Confusion (Commonly 0.03mm for 35mm)","hero":false,"slider":null,"value":null,"display":null},{"text":"coc = 0.03 / sensor crop factor","label":null,"prefix":null,"suffix":null,"section":"Circle of Confusion (Commonly 0.03mm for 35mm)","hidden":false,"hero":false,"slider":null,"value":0.02,"display":"0.02"},{"text":"# Formula: H = (f^2 / (N * c)) + f","label":null,"prefix":null,"suffix":null,"section":"Formula: H = (f^2 / (N * c)) + f","hero":false,"slider":null,"value":null,"display":null},{"text":"hyperfocal mm = (focal length^2 / (aperture * coc)) + focal length","label":null,"prefix":null,"suffix":null,"section":"Formula: H = (f^2 / (N * c)) + f","hidden":false,"hero":false,"slider":null,"value":15675,"display":"15,675"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"hyperfocal distance = hyperfocal mm / 1000 // meters @hero","label":null,"prefix":null,"suffix":"meters","section":"Result","hidden":false,"hero":true,"slider":null,"value":15.675,"display":"15.68"},{"text":"distance in feet = hyperfocal distance * 3.28084","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":51.427167,"display":"51.43"},{"text":"near limit at focus = hyperfocal distance / 2 // meters","label":null,"prefix":null,"suffix":"meters","section":"Result","hidden":false,"hero":false,"slider":null,"value":7.8375,"display":"7.838"},{"text":"far limit at focus = 9999 // infinity","label":null,"prefix":null,"suffix":"infinity","section":"Result","hidden":false,"hero":false,"slider":null,"value":9999,"display":"9,999"}]},{"id":"ice-cube-melt-time","title":"Ice Cube Melt Time","description":"Estimate ice cube melt time in minutes from size and ambient temperature.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"cube_side_cm = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"ambient_temp_c = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"melt_rate_factor = 0.01","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"time_minutes = (cube_side_cm^2) / (melt_rate_factor * (ambient_temp_c)) // minutes @hero","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"ideal-gas-law","title":"Ideal Gas Law","description":"Solve PV=nRT for any variable — pressure, volume, temperature, or moles.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Conditions","label":null,"prefix":null,"suffix":null,"section":"Conditions","hero":false,"slider":null,"value":null,"display":null},{"text":"pressure = 1 // atm 0.1..100","label":null,"prefix":null,"suffix":"atm","section":"Conditions","hidden":false,"hero":false,"slider":{"min":0.1,"max":100,"step":1},"value":1,"display":"1"},{"text":"volume = 22.4 // L 0.1..1k","label":null,"prefix":null,"suffix":"L","section":"Conditions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":22.4,"display":"22.4"},{"text":"temperature = 273.15 // K 1..1k","label":null,"prefix":null,"suffix":"K","section":"Conditions","hidden":false,"hero":false,"slider":{"min":1,"max":1000,"step":1},"value":273.15,"display":"273.15"},{"text":"# Constants","label":null,"prefix":null,"suffix":null,"section":"Constants","hero":false,"slider":null,"value":null,"display":null},{"text":"gas constant R = 0.08206 // L·atm/mol·K","label":null,"prefix":null,"suffix":"L·atm/mol·K","section":"Constants","hidden":false,"hero":false,"slider":null,"value":0.08206,"display":"0.0821"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"moles of gas = (pressure * volume) / (gas_constant_R * temperature) // mol @hero @label(Amount of Gas (n = PV/RT))","label":"Amount of Gas (n = PV/RT)","prefix":null,"suffix":"mol","section":"Results","hidden":false,"hero":true,"slider":null,"value":0.9993446708093965,"display":"0.9993"},{"text":"number of molecules = moles_of_gas * 6.022e23","label":null,"prefix":null,"suffix":null,"section":"Results","hidden":false,"hero":false,"slider":null,"value":6.0180536076141854e+23,"display":"6.0181e23"},{"text":"mass if O2 = moles_of_gas * 32 // g @label(Mass if O₂ (MW=32))","label":"Mass if O₂ (MW=32)","prefix":null,"suffix":"g","section":"Results","hidden":false,"hero":false,"slider":null,"value":31.979029465900684,"display":"31.98"},{"text":"mass if N2 = moles_of_gas * 28 // g @label(Mass if N₂ (MW=28))","label":"Mass if N₂ (MW=28)","prefix":null,"suffix":"g","section":"Results","hidden":false,"hero":false,"slider":null,"value":27.9816507826631,"display":"27.98"}]},{"id":"image-resize","title":"Image Resize","description":"Calculate new dimensions when resizing an image.","category":"design","icon":"image","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Original Image","label":null,"prefix":null,"suffix":null,"section":"Original Image","hero":false,"slider":null,"value":null,"display":null},{"text":"original width = 4032 // px 1..10k","label":null,"prefix":null,"suffix":"px","section":"Original Image","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":4032,"display":"4,032"},{"text":"original height = 3024 // px 1..10k","label":null,"prefix":null,"suffix":"px","section":"Original Image","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":3024,"display":"3,024"},{"text":"# Target","label":null,"prefix":null,"suffix":null,"section":"Target","hero":false,"slider":null,"value":null,"display":null},{"text":"target width = 1200 // px 1..10k","label":null,"prefix":null,"suffix":"px","section":"Target","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":1200,"display":"1,200"},{"text":"# Calculated Dimensions","label":null,"prefix":null,"suffix":null,"section":"Calculated Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"target height = round(original height * (target width / original width)) // px @hero","label":null,"prefix":null,"suffix":"px","section":"Calculated Dimensions","hidden":false,"hero":true,"slider":null,"value":900,"display":"900"},{"text":"scale factor = round(target width / original width * 10000) / 10000","label":null,"prefix":null,"suffix":null,"section":"Calculated Dimensions","hidden":false,"hero":false,"slider":null,"value":0.2976,"display":"0.2976"},{"text":"# File Size Estimate","label":null,"prefix":null,"suffix":null,"section":"File Size Estimate","hero":false,"slider":null,"value":null,"display":null},{"text":"original megapixels = round((original width * original height) / 1000000 * 100) / 100 // MP","label":null,"prefix":null,"suffix":"MP","section":"File Size Estimate","hidden":false,"hero":false,"slider":null,"value":12.19,"display":"12.19"},{"text":"new megapixels = round((target width * target height) / 1000000 * 100) / 100 // MP","label":null,"prefix":null,"suffix":"MP","section":"File Size Estimate","hidden":false,"hero":false,"slider":null,"value":1.08,"display":"1.08"},{"text":"size reduction pct = round((1 - (new megapixels / original megapixels)) * 100 * 10) / 10 // % @label(Pixel reduction)","label":"Pixel reduction","prefix":null,"suffix":"%","section":"File Size Estimate","hidden":false,"hero":false,"slider":null,"value":91.1,"display":"91.1"},{"text":"# Aspect Ratio","label":null,"prefix":null,"suffix":null,"section":"Aspect Ratio","hero":false,"slider":null,"value":null,"display":null},{"text":"ratio = round(original width / original height * 10000) / 10000 // @label(Aspect ratio (decimal))","label":"Aspect ratio (decimal)","prefix":null,"suffix":null,"section":"Aspect Ratio","hidden":false,"hero":false,"slider":null,"value":1.3333,"display":"1.333"}]},{"id":"inbound-freight-cost","title":"Inbound Freight Cost","description":"Track the average cost of shipments coming into your facility.","category":"business","icon":"corner-down-left","tags":["freight"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"totalInboundFreight = 8000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":8000,"display":"8,000"},{"text":"totalInboundShipments = 40 // shipments","label":null,"prefix":null,"suffix":"shipments","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"averageInboundCost = totalInboundFreight / totalInboundShipments // dollars per shipment @hero","label":null,"prefix":null,"suffix":"dollars per shipment","section":null,"hidden":false,"hero":true,"slider":null,"value":200,"display":"200"}]},{"id":"inductor-energy-storage","title":"Inductor Energy Storage","description":"Calculate energy stored in an inductor from inductance and current.","category":"health","icon":"activity","tags":["storage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"inductance_millihenries = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"current_amps = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"energy_stored_joules = 0.5 * (inductance_millihenries / 1000) * current_amps ** 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.2,"display":"0.2"}]},{"id":"inflation-adjusted-salary-history","title":"Inflation Adjusted Salary History","description":"Adjust a historical salary to today's dollars using CPI ratios.","category":"finance","icon":"dollar-sign","tags":["inflation","salary","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"past_salary = 50000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"past_cpi = 180","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":180,"display":"180"},{"text":"current_cpi = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"adjusted_salary = past_salary * (current_cpi / past_cpi)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":83333.33333333334,"display":"83,333.33"}]},{"id":"inflation-calculator","title":"Inflation Calculator","description":"See how inflation erodes purchasing power over time.","category":"finance","icon":"arrow-up-right","tags":["inflation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"$amount today = 1000 // 1..1M","label":null,"prefix":"$","suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":1000000,"step":10000},"value":1000,"display":"$1,000.00"},{"text":"inflation rate = 3 // % 0.5..15 by 0.5","label":null,"prefix":null,"suffix":"%","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.5,"max":15,"step":0.5},"value":3,"display":"3"},{"text":"years = 10 // 1..50","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":10,"display":"10"},{"text":"# Future Cost","label":null,"prefix":null,"suffix":null,"section":"Future Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$future equivalent = round(amount today * (1 + inflation rate / 100)^years * 100) / 100 // @label(Cost of Same Goods in Future) @hero","label":"Cost of Same Goods in Future","prefix":"$","suffix":null,"section":"Future Cost","hidden":false,"hero":true,"slider":null,"value":1343.92,"display":"$1,343.92"},{"text":"# Purchasing Power","label":null,"prefix":null,"suffix":null,"section":"Purchasing Power","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchasing power = round(amount today / (1 + inflation rate / 100)^years * 100) / 100 // @label(What Your Money Will Buy)","label":"What Your Money Will Buy","prefix":"$","suffix":null,"section":"Purchasing Power","hidden":false,"hero":false,"slider":null,"value":744.09,"display":"$744.09"},{"text":"$value lost = round((amount today - purchasing power) * 100) / 100 // @label(Purchasing Power Lost)","label":"Purchasing Power Lost","prefix":"$","suffix":null,"section":"Purchasing Power","hidden":false,"hero":false,"slider":null,"value":255.91,"display":"$255.91"},{"text":"loss pct = round((value lost / amount today) * 100 * 10) / 10 // % @label(Loss %)","label":"Loss %","prefix":null,"suffix":"%","section":"Purchasing Power","hidden":false,"hero":false,"slider":null,"value":25.6,"display":"25.6"}]},{"id":"information-overload-content-threshold","title":"Information Overload Content Threshold","description":"Calculate cognitive capacity utilization from items processed vs limit.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"items_processed_per_hour = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"cognitive_limit_per_hour = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"capacity_utilization_percent = (items_processed_per_hour / cognitive_limit_per_hour) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"information-ratio-investment","title":"Information Ratio Investment","description":"Calculate the information ratio for a portfolio from excess return and tracking error.","category":"math","icon":"ratio","tags":["investment","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"portfolio_return = 0.12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.12,"display":"0.12"},{"text":"benchmark_return = 0.10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"tracking_error = 0.04","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.04,"display":"0.04"},{"text":"information_ratio = (portfolio_return - benchmark_return) / tracking_error","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"insta-calc-completion-celebration","title":"Insta Calc Completion Celebration","description":"Calculate the completion percentage of an Instacalc gallery milestone.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"calculators_completed = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"target_goal = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"completion_percent = (calculators_completed / target_goal) * 100 // percent complete! 1000/1000 @suffix(%) @hero","label":null,"prefix":null,"suffix":"percent complete! 1000/1000","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"insulation-savings-r-value","title":"Insulation Savings R Value","description":"Estimate annual heating savings from upgrading attic insulation R-value.","category":"finance","icon":"dollar-sign","tags":["insulation","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"current_r_value = 11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":11,"display":"11"},{"text":"target_r_value = 38","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":38,"display":"38"},{"text":"attic_area_square_feet = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"heating_degree_days = 4000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4000,"display":"4,000"},{"text":"cost_per_therm = 1.20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.2,"display":"1.2"},{"text":"annual_heat_loss_reduction_therms = (attic_area_square_feet * heating_degree_days * 24) / 100000 * (1/current_r_value - 1/target_r_value)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":62.00956937799045,"display":"62.01"},{"text":"annual_savings_dollars = annual_heat_loss_reduction_therms * cost_per_therm // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":74.41148325358854,"display":"74.41"}]},{"id":"integral-power-rule","title":"Integral — Power Rule","description":"Evaluate ∫a·xⁿ dx = a·x^(n+1)/(n+1) at a given x.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"# Function: f(x) = a · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 4 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":4,"display":"4"},{"text":"x = 2 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = a · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":2,"display":"2"},{"text":"# Antiderivative at x","label":null,"prefix":null,"suffix":null,"section":"Antiderivative at x","hero":false,"slider":null,"value":null,"display":null},{"text":"antiderivative = a * x^(n + 1) / (n + 1) // @label(∫f(x) dx)","label":"∫f(x) dx","prefix":null,"suffix":null,"section":"Antiderivative at x","hidden":false,"hero":true,"slider":null,"value":19.2,"display":"19.2"}]},{"id":"intellectual-property-portfolio-value","title":"IP Portfolio Value","description":"Estimate the combined value of patents and trademarks.","category":"other","icon":"briefcase","tags":["property"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"numberOfPatents = 5 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"averageValuePerPatent = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"numberOfTrademarks = 3 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"averageValuePerTrademark = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"totalPortfolioValue = (numberOfPatents * averageValuePerPatent) + (numberOfTrademarks * averageValuePerTrademark) // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":295000,"display":"295,000"}]},{"id":"internal-rate-of-return-real-estate","title":"Real Estate IRR Estimator","description":"Estimate the internal rate of return for a property investment.","category":"real-estate","icon":"trending-up","tags":["estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.704Z"},"rows":[{"text":"initialInvestment = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"saleProceeds = 150000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":150000,"display":"150,000"},{"text":"yearsHeld = 5 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"estimatedIRR = ((saleProceeds / initialInvestment) ^ (1 / yearsHeld) - 1) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8.44717711976986,"display":"8.447"}]},{"id":"internal-rate-of-return","title":"Internal Rate of Return","description":"Calculate internal rate of return (IRR) from initial and final investment values.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Investment Return (CAGR Proxy for IRR)","label":null,"prefix":null,"suffix":null,"section":"Investment Return (CAGR Proxy for IRR)","hero":false,"slider":null,"value":null,"display":null},{"text":"$initial investment = 10000 // 100..1M","label":null,"prefix":"$","suffix":null,"section":"Investment Return (CAGR Proxy for IRR)","hidden":false,"hero":false,"slider":{"min":100,"max":1000000,"step":10000},"value":10000,"display":"$10,000.00"},{"text":"$final value = 15000 // 100..2M","label":null,"prefix":"$","suffix":null,"section":"Investment Return (CAGR Proxy for IRR)","hidden":false,"hero":false,"slider":{"min":100,"max":2000000,"step":20000},"value":15000,"display":"$15,000.00"},{"text":"years held = 3 // years 1..30","label":null,"prefix":null,"suffix":"years","section":"Investment Return (CAGR Proxy for IRR)","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":3,"display":"3"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"internal rate of return = ((final value / initial investment)^(1 / years held) - 1) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":14.471424255333181,"display":"14.47"},{"text":"$total profit = final value - initial investment","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":5000,"display":"$5,000.00"},{"text":"total return percentage = (final value / initial investment - 1) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"doubling time = 72 / internal rate of return // years (approx)","label":null,"prefix":null,"suffix":"years (approx)","section":"Result","hidden":false,"hero":false,"slider":null,"value":4.975322313107205,"display":"4.975"}]},{"id":"intrinsic-motivation-ratio","title":"Intrinsic Motivation Ratio","description":"Calculate the intrinsic-to-total motivation ratio from internal and external rewards.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"internal_rewards = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"external_rewards = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"motivation_ratio = internal_rewards / (internal_rewards + external_rewards) // intrinsic fraction @hero","label":null,"prefix":null,"suffix":"intrinsic fraction","section":null,"hidden":false,"hero":true,"slider":null,"value":0.7142857142857143,"display":"0.7143"}]},{"id":"inventory-carrying-cost","title":"Inventory Carrying Cost","description":"Determine the total cost of holding inventory in your facility.","category":"business","icon":"box","tags":["inventory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"averageInventoryValue = 200000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"carryingCostPercentage = 25 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"annualInventoryCarryingCost = averageInventoryValue * (carryingCostPercentage / 100) // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":50000,"display":"50,000"}]},{"id":"inventory-days-on-hand","title":"Inventory Days On Hand","description":"Calculate inventory days on hand from average inventory and COGS.","category":"business","icon":"briefcase","tags":["inventory","business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"average_inventory = 500000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500000,"display":"500,000"},{"text":"cost_of_goods_sold = 2000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000000,"display":"2,000,000"},{"text":"inventory_days = (average_inventory / cost_of_goods_sold) * 365","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":91.25,"display":"91.25"}]},{"id":"inventory-space-weight-capacity","title":"Inventory Space Weight Capacity","description":"Calculate remaining inventory weight capacity.","category":"productivity","icon":"archive","tags":["gaming","inventory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Inventory Settings","label":null,"prefix":null,"suffix":null,"section":"Inventory Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"max weight = 200","label":null,"prefix":null,"suffix":null,"section":"Inventory Settings","hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"current items weight = 145","label":null,"prefix":null,"suffix":null,"section":"Inventory Settings","hidden":false,"hero":false,"slider":null,"value":145,"display":"145"},{"text":"new item weight = 10","label":null,"prefix":null,"suffix":null,"section":"Inventory Settings","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"new item quantity = 3","label":null,"prefix":null,"suffix":null,"section":"Inventory Settings","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_new_weight = new item weight * new item quantity","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"remaining capacity = max weight - (current items weight + total_new_weight)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":25,"display":"25"}]},{"id":"inventory-turnover-ratio-logistics","title":"Inventory Turnover Ratio","description":"Measure how often inventory is replaced during a specific period.","category":"business","icon":"refresh-cw","tags":["inventory","turnover","logistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"costOfGoodsSold = 500000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":500000,"display":"500,000"},{"text":"averageInventoryValue = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"turnoverRatio = costOfGoodsSold / averageInventoryValue // times per year @hero","label":null,"prefix":null,"suffix":"times per year","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"inventory-turnover","title":"Inventory Turnover","description":"Calculate inventory turnover ratio and days to sell inventory.","category":"business","icon":"briefcase","tags":["inventory","turnover","business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Inventory Data","label":null,"prefix":null,"suffix":null,"section":"Inventory Data","hero":false,"slider":null,"value":null,"display":null},{"text":"$cost of goods sold = 250000 // 0..5M","label":null,"prefix":"$","suffix":null,"section":"Inventory 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(degrees)","hidden":false,"hero":true,"slider":null,"value":60.00000000000001,"display":"60"},{"text":"arctan_deg = atan(ratio) // @hero @label(arctan)","label":"arctan","prefix":null,"suffix":null,"section":"Inverse trig (degrees)","hidden":false,"hero":true,"slider":null,"value":26.56505117707799,"display":"26.5651"}]},{"id":"invoice-late-fee","title":"Invoice Late Fee","description":"Calculate interest owed on a late invoice.","category":"business","icon":"file-text","tags":["fee","interest"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Invoice Details","label":null,"prefix":null,"suffix":null,"section":"Invoice Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$invoice amount = 5000 // 100..1M","label":null,"prefix":"$","suffix":null,"section":"Invoice Details","hidden":false,"hero":false,"slider":{"min":100,"max":1000000,"step":10000},"value":5000,"display":"$5,000.00"},{"text":"annual interest 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Calculation","hidden":false,"hero":false,"slider":null,"value":110.96,"display":"$110.96"},{"text":"$total due = round((invoice amount + interest owed) * 100) / 100 // @hero","label":null,"prefix":"$","suffix":null,"section":"Interest Calculation","hidden":false,"hero":true,"slider":null,"value":5110.96,"display":"$5,110.96"},{"text":"# Rates","label":null,"prefix":null,"suffix":null,"section":"Rates","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly rate = round(annual interest rate / 12 * 100) / 100 // %","label":null,"prefix":null,"suffix":"%","section":"Rates","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"daily rate display = round(daily_rate * 100 * 10000) / 10000 // % @label(Daily rate)","label":"Daily rate","prefix":null,"suffix":"%","section":"Rates","hidden":false,"hero":false,"slider":null,"value":0.0493,"display":"0.0493"},{"text":"# If Payment Delayed Further","label":null,"prefix":null,"suffix":null,"section":"If 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Prefix","hero":false,"slider":null,"value":null,"display":null},{"text":"cidr prefix = 24 // /0..32","label":null,"prefix":null,"suffix":"0..32","section":"Subnet Prefix","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_bits_remaining = 32 - cidr prefix","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"total addresses = 2 ^ bits_remaining // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":256,"display":"256"},{"text":"usable hosts = total addresses - 2 // (subtract network and broadcast) @hero","label":null,"prefix":null,"suffix":"(subtract network and broadcast)","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":254,"display":"254"}]},{"id":"ip-v4-to-binary","title":"Ip V4 To Binary","description":"Convert an IPv4 address to its decimal integer value.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# IP Octets","label":null,"prefix":null,"suffix":null,"section":"IP Octets","hero":false,"slider":null,"value":null,"display":null},{"text":"octet 1 = 192 // 0..255","label":null,"prefix":null,"suffix":null,"section":"IP Octets","hidden":false,"hero":false,"slider":{"min":0,"max":255,"step":1},"value":192,"display":"192"},{"text":"octet 2 = 168 // 0..255","label":null,"prefix":null,"suffix":null,"section":"IP Octets","hidden":false,"hero":false,"slider":{"min":0,"max":255,"step":1},"value":168,"display":"168"},{"text":"octet 3 = 1 // 0..255","label":null,"prefix":null,"suffix":null,"section":"IP Octets","hidden":false,"hero":false,"slider":{"min":0,"max":255,"step":1},"value":1,"display":"1"},{"text":"octet 4 = 1 // 0..255","label":null,"prefix":null,"suffix":null,"section":"IP Octets","hidden":false,"hero":false,"slider":{"min":0,"max":255,"step":1},"value":1,"display":"1"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"decimal value = (octet 1 * 2^24) + (octet 2 * 2^16) + (octet 3 * 2^8) + octet 4","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":3232235777,"display":"3,232,235,777"}]},{"id":"ironman-finish-time-estimate","title":"Ironman Finish Time Estimate","description":"Estimate Ironman finish time in hours from swim, bike, run, and transition times.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"swim_time_minutes = 75","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":75,"display":"75"},{"text":"bike_time_minutes = 360","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"run_time_minutes = 270","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":270,"display":"270"},{"text":"transition_time_minutes = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"total_finish_time_hours = (swim_time_minutes + bike_time_minutes + run_time_minutes + transition_time_minutes) / 60 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12.083333333333334,"display":"12.08"}]},{"id":"irrigation-run-time","title":"Irrigation Run Time","description":"Calculate how many minutes to run sprinklers for target depth.","category":"everyday","icon":"sprinklers","tags":["garden","water"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"target_water_depth_mm = 25 // mm (typically 1 inch per week)","label":null,"prefix":null,"suffix":"mm (typically 1 inch per week)","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"sprinkler_output_liters_per_minute = 10 // liters per minute","label":null,"prefix":null,"suffix":"liters per minute","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"area_square_meters = 100 // square meters","label":null,"prefix":null,"suffix":"square 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level)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"iv-drip-rate","title":"Iv Drip Rate","description":"Calculate IV drip rate in drops per minute from volume, time, and drop factor.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Infusion Details","label":null,"prefix":null,"suffix":null,"section":"Infusion Details","hero":false,"slider":null,"value":null,"display":null},{"text":"total volume = 1000 // ml 50..3k","label":null,"prefix":null,"suffix":"ml","section":"Infusion Details","hidden":false,"hero":false,"slider":{"min":50,"max":3000,"step":50},"value":1000,"display":"1,000"},{"text":"time duration = 8 // hours 1..24","label":null,"prefix":null,"suffix":"hours","section":"Infusion Details","hidden":false,"hero":false,"slider":{"min":1,"max":24,"step":1},"value":8,"display":"8"},{"text":"drop factor = 20 // gtt/ml 10..60","label":null,"prefix":null,"suffix":"gtt/ml","section":"Infusion Details","hidden":false,"hero":false,"slider":{"min":10,"max":60,"step":1},"value":20,"display":"20"},{"text":"# Formula","label":null,"prefix":null,"suffix":null,"section":"Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"total minutes = time duration * 60","label":null,"prefix":null,"suffix":null,"section":"Formula","hidden":false,"hero":false,"slider":null,"value":480,"display":"480"},{"text":"iv drip rate = (total volume * drop factor) / total minutes // gtt/min @hero","label":null,"prefix":null,"suffix":"gtt/min","section":"Formula","hidden":false,"hero":true,"slider":null,"value":41.666666666666664,"display":"41.67"},{"text":"# Hourly Rate","label":null,"prefix":null,"suffix":null,"section":"Hourly Rate","hero":false,"slider":null,"value":null,"display":null},{"text":"flow rate ml per hour = total volume / time duration","label":null,"prefix":null,"suffix":null,"section":"Hourly Rate","hidden":false,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"drops per second = iv drip rate / 60","label":null,"prefix":null,"suffix":null,"section":"Hourly Rate","hidden":false,"hero":false,"slider":null,"value":0.6944444444444444,"display":"0.6944"},{"text":"ml per minute = total volume / total minutes","label":null,"prefix":null,"suffix":null,"section":"Hourly Rate","hidden":false,"hero":false,"slider":null,"value":2.0833333333333335,"display":"2.083"}]},{"id":"jupiter-weight-comparison","title":"Jupiter Weight Comparison","description":"Calculate your equivalent weight on Jupiter from Earth weight and gravity ratio.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"earth_weight_pounds = 150","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"jupiter_gravity_ratio = 2.528","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.528,"display":"2.528"},{"text":"jupiter_weight = earth_weight_pounds * jupiter_gravity_ratio // pounds on Jupiter @hero","label":null,"prefix":null,"suffix":"pounds on Jupiter","section":null,"hidden":false,"hero":true,"slider":null,"value":379.2,"display":"379.2"}]},{"id":"kerning-spacing-pixel-multiplier","title":"Kerning Spacing Pixel Multiplier","description":"Calculate character kerning spacing in pixels from font size and multiplier.","category":"design","icon":"palette","tags":["pixel"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"font_size = 24 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"kerning_multiplier = 0.05 // relative to font size","label":null,"prefix":null,"suffix":"relative to font size","section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"character_spacing_pixels = font_size * kerning_multiplier // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":1.2,"display":"1.2"}]},{"id":"kinetic-energy-relativistic","title":"Kinetic Energy Relativistic","description":"Calculate relativistic kinetic energy of an object near the speed of light.","category":"education","icon":"book-open","tags":["relativistic"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"mass = 1 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"velocity = 0.5 // fraction of light speed (c)","label":null,"prefix":null,"suffix":"fraction of light speed (c)","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"_c = 299792458 // m/s","label":null,"prefix":null,"suffix":"m/s","section":null,"hidden":true,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"_v = velocity * c","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":149896229,"display":"149,896,229"},{"text":"_gamma = 1 / sqrt(1 - (v/c)^2)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":1.1547005383792517,"display":"1.155"},{"text":"relativistic_kinetic_energy = (gamma - 1) * mass * c^2 // Joules @hero","label":null,"prefix":null,"suffix":"Joules","section":null,"hidden":false,"hero":true,"slider":null,"value":13903791002172618,"display":"13,903,791,002,172,618"}]},{"id":"kinetic-energy","title":"Kinetic Energy","description":"KE = ½ · m · v² — kinetic energy of a moving object.","category":"formulas","icon":"zap","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"mass = 10 // kg 0.001..10k","label":null,"prefix":null,"suffix":"kg","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000,"step":100},"value":10,"display":"10"},{"text":"velocity = 5 // m/s 0..1k","label":null,"prefix":null,"suffix":"m/s","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":5,"display":"5"},{"text":"# Kinetic energy","label":null,"prefix":null,"suffix":null,"section":"Kinetic energy","hero":false,"slider":null,"value":null,"display":null},{"text":"kinetic_energy = 0.5 * mass * velocity^2 // @label(KE) @suffix(J)","label":"KE","prefix":null,"suffix":null,"section":"Kinetic energy","hidden":false,"hero":true,"slider":null,"value":125,"display":"125"}]},{"id":"kinetic-friction-force","title":"Kinetic Friction Force","description":"Calculate kinetic friction force from normal force and friction coefficient.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"normal_force = 100 // Newtons","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"coefficient_of_kinetic_friction = 0.3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"kinetic_frictional_force = normal_force * coefficient_of_kinetic_friction // Newtons @hero","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"kitchen-converter","title":"Kitchen Converter","description":"Convert between cups, tablespoons, milliliters, ounces, grams, and temperatures.","category":"cooking","icon":"chef-hat","tags":["temperature"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Volume Conversions","label":null,"prefix":null,"suffix":null,"section":"Volume Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"cups = 2 // cups 0.25..20 by 0.25","label":null,"prefix":null,"suffix":"cups","section":"Volume Conversions","hidden":false,"hero":false,"slider":{"min":0.25,"max":20,"step":0.25},"value":2,"display":"2"},{"text":"tablespoons = cups * 16 // tbsp","label":null,"prefix":null,"suffix":"tbsp","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"teaspoons = cups * 48 // tsp","label":null,"prefix":null,"suffix":"tsp","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":96,"display":"96"},{"text":"fluid ounces = cups * 8 // fl oz","label":null,"prefix":null,"suffix":"fl oz","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"milliliters = cups * 236.588 // mL @hero","label":null,"prefix":null,"suffix":"mL","section":"Volume Conversions","hidden":false,"hero":true,"slider":null,"value":473.176,"display":"473.18"},{"text":"liters = milliliters / 1000 // L","label":null,"prefix":null,"suffix":"L","section":"Volume Conversions","hidden":false,"hero":false,"slider":null,"value":0.473176,"display":"0.4732"},{"text":"# Weight Conversions","label":null,"prefix":null,"suffix":null,"section":"Weight Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"weight in ounces = 8 // oz 0.5..128 by 0.5","label":null,"prefix":null,"suffix":"oz","section":"Weight Conversions","hidden":false,"hero":false,"slider":{"min":0.5,"max":128,"step":0.5},"value":8,"display":"8"},{"text":"grams = weight_in_ounces * 28.3495 // g","label":null,"prefix":null,"suffix":"g","section":"Weight 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°C","label":null,"prefix":null,"suffix":"°C","section":"Temperature","hidden":false,"hero":false,"slider":null,"value":176.66666666666666,"display":"176.67"},{"text":"gas mark approx = (celsius - 121) / 14","label":null,"prefix":null,"suffix":null,"section":"Temperature","hidden":false,"hero":false,"slider":null,"value":3.976190476190476,"display":"3.976"}]},{"id":"kitchen-island-clearance","title":"Kitchen Island Clearance","description":"Calculate total floor footprint including aisle clearance.","category":"design","icon":"layout","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"island_width_inches = 36 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"island_length_inches = 72 // 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kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"latent_heat_of_fusion = 334000 // J/kg (ice to water)","label":null,"prefix":null,"suffix":"J/kg (ice to water)","section":null,"hidden":false,"hero":false,"slider":null,"value":334000,"display":"334,000"},{"text":"energy_required = mass * latent_heat_of_fusion // Joules @hero","label":null,"prefix":null,"suffix":"Joules","section":null,"hidden":false,"hero":true,"slider":null,"value":668000,"display":"668,000"}]},{"id":"law-of-cosines","title":"Law of Cosines","description":"Find the third side of a triangle: c² = a² + b² − 2ab·cos C.","category":"formulas","icon":"triangle","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Two sides and the included angle (degrees)","label":null,"prefix":null,"suffix":null,"section":"Two sides and the included angle 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80","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"mowing_speed_feet_per_minute = mowing_speed_miles_per_hour * 5280 / 60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":264,"display":"264"},{"text":"effective_mower_width_feet = (mower_width_inches / 12) * (mowing_efficiency_percentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.4,"display":"1.4"},{"text":"area_mowed_per_minute = effective_mower_width_feet * mowing_speed_feet_per_minute","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":369.6,"display":"369.6"},{"text":"estimated_mowing_time_minutes = lawn_area_square_feet / area_mowed_per_minute","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":13.528138528138529,"display":"13.53"}]},{"id":"lcm-least-common-multiple","title":"LCM (Least Common Multiple)","description":"Find the least common multiple of two integers: LCM(a, b) = |a·b| / GCD(a, b).","category":"formulas","icon":"sigma","tags":["number-theory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Two integers","label":null,"prefix":null,"suffix":null,"section":"Two integers","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 12 // 1..10k","label":null,"prefix":null,"suffix":null,"section":"Two integers","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":12,"display":"12"},{"text":"b = 18 // 1..10k","label":null,"prefix":null,"suffix":null,"section":"Two 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100..400","label":null,"prefix":null,"suffix":"lbs","section":"Measurements","hidden":false,"hero":false,"slider":{"min":100,"max":400,"step":1},"value":180,"display":"180"},{"text":"height = 70 // inches 48..84","label":null,"prefix":null,"suffix":"inches","section":"Measurements","hidden":false,"hero":false,"slider":{"min":48,"max":84,"step":1},"value":70,"display":"70"},{"text":"is male = 1 // dropdown({Male: 1, Female: 0})","label":null,"prefix":null,"suffix":null,"section":"Measurements","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Boer Formula","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"weight kg = weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":81.64656,"display":"81.65"},{"text":"height cm = height * 2.54","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":177.8,"display":"177.8"},{"text":"lean body mass male = 0.407 * weight kg + 0.267 * height cm - 19.2","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":61.50274992,"display":"61.5"},{"text":"lean body mass female = 0.252 * weight kg + 0.473 * height cm - 48.3","label":null,"prefix":null,"suffix":null,"section":"Boer Formula","hidden":false,"hero":false,"slider":null,"value":56.37433312,"display":"56.37"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"lean body mass kg = is male * lean body mass male + (1 - is male) * lean body mass female","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":61.50274992,"display":"61.5"},{"text":"lean body mass lbs = lean body mass kg * 2.20462","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":135.5901925286304,"display":"135.59"}]},{"id":"lease-buyback-analysis","title":"Lease Buyback Analysis","description":"Analyze profit potential of buying out a car lease versus market value.","category":"other","icon":"calculator","tags":["lease"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Lease Buyback","label":null,"prefix":null,"suffix":null,"section":"Lease Buyback","hero":false,"slider":null,"value":null,"display":null},{"text":"$lease residual value = 22000 // 5k..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Lease Buyback","hidden":false,"hero":false,"slider":{"min":5000,"max":100000,"step":500},"value":22000,"display":"$22,000.00"},{"text":"$estimated market value = 26000 // 5k..120k by 500","label":null,"prefix":"$","suffix":null,"section":"Lease 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and cost savings from switching to LED bulbs.","category":"science","icon":"lightbulb","tags":["eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"old_bulb_watts = 60 // watts","label":null,"prefix":null,"suffix":"watts","section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"led_bulb_watts = 9 // watts","label":null,"prefix":null,"suffix":"watts","section":null,"hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"hours_used_per_day = 5 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"days_per_year = 365 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":365,"display":"365"},{"text":"annual_kwh_saved = (old_bulb_watts - led_bulb_watts) * hours_used_per_day * days_per_year / 1000 // kWh","label":null,"prefix":null,"suffix":"kWh","section":null,"hidden":false,"hero":false,"slider":null,"value":93.075,"display":"93.08"},{"text":"co2_per_kwh = 0.4 // kg CO2","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.4,"display":"0.4"},{"text":"annual_co2_reduction_kg = annual_kwh_saved * co2_per_kwh // kg CO2 @hero","label":null,"prefix":null,"suffix":"kg CO2","section":null,"hidden":false,"hero":true,"slider":null,"value":37.23,"display":"37.23"}]},{"id":"led-resistor-calculator","title":"Led Resistor Calculator","description":"Calculate required resistor ohms for an LED from supply voltage and current.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"supply_voltage = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"led_forward_voltage = 3.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.2,"display":"3.2"},{"text":"desired_led_current_milliamps = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"required_resistor_ohms = (supply_voltage - led_forward_voltage) / (desired_led_current_milliamps / 1000)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":440,"display":"440"}]},{"id":"legal-fee-hourly-vs-flat-rate","title":"Legal Fee Comparison","description":"Compare total costs between hourly billing and flat rate 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@hero","label":null,"prefix":null,"suffix":"cm","section":null,"hidden":false,"hero":true,"slider":null,"value":5.999999999999999,"display":"6"},{"text":"magnification = -image_distance / object_distance // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":-1.5,"display":"-1.5"}]},{"id":"life-expectancy-simple","title":"Life Expectancy Simple","description":"Calculate remaining years, weeks, and days based on current age and life expectancy.","category":"math","icon":"infinity","tags":["life","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Personal Stats","label":null,"prefix":null,"suffix":null,"section":"Personal Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"current age = 30 // 0..100","label":null,"prefix":null,"suffix":null,"section":"Personal 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250000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250000,"display":"250,000"},{"text":"total_needs = (annual_income * years_to_replace) + total_debt","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1050000,"display":"1,050,000"}]},{"id":"life-path-number","title":"Life Path Number","description":"Calculate a numerology life path number from birth date digits.","category":"everyday","icon":"smile","tags":["life"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.129Z"},"rows":[{"text":"birth_day = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"birth_month = 6","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"birth_year = 1990","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1990,"display":"1,990"},{"text":"sum_digits = (floor(birth_day / 10) + mod(birth_day, 10)) + (floor(birth_month / 10) + mod(birth_month, 10)) + (floor(birth_year / 1000) + mod(floor(birth_year / 100), 10) + mod(floor(birth_year / 10), 10) + mod(birth_year, 10))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":31,"display":"31"},{"text":"life_path = mod(sum_digits - 1, 9) + 1 // number @hero","label":null,"prefix":null,"suffix":"number","section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"lift-coefficient","title":"Lift Coefficient","description":"Calculate aircraft lift coefficient from lift force, velocity, and wing 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= 200 // sq ft 50..2k","label":null,"prefix":null,"suffix":"sq ft","section":"Aerodynamics","hidden":false,"hero":false,"slider":{"min":50,"max":2000,"step":20},"value":200,"display":"200"},{"text":"# Formula: Cl = L / (0.5 * rho * v^2 * S)","label":null,"prefix":null,"suffix":null,"section":"Formula: Cl = L / (0.5 * rho * v^2 * S)","hero":false,"slider":null,"value":null,"display":null},{"text":"velocity fps = velocity * 1.68781","label":null,"prefix":null,"suffix":null,"section":"Formula: Cl = L / (0.5 * rho * v^2 * S)","hidden":false,"hero":false,"slider":null,"value":253.1715,"display":"253.17"},{"text":"dynamic pressure = 0.5 * air density * (velocity fps^2)","label":null,"prefix":null,"suffix":null,"section":"Formula: Cl = L / (0.5 * rho * v^2 * S)","hidden":false,"hero":false,"slider":null,"value":76.17466350753853,"display":"76.17"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"lift coefficient = lift force / (dynamic pressure * wing area) // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":0.1640965568395711,"display":"0.1641"},{"text":"# Efficiency","label":null,"prefix":null,"suffix":null,"section":"Efficiency","hero":false,"slider":null,"value":null,"display":null},{"text":"required cl = lift coefficient","label":null,"prefix":null,"suffix":null,"section":"Efficiency","hidden":false,"hero":false,"slider":null,"value":0.1640965568395711,"display":"0.1641"},{"text":"stall cl = 1.5 // typical","label":null,"prefix":null,"suffix":"typical","section":"Efficiency","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"angle of attack estimate = lift coefficient / 0.1 // degrees (linear 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13","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":13,"display":"13"},{"text":"indoor home = 5","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"moonlight = -3","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":-3,"display":"-3"},{"text":"night street = 8","label":null,"prefix":null,"suffix":null,"section":"Typical Benchmarks","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"}]},{"id":"limit-evaluation","title":"Limit Evaluation","description":"Evaluate lim x→a [c·xⁿ] = c·aⁿ for continuous polynomial functions.","category":"formulas","icon":"sigma","tags":["calculus"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Function: f(x) = c · x^n","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hero":false,"slider":null,"value":null,"display":null},{"text":"c = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"n = 2 // -10..10","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":1},"value":2,"display":"2"},{"text":"a = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Function: f(x) = c · x^n","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"# Limit (substitution for continuous functions)","label":null,"prefix":null,"suffix":null,"section":"Limit (substitution for continuous functions)","hero":false,"slider":null,"value":null,"display":null},{"text":"limit_value = c * a^n // @label(lim f(x))","label":"lim f(x)","prefix":null,"suffix":null,"section":"Limit (substitution for continuous functions)","hidden":false,"hero":true,"slider":null,"value":75,"display":"75"}]},{"id":"line-equation-from-two-points","title":"Line Equation From Two Points","description":"Find the slope and y-intercept of the line through two points.","category":"formulas","icon":"trending-up","tags":["equation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Two points","label":null,"prefix":null,"suffix":null,"section":"Two points","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"y1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Two 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intercept","hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"line-height-optimal-typography","title":"Line Height Optimal Typography","description":"Calculate optimal CSS line-height from font size and ratio.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"font_size = 16 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"optimal_ratio = 1.5 // (1.4 to 1.6 recommended)","label":null,"prefix":null,"suffix":"(1.4 to 1.6 recommended)","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"line_height_pixels = font_size * optimal_ratio // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":24,"display":"24"}]},{"id":"linear-regression-slope","title":"Linear Regression Slope","description":"Slope of the least-squares regression line: m = cov(X,Y) / var(X).","category":"formulas","icon":"trending-up","tags":["slope","statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Dataset X","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"x2 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"x3 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"x4 = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"x5 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset X","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# Dataset Y","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hero":false,"slider":null,"value":null,"display":null},{"text":"y1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"y2 = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"y3 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"y4 = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":4,"display":"4"},{"text":"y5 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Dataset Y","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# Means","label":null,"prefix":null,"suffix":null,"section":"Means","hero":false,"slider":null,"value":null,"display":null},{"text":"_n = 5","label":null,"prefix":null,"suffix":null,"section":"Means","hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"mean_x = (x1 + x2 + x3 + x4 + x5) / n","label":null,"prefix":null,"suffix":null,"section":"Means","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"mean_y = (y1 + y2 + y3 + y4 + y5) / n","label":null,"prefix":null,"suffix":null,"section":"Means","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"# Slope (least squares)","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hero":false,"slider":null,"value":null,"display":null},{"text":"_num = (x1 - mean_x) * (y1 - mean_y) + (x2 - mean_x) * (y2 - mean_y) + (x3 - mean_x) * (y3 - mean_y) + (x4 - mean_x) * (y4 - mean_y) + (x5 - mean_x) * (y5 - mean_y)","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":true,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"_denom = (x1 - mean_x)^2 + (x2 - mean_x)^2 + (x3 - mean_x)^2 + (x4 - mean_x)^2 + (x5 - mean_x)^2","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":true,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"slope = num / denom // @hero","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":false,"hero":true,"slider":null,"value":0.6,"display":"0.6"},{"text":"intercept = mean_y - slope * mean_x // @hero","label":null,"prefix":null,"suffix":null,"section":"Slope (least squares)","hidden":false,"hero":true,"slider":null,"value":2.2,"display":"2.2"}]},{"id":"liquid-net-worth-calculator","title":"Liquid Net Worth Calculator","description":"Calculate liquid net worth from cash, investments, and discounted retirement accounts.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"cash_savings = 15000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"stock_investments = 50000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"retirement_accounts = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"retirement_liquidity_factor = 0.70","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.7,"display":"0.7"},{"text":"liquid_net_worth = cash_savings + stock_investments + (retirement_accounts * retirement_liquidity_factor)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":135000,"display":"135,000"}]},{"id":"livestock-feed-conversion-ratio","title":"Livestock Feed Conversion Ratio","description":"Calculate feed conversion ratio from total feed consumed and weight gained.","category":"finance","icon":"ratio","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"total_feed_consumed_pounds = 500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"total_weight_gain_pounds = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"feed_conversion_ratio = total_feed_consumed_pounds / total_weight_gain_pounds // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"loan-payment","title":"Loan Payment","description":"Monthly payment for a fixed-rate loan: P = L · i / (1 − (1 + i)^−n).","category":"formulas","icon":"dollar-sign","tags":["mortgage","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Loan terms","label":null,"prefix":null,"suffix":null,"section":"Loan terms","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan_amount = 300000 // 1k..10M","label":null,"prefix":"$","suffix":null,"section":"Loan terms","hidden":false,"hero":false,"slider":{"min":1000,"max":10000000,"step":100000},"value":300000,"display":"$300,000.00"},{"text":"annual_rate = 6.5 // % 0..30","label":null,"prefix":null,"suffix":"%","section":"Loan terms","hidden":false,"hero":false,"slider":{"min":0,"max":30,"step":1},"value":6.5,"display":"6.5"},{"text":"$term_years = 30 // 1..50","label":null,"prefix":"$","suffix":null,"section":"Loan terms","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":1},"value":30,"display":"$30.00"},{"text":"# Monthly payment","label":null,"prefix":null,"suffix":null,"section":"Monthly payment","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly_rate = annual_rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"total_payments = term_years * 12","label":null,"prefix":null,"suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"$monthly_payment = loan_amount * monthly_rate / (1 - (1 + monthly_rate)^(-total_payments)) // @hero","label":null,"prefix":"$","suffix":null,"section":"Monthly payment","hidden":false,"hero":true,"slider":null,"value":1896.2040704788958,"display":"$1,896.20"},{"text":"$total_paid = monthly_payment * total_payments","label":null,"prefix":"$","suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":682633.4653724026,"display":"$682,633.47"},{"text":"$total_interest = total_paid - loan_amount","label":null,"prefix":"$","suffix":null,"section":"Monthly payment","hidden":false,"hero":false,"slider":null,"value":382633.4653724026,"display":"$382,633.47"}]},{"id":"loan-payoff","title":"Loan Payoff","description":"Find out how long to pay off a loan and how much interest you'll pay total.","category":"finance","icon":"credit-card","tags":["loan","payoff","debt","interest"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Loan Details","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hero":false,"slider":null,"value":null,"display":null},{"text":"current balance = $25000 // 500..200k by 500","label":null,"prefix":"$","suffix":null,"section":"Loan Details","hidden":false,"hero":false,"slider":{"min":500,"max":200000,"step":500},"value":25000,"display":"$25,000.00"},{"text":"annual interest rate = 6.5 // % 0.5..30 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":0.5,"max":30,"step":0.1},"value":6.5,"display":"6.5"},{"text":"monthly payment = $500 // 50..5k by 25","label":null,"prefix":"$","suffix":null,"section":"Loan Details","hidden":false,"hero":false,"slider":{"min":50,"max":5000,"step":25},"value":500,"display":"$500.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly rate = annual_interest_rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"months to pay off = -ln(1 - (current_balance * monthly_rate / monthly_payment)) / ln(1 + monthly_rate)","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":false,"slider":null,"value":58.46909802580794,"display":"58.47"},{"text":"years to pay off = months_to_pay_off / 12 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":false,"hero":true,"slider":null,"value":4.872424835483995,"display":"4.872"},{"text":"# Cost Summary","label":null,"prefix":null,"suffix":null,"section":"Cost Summary","hero":false,"slider":null,"value":null,"display":null},{"text":"$total amount paid = monthly_payment * months_to_pay_off","label":null,"prefix":"$","suffix":null,"section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":29234.54901290397,"display":"$29,234.55"},{"text":"$total interest paid = total_amount_paid - current_balance","label":null,"prefix":"$","suffix":null,"section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":4234.54901290397,"display":"$4,234.55"},{"text":"interest as pct of principal = (total_interest_paid / current_balance) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Cost Summary","hidden":false,"hero":false,"slider":null,"value":16.93819605161588,"display":"16.94"}]},{"id":"loan-target-payoff","title":"Loan: Target a Payoff Date","description":"Standard loan math says monthly payment P = L · r / (1 − (1+r)^−n). Want to be debt-free by year 7 — what monthly payment do you need?","category":"finance","icon":"dollar-sign","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Loan setup","label":null,"prefix":null,"suffix":null,"section":"Loan setup","hero":false,"slider":null,"value":null,"display":null},{"text":"loan = 250000 // 1k..1M — principal ($)","label":null,"prefix":null,"suffix":"1k..1M — principal ($)","section":"Loan setup","hidden":false,"hero":false,"slider":null,"value":250000,"display":"250,000"},{"text":"apr = 0.065 // 0..0.2 — annual rate","label":null,"prefix":null,"suffix":"0..0.2 — annual rate","section":"Loan setup","hidden":false,"hero":false,"slider":null,"value":0.065,"display":"0.065"},{"text":"years = 7 // 1..30 — payoff target","label":null,"prefix":null,"suffix":"1..30 — payoff target","section":"Loan setup","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"# Derived","label":null,"prefix":null,"suffix":null,"section":"Derived","hero":false,"slider":null,"value":null,"display":null},{"text":"_r = apr / 12","label":null,"prefix":null,"suffix":null,"section":"Derived","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"_n = years * 12","label":null,"prefix":null,"suffix":null,"section":"Derived","hidden":true,"hero":false,"slider":null,"value":84,"display":"84"},{"text":"# Required payment (closed-form)","label":null,"prefix":null,"suffix":null,"section":"Required payment (closed-form)","hero":false,"slider":null,"value":null,"display":null},{"text":"monthly = loan * _r / (1 - (1 + _r)^(-_n))","label":null,"prefix":null,"suffix":null,"section":"Required payment (closed-form)","hidden":false,"hero":false,"slider":null,"value":3712.359117957795,"display":"3,712.36"},{"text":"# Total interest paid over the loan","label":null,"prefix":null,"suffix":null,"section":"Total interest paid over the loan","hero":false,"slider":null,"value":null,"display":null},{"text":"total_interest = monthly * _n - loan","label":null,"prefix":null,"suffix":null,"section":"Total interest paid over the loan","hidden":false,"hero":false,"slider":null,"value":61838.1659084548,"display":"61,838.17"},{"text":"# Visualize remaining balance over time","label":null,"prefix":null,"suffix":null,"section":"Visualize remaining balance over time","hero":false,"slider":null,"value":null,"display":null},{"text":"balance = t => loan * ((1 + _r)^_n - (1 + _r)^t) / ((1 + _r)^_n - 1)","label":null,"prefix":null,"suffix":null,"section":"Visualize remaining balance over time","hidden":false,"hero":true,"slider":null,"value":{"type":"function","params":["t"],"body":["div",["mul",["parenExpr",{"type":"id","value":"loan","text":"loan","offset":16,"lineBreaks":0,"line":1,"col":17,"canonicalName":"loan"}],["parenExpr",["sub",["power",["parenExpr",["add",{"type":"decimal","value":"1","text":"1","offset":26,"lineBreaks":0,"line":1,"col":27},["parenExpr",{"type":"id","value":"r","text":"r","offset":31,"lineBreaks":0,"line":1,"col":32,"canonicalName":"r"}]]],["parenExpr",{"type":"id","value":"n","text":"n","offset":36,"lineBreaks":0,"line":1,"col":37,"canonicalName":"n"}]],["power",["parenExpr",["add",{"type":"decimal","value":"1","text":"1","offset":42,"lineBreaks":0,"line":1,"col":43},["parenExpr",{"type":"id","value":"r","text":"r","offset":47,"lineBreaks":0,"line":1,"col":48,"canonicalName":"r"}]]],["parenExpr",{"type":"id","value":"t","text":"t","offset":52,"lineBreaks":0,"line":1,"col":53,"canonicalName":"t"}]]]]],["parenExpr",["sub",["power",["parenExpr",["add",{"type":"decimal","value":"1","text":"1","offset":60,"lineBreaks":0,"line":1,"col":61},["parenExpr",{"type":"id","value":"r","text":"r","offset":65,"lineBreaks":0,"line":1,"col":66,"canonicalName":"r"}]]],["parenExpr",{"type":"id","value":"n","text":"n","offset":70,"lineBreaks":0,"line":1,"col":71,"canonicalName":"n"}]],{"type":"decimal","value":"1","text":"1","offset":75,"lineBreaks":0,"line":1,"col":76}]]],"name":"balance"},"display":null},{"text":"# Same answer via goalseek — fix payment, solve for years.","label":null,"prefix":null,"suffix":null,"section":"Same answer via goalseek — fix payment, solve for years.","hero":false,"slider":null,"value":null,"display":null},{"text":"# Uncomment to find: \"if I can only afford $X/month, when am I done?\"","label":null,"prefix":null,"suffix":null,"section":"Uncomment to find: \"if I can only afford $X/month, when am I done?\"","hero":false,"slider":null,"value":null,"display":null},{"text":"# target_monthly = 2500","label":null,"prefix":null,"suffix":null,"section":"target_monthly = 2500","hero":false,"slider":null,"value":null,"display":null},{"text":"# set monthly = target_monthly using years","label":null,"prefix":null,"suffix":null,"section":"set monthly = target_monthly using years","hero":false,"slider":null,"value":null,"display":null}]},{"id":"loan-to-value-ratio-advanced","title":"Loan-to-Value Ratio","description":"Calculate the current LTV ratio based on loan balance and value.","category":"real-estate","icon":"percent","tags":["loan"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"mortgageBalance = 240000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":240000,"display":"240,000"},{"text":"appraisedValue = 300000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"ltvPercent = (mortgageBalance / appraisedValue) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":80,"display":"80"}]},{"id":"logarithm-any-base","title":"Logarithm Any Base","description":"Compute log base b of x: log_b(x) = ln(x) / ln(b).","category":"formulas","icon":"sigma","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"x = 100 // 0.001..1M","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":1000000,"step":10000},"value":100,"display":"100"},{"text":"base = 10 // 2..1k","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":2,"max":1000,"step":1},"value":10,"display":"10"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"result = log(x) / log(base) // @label(log_b(x))","label":"log_b(x)","prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"logarithm-base-10","title":"Logarithm Base 10","description":"Calculate the base-10 logarithm of a number.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"number = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"result = log10(number)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"logic-gate-propagation-delay","title":"Logic Gate Propagation Delay","description":"Calculate total delay and max frequency for logic paths.","category":"engineering","icon":"cpu","tags":["engineering","electronics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"number_of_gates_in_path = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"delay_per_gate_nanoseconds = 0.5 // ns","label":null,"prefix":null,"suffix":"ns","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"total_propagation_delay_nanoseconds = number_of_gates_in_path * delay_per_gate_nanoseconds // ns @hero","label":null,"prefix":null,"suffix":"ns","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"max_frequency_mhz = 1000 / total_propagation_delay_nanoseconds // MHz","label":null,"prefix":null,"suffix":"MHz","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"}]},{"id":"logistics-labor-productivity","title":"Logistics Labor Productivity","description":"Measure units processed per labor hour in your warehouse.","category":"business","icon":"users","tags":["logistics","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"totalUnitsProcessed = 10000 // units","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"totalLaborHours = 500 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"productivityRate = totalUnitsProcessed / totalLaborHours // units per hour @hero","label":null,"prefix":null,"suffix":"units per hour","section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"}]},{"id":"loot-drop-probability","title":"Loot Drop Probability","description":"Calculate the probability of getting a specific loot drop.","category":"math","icon":"gift","tags":["gaming","probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Loot Settings","label":null,"prefix":null,"suffix":null,"section":"Loot Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base drop rate percent = 2 // %","label":null,"prefix":null,"suffix":"%","section":"Loot Settings","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"luck stat = 50","label":null,"prefix":null,"suffix":null,"section":"Loot Settings","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"luck multiplier = 0.01","label":null,"prefix":null,"suffix":null,"section":"Loot Settings","hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"adjusted drop rate percent = base drop rate percent * (1 + (luck stat * luck multiplier))","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"loss-aversion-impact","title":"Loss Aversion Impact","description":"Quantify perceived pain from loss using a loss-aversion coefficient.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"potential_gain = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"potential_loss = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"loss_aversion_coefficient = 2.25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.25,"display":"2.25"},{"text":"perceived_pain = potential_loss * loss_aversion_coefficient // perceived units of pain @hero","label":null,"prefix":null,"suffix":"perceived units of pain","section":null,"hidden":false,"hero":true,"slider":null,"value":225,"display":"225"},{"text":"perceived_pleasure = potential_gain","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"}]},{"id":"lottery-odds-calculator","title":"Lottery Odds Calculator","description":"Calculate lottery odds (1-in-X) for picking k correct numbers from n.","category":"other","icon":"calculator","tags":["odds"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Lottery Parameters","label":null,"prefix":null,"suffix":null,"section":"Lottery Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 49 // total numbers e.g. 49","label":null,"prefix":null,"suffix":"total numbers e.g. 49","section":"Lottery Parameters","hidden":false,"hero":false,"slider":null,"value":49,"display":"49"},{"text":"k = 6 // picks e.g. 6","label":null,"prefix":null,"suffix":"picks e.g. 6","section":"Lottery Parameters","hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"# Calculation — combinations n! / (k! * (n-k)!)","label":null,"prefix":null,"suffix":null,"section":"Calculation — combinations n! / (k! * (n-k)!)","hero":false,"slider":null,"value":null,"display":null},{"text":"# For 6 of 49, it is roughly 1 in 13.9M","label":null,"prefix":null,"suffix":null,"section":"For 6 of 49, it is roughly 1 in 13.9M","hero":false,"slider":null,"value":null,"display":null},{"text":"odds = factorial(n) / (factorial(k) * factorial(n - k)) // 1 in X","label":null,"prefix":null,"suffix":"1 in X","section":"For 6 of 49, it is roughly 1 in 13.9M","hidden":false,"hero":true,"slider":null,"value":13983816.000000006,"display":"13,983,816"}]},{"id":"ltv-ratio","title":"Ltv Ratio","description":"Calculate loan-to-value (LTV) ratio and equity from loan amount and property value.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Loan and Value","label":null,"prefix":null,"suffix":null,"section":"Loan and Value","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = 320000 // 10k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Loan and Value","hidden":false,"hero":false,"slider":{"min":10000,"max":1000000,"step":5000},"value":320000,"display":"$320,000.00"},{"text":"$appraised property value = 400000 // 10k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Loan and Value","hidden":false,"hero":false,"slider":{"min":10000,"max":1000000,"step":5000},"value":400000,"display":"$400,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"loan to value ratio = (loan amount / appraised property value) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":80,"display":"80"},{"text":"$equity in property = appraised property value - loan amount","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":80000,"display":"$80,000.00"},{"text":"status = if(loan to value ratio > 80, \"PMI likely required\", \"Standard loan\")","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Standard loan","display":"Standard loan"}]},{"id":"lumber-estimator","title":"Lumber Estimator","description":"Calculate board feet and lumber costs for your woodworking project.","category":"construction","icon":"hammer","tags":["woodworking"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# Board Dimensions","label":null,"prefix":null,"suffix":null,"section":"Board Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"board length = 8 // ft 2..20","label":null,"prefix":null,"suffix":"ft","section":"Board Dimensions","hidden":false,"hero":false,"slider":{"min":2,"max":20,"step":0.2},"value":8,"display":"8"},{"text":"nominal width = 6 // in 2..12","label":null,"prefix":null,"suffix":"in","section":"Board Dimensions","hidden":false,"hero":false,"slider":{"min":2,"max":12,"step":0.1},"value":6,"display":"6"},{"text":"nominal thickness = 2 // in 1..6","label":null,"prefix":null,"suffix":"in","section":"Board Dimensions","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":2,"display":"2"},{"text":"# Quantity","label":null,"prefix":null,"suffix":null,"section":"Quantity","hero":false,"slider":null,"value":null,"display":null},{"text":"number of boards = 24 // 1..200","label":null,"prefix":null,"suffix":null,"section":"Quantity","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":24,"display":"24"},{"text":"# Board Feet","label":null,"prefix":null,"suffix":null,"section":"Board Feet","hero":false,"slider":null,"value":null,"display":null},{"text":"board feet per board = (nominal_thickness * nominal_width * board_length * 12) / 144","label":null,"prefix":null,"suffix":null,"section":"Board Feet","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"total board feet = board_feet_per_board * number_of_boards // @hero","label":null,"prefix":null,"suffix":null,"section":"Board Feet","hidden":false,"hero":true,"slider":null,"value":192,"display":"192"},{"text":"# Cost","label":null,"prefix":null,"suffix":null,"section":"Cost","hero":false,"slider":null,"value":null,"display":null},{"text":"$price per board foot = 6.50 // 1..25 by 0.25","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":{"min":1,"max":25,"step":0.25},"value":6.5,"display":"$6.50"},{"text":"$total lumber cost = total_board_feet * price_per_board_foot","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":null,"value":1248,"display":"$1,248.00"},{"text":"waste allowance = 15 // % 0..30","label":null,"prefix":null,"suffix":"%","section":"Cost","hidden":false,"hero":false,"slider":{"min":0,"max":30,"step":1},"value":15,"display":"15"},{"text":"$cost with waste = total_lumber_cost * (1 + waste_allowance / 100)","label":null,"prefix":"$","suffix":null,"section":"Cost","hidden":false,"hero":false,"slider":null,"value":1435.2,"display":"$1,435.20"}]},{"id":"lunar-phase-percentage","title":"Lunar Phase Percentage","description":"Calculate moon illumination percentage from days since the last new moon.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"days_since_new_moon = 14.7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14.7,"display":"14.7"},{"text":"lunar_cycle_days = 29.53","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":29.53,"display":"29.53"},{"text":"illumination_percentage = (1 - cos(2 * pi * days_since_new_moon / lunar_cycle_days)) / 2 * 100 // percent illuminated @suffix(%) @hero","label":null,"prefix":null,"suffix":"percent illuminated","section":null,"hidden":false,"hero":true,"slider":null,"value":0.07448252690752,"display":"0.0745"}]},{"id":"mac-address-format","title":"Mac Address Format","description":"Calculate the total number of possible MAC addresses from 48-bit address space.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"# MAC address is 48 bits","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hero":false,"slider":null,"value":null,"display":null},{"text":"_bits = 48","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hidden":true,"hero":false,"slider":null,"value":48,"display":"48"},{"text":"total possible addresses = 2 ^ bits","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hidden":false,"hero":true,"slider":null,"value":281474976710656,"display":"281,474,976,710,656"},{"text":"_oui_bits = 24 // Organizationally Unique Identifier","label":null,"prefix":null,"suffix":"Organizationally Unique Identifier","section":"MAC address is 48 bits","hidden":true,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"_nic_specific_bits = 24","label":null,"prefix":null,"suffix":null,"section":"MAC address is 48 bits","hidden":true,"hero":false,"slider":null,"value":24,"display":"24"}]},{"id":"mach-number-supersonic","title":"Mach Number Supersonic","description":"Calculate Mach number based on speed and 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@hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3.75,"display":"3.75"}]},{"id":"matchstick-burn-speed","title":"Matchstick Burn Speed","description":"Calculate matchstick burn speed in cm per second from length and burn time.","category":"everyday","icon":"smile","tags":["burn"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.708Z"},"rows":[{"text":"match_length_cm = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"burn_time_seconds = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"burn_speed_cm_per_s = match_length_cm / burn_time_seconds // cm per second @hero","label":null,"prefix":null,"suffix":"cm per 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299792458","label":null,"prefix":null,"suffix":null,"section":"Energy-Mass Equivalence","hidden":false,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"energy_joules = mass_kg * c_ms^2","label":null,"prefix":null,"suffix":null,"section":"Energy-Mass Equivalence","hidden":false,"hero":false,"slider":null,"value":89875517873681760,"display":"89,875,517,873,681,760"},{"text":"# Pythagorean Theorem","label":null,"prefix":null,"suffix":null,"section":"Pythagorean Theorem","hero":false,"slider":null,"value":null,"display":null},{"text":"leg_a = 3","label":null,"prefix":null,"suffix":null,"section":"Pythagorean Theorem","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"leg_b = 4","label":null,"prefix":null,"suffix":null,"section":"Pythagorean Theorem","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"hypotenuse = sqrt(leg_a^2 + leg_b^2)","label":null,"prefix":null,"suffix":null,"section":"Pythagorean 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compounds_per_year)^(compounds_per_year * years)","label":null,"prefix":null,"suffix":null,"section":"Compound Interest","hidden":false,"hero":true,"slider":null,"value":2009.661376695633,"display":"2,009.66"},{"text":"# Greek Letters and Operators","label":null,"prefix":null,"suffix":null,"section":"Greek Letters and Operators","hero":false,"slider":null,"value":null,"display":null}]},{"id":"matrix-2x2-determinant","title":"Matrix 2x2 Determinant","description":"Calculate the determinant of a 2x2 matrix from its four elements.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"a = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"b = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"c = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"d = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"determinant = (a * d) - (b * c)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":-2,"display":"-2"}]},{"id":"matrix-2x2-inverse","title":"Matrix 2x2 Inverse","description":"Find the inverse of a 2×2 matrix: A⁻¹ = (1/det) · [[d, -b], [-c, a]].","category":"formulas","icon":"grid-2x2","tags":["linear-algebra"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Matrix [[a, b], [c, d]]","label":null,"prefix":null,"suffix":null,"section":"Matrix [[a, b], [c, d]]","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 4 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Matrix [[a, b], 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6","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"g = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"h = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"i = 9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"determinant = a*(e*i - f*h) - b*(d*i - f*g) + c*(d*h - e*g)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0,"display":"0"}]},{"id":"matrix-multiplication-2x2","title":"Matrix Multiplication 2x2","description":"Multiply two 2×2 matrices: C = A · 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-100..100","label":null,"prefix":null,"suffix":null,"section":"Matrix A [[a, b], [c, d]]","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":4,"display":"4"},{"text":"# Matrix B [[e, f], [g, h]]","label":null,"prefix":null,"suffix":null,"section":"Matrix B [[e, f], [g, h]]","hero":false,"slider":null,"value":null,"display":null},{"text":"e = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Matrix B [[e, f], [g, h]]","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"f = 6 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Matrix B [[e, f], [g, h]]","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":6,"display":"6"},{"text":"g = 7 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Matrix B [[e, f], [g, h]]","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":7,"display":"7"},{"text":"h = 8 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Matrix B [[e, f], [g, h]]","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":8,"display":"8"},{"text":"# Product C = A · B","label":null,"prefix":null,"suffix":null,"section":"Product C = A · B","hero":false,"slider":null,"value":null,"display":null},{"text":"c00 = a * e + b * g // @hero @label(C[0,0])","label":"C[0,0]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":19,"display":"19"},{"text":"c01 = a * f + b * h // @hero @label(C[0,1])","label":"C[0,1]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":22,"display":"22"},{"text":"c10 = c * e + d * g // @hero @label(C[1,0])","label":"C[1,0]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":43,"display":"43"},{"text":"c11 = c * f + d * h // @hero @label(C[1,1])","label":"C[1,1]","prefix":null,"suffix":null,"section":"Product C = A · B","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"}]},{"id":"maximum-allowable-offer","title":"Maximum Allowable Offer","description":"Calculate the maximum price an investor should pay for a flip.","category":"real-estate","icon":"shopping-cart","tags":["real-estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"afterRepairValue = 300000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"repairCosts = 40000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":40000,"display":"40,000"},{"text":"profitMarginPercentage = 70 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":70,"display":"70"},{"text":"mao = (afterRepairValue * (profitMarginPercentage / 100)) - repairCosts // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":170000,"display":"170,000"}]},{"id":"mean","title":"Mean (Arithmetic Average)","description":"Find the arithmetic mean of a dataset: x̄ = Σxᵢ / n.","category":"formulas","icon":"sigma","tags":["statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Data points","label":null,"prefix":null,"suffix":null,"section":"Data points","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 10 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":10,"display":"10"},{"text":"x2 = 20 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":20,"display":"20"},{"text":"x3 = 30 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":30,"display":"30"},{"text":"x4 = 40 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":40,"display":"40"},{"text":"x5 = 50 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":50,"display":"50"},{"text":"# Mean","label":null,"prefix":null,"suffix":null,"section":"Mean","hero":false,"slider":null,"value":null,"display":null},{"text":"_n = 5","label":null,"prefix":null,"suffix":null,"section":"Mean","hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"sum = x1 + x2 + x3 + x4 + x5","label":null,"prefix":null,"suffix":null,"section":"Mean","hidden":false,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"mean = sum / n","label":null,"prefix":null,"suffix":null,"section":"Mean","hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"meat-smoking-wood-required","title":"Meat Smoking Wood Required","description":"Estimate pounds of wood needed to smoke meat for a given duration.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"smoke_time_hours = 6","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6,"display":"6"},{"text":"smoker_type_offset = 1 // dropdown({Offset: 1, Pellet: 0.5, Electric: 0.2})","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"pounds_per_hour = 2 * smoker_type_offset","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total_wood_pounds = smoke_time_hours * pounds_per_hour // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12,"display":"12"}]},{"id":"mechanical-torque-lever-arm","title":"Mechanical Torque Lever Arm","description":"Calculate mechanical torque from force, lever arm length, and angle.","category":"education","icon":"book-open","tags":["mechanical"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"force = 50 // Newtons","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"lever_arm_length = 2 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"angle_degrees = 90 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":90,"display":"90"},{"text":"torque = force * lever_arm_length * sin(angle_degrees) // Newton-meters @hero","label":null,"prefix":null,"suffix":"Newton-meters","section":null,"hidden":false,"hero":true,"slider":null,"value":100,"display":"100"}]},{"id":"median","title":"Median (5 values)","description":"Find the median of 5 values — the middle value after sorting. Enter values in any order.","category":"formulas","icon":"sigma","tags":["statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Data points (any order)","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 7 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":7,"display":"7"},{"text":"x2 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"x3 = 9 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":9,"display":"9"},{"text":"x4 = 1 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":1,"display":"1"},{"text":"x5 = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Data points (any order)","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# For n=5 the median is the 3rd-largest value: take max-of-every 3-element min.","label":null,"prefix":null,"suffix":null,"section":"For n=5 the median is the 3rd-largest value: take max-of-every 3-element min.","hero":false,"slider":null,"value":null,"display":null},{"text":"median = max(min(x1, x2, x3), min(x1, x2, x4), min(x1, x2, x5), min(x1, x3, x4), min(x1, x3, x5), min(x1, x4, x5), min(x2, x3, x4), min(x2, x3, x5), min(x2, x4, x5), min(x3, x4, x5))","label":null,"prefix":null,"suffix":null,"section":"For n=5 the median is the 3rd-largest value: take max-of-every 3-element min.","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"medication-dosage-by-weight","title":"Medication Dosage By Weight","description":"Calculate total medication dose in mg and ml from weight-based dosage rate.","category":"health","icon":"activity","tags":["dosage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Prescription Info","label":null,"prefix":null,"suffix":null,"section":"Prescription Info","hero":false,"slider":null,"value":null,"display":null},{"text":"dosage per kg = 15 // mg/kg 0.1..500","label":null,"prefix":null,"suffix":"mg/kg","section":"Prescription Info","hidden":false,"hero":false,"slider":{"min":0.1,"max":500,"step":5},"value":15,"display":"15"},{"text":"patient weight = 165 // lbs 5..400","label":null,"prefix":null,"suffix":"lbs","section":"Prescription Info","hidden":false,"hero":false,"slider":{"min":5,"max":400,"step":1},"value":165,"display":"165"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"weight kg = patient weight * 0.453592","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":false,"slider":null,"value":74.84268,"display":"74.84"},{"text":"total dosage = dosage per kg * weight kg // mg @hero","label":null,"prefix":null,"suffix":"mg","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":1122.6402,"display":"1,122.64"},{"text":"# Liquid Form (Optional)","label":null,"prefix":null,"suffix":null,"section":"Liquid Form (Optional)","hero":false,"slider":null,"value":null,"display":null},{"text":"concentration = 100 // mg per 5ml","label":null,"prefix":null,"suffix":"mg per 5ml","section":"Liquid Form (Optional)","hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"volume needed = (total dosage / concentration) * 5 // ml","label":null,"prefix":null,"suffix":"ml","section":"Liquid Form (Optional)","hidden":false,"hero":false,"slider":null,"value":56.13201,"display":"56.13"},{"text":"total grams = total dosage / 1000","label":null,"prefix":null,"suffix":null,"section":"Liquid Form (Optional)","hidden":false,"hero":false,"slider":null,"value":1.1226402,"display":"1.123"}]},{"id":"meeting-cost-person-hour-total","title":"Meeting Cost Person Hour Total","description":"Calculate the total dollar cost of a meeting from attendees, rate, and duration.","category":"productivity","icon":"clock","tags":["meeting"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"number_of_attendees = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"average_hourly_rate = 75 // dollars per hour","label":null,"prefix":null,"suffix":"dollars per 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Revenue","description":"Calculate the revenue opportunity cost of a meeting from attendee billable rates.","category":"productivity","icon":"clock","tags":["meeting","revenue"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"number_of_attendees = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"average_revenue_per_hour_per_person = 200 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"meeting_duration_hours = 1.5 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"total_opportunity_cost = number_of_attendees * average_revenue_per_hour_per_person * meeting_duration_hours // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1500,"display":"1,500"}]},{"id":"megapixels-to-print-dimensions","title":"Megapixels To Print Dimensions","description":"Calculate maximum print dimensions in inches from camera megapixels and DPI.","category":"design","icon":"palette","tags":["print"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"megapixels = 24 // MP","label":null,"prefix":null,"suffix":"MP","section":null,"hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"aspect_ratio_width = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"aspect_ratio_height = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"dpi = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"_total_pixels = megapixels * 1000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":24000000,"display":"24,000,000"},{"text":"_pixel_width = sqrt(total_pixels * (aspect_ratio_width / aspect_ratio_height))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":6000,"display":"6,000"},{"text":"_pixel_height = total_pixels / pixel_width","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":4000,"display":"4,000"},{"text":"print_width_inches = pixel_width / dpi // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":20,"display":"20"},{"text":"print_height_inches = pixel_height / dpi // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":13.333333333333334,"display":"13.33"}]},{"id":"memory-retention-forgetting-curve","title":"Memory Retention Forgetting Curve","description":"Calculate retention percentage after time elapsed using the forgetting curve.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"time_days = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"retention_base = 0.9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.9,"display":"0.9"},{"text":"retention = retention_base * exp(-time_days / 10) // retention percentage @hero","label":null,"prefix":null,"suffix":"retention percentage","section":null,"hidden":false,"hero":true,"slider":null,"value":0.44692677341226855,"display":"0.4469"}]},{"id":"mental-rotation-speed","title":"Mental Rotation Speed","description":"Calculate mental rotation speed in milliseconds per degree.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"rotation_angle_degrees = 90","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":90,"display":"90"},{"text":"reaction_time_ms = 1500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"ms_per_degree = reaction_time_ms / rotation_angle_degrees // ms per degree @hero","label":null,"prefix":null,"suffix":"ms per degree","section":null,"hidden":false,"hero":true,"slider":null,"value":16.666666666666668,"display":"16.67"}]},{"id":"metabolic-heat","title":"Metabolic Heat","description":"Convert daily calorie burn to watts, then to room heating output.","category":"health","icon":"flame","tags":["calories","heat"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Person","label":null,"prefix":null,"suffix":null,"section":"Person","hero":false,"slider":null,"value":null,"display":null},{"text":"daily kcal = 2100 // kcal/day 800..6k by 50","label":null,"prefix":null,"suffix":"kcal/day","section":"Person","hidden":false,"hero":false,"slider":{"min":800,"max":6000,"step":50},"value":2100,"display":"2,100"},{"text":"activity factor = 1.0 // 1..5 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Person","hidden":false,"hero":false,"slider":{"min":1,"max":5,"step":0.1},"value":1,"display":"1"},{"text":"# Conversion to Watts","label":null,"prefix":null,"suffix":null,"section":"Conversion to Watts","hero":false,"slider":null,"value":null,"display":null},{"text":"_joules_per_kcal = 4184","label":null,"prefix":null,"suffix":null,"section":"Conversion to Watts","hidden":true,"hero":false,"slider":null,"value":4184,"display":"4,184"},{"text":"_seconds_per_day = 86400","label":null,"prefix":null,"suffix":null,"section":"Conversion to Watts","hidden":true,"hero":false,"slider":null,"value":86400,"display":"86,400"},{"text":"watts at rest = round(daily kcal * joules_per_kcal / seconds_per_day, 1) // W @label(Heat output at rest)","label":"Heat output at rest","prefix":null,"suffix":"W","section":"Conversion to Watts","hidden":false,"hero":false,"slider":null,"value":101.7,"display":"101.7"},{"text":"watts active = round(watts at rest * activity factor, 1) // W @hero @label(Heat output now)","label":"Heat output now","prefix":null,"suffix":"W","section":"Conversion to Watts","hidden":false,"hero":true,"slider":null,"value":101.7,"display":"101.7"},{"text":"# Room Heating","label":null,"prefix":null,"suffix":null,"section":"Room Heating","hero":false,"slider":null,"value":null,"display":null},{"text":"people in room = 10 // 1..200","label":null,"prefix":null,"suffix":null,"section":"Room Heating","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":10,"display":"10"},{"text":"total watts = round(watts active * people in room, 0) // W @label(Total body heat in room)","label":"Total body heat in room","prefix":null,"suffix":"W","section":"Room Heating","hidden":false,"hero":false,"slider":null,"value":1017,"display":"1,017"},{"text":"btu per hour = round(total watts * 3.412, 0) // BTU/hr @label(Equivalent BTU/hr)","label":"Equivalent BTU/hr","prefix":null,"suffix":"BTU/hr","section":"Room Heating","hidden":false,"hero":false,"slider":null,"value":3470,"display":"3,470"}]},{"id":"methane-emissions-from-landfill","title":"Methane Emissions from Landfill","description":"Estimate methane and CO2e emissions from organic waste.","category":"science","icon":"wind","tags":["eco","emissions"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"organic_waste_kg = 1000 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"methane_yield_per_kg = 0.05 // kg methane","label":null,"prefix":null,"suffix":"kg methane","section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"total_methane_emissions_kg = organic_waste_kg * methane_yield_per_kg // kg @hero","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":true,"slider":null,"value":50,"display":"50"},{"text":"co2_equivalent_factor = 25 // methane is 25x stronger than CO2","label":null,"prefix":null,"suffix":"methane is 25x stronger than CO2","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"total_co2_equivalent_kg = total_methane_emissions_kg * co2_equivalent_factor // kg CO2e","label":null,"prefix":null,"suffix":"kg CO2e","section":null,"hidden":false,"hero":false,"slider":null,"value":1250,"display":"1,250"}]},{"id":"microscope-resolution","title":"Microscope Resolution","description":"Calculate the Abbe diffraction limit of a microscope from wavelength and numerical aperture.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Optics","label":null,"prefix":null,"suffix":null,"section":"Optics","hero":false,"slider":null,"value":null,"display":null},{"text":"light wavelength = 550 // nm (green light)","label":null,"prefix":null,"suffix":"nm (green light)","section":"Optics","hidden":false,"hero":false,"slider":null,"value":550,"display":"550"},{"text":"numerical aperture = 1.25 // 0.1..1.4","label":null,"prefix":null,"suffix":null,"section":"Optics","hidden":false,"hero":false,"slider":{"min":0.1,"max":1.4,"step":0.02},"value":1.25,"display":"1.25"},{"text":"# Abbe Resolution Limit: d = lambda / (2 * NA)","label":null,"prefix":null,"suffix":null,"section":"Abbe Resolution Limit: d = lambda / (2 * NA)","hero":false,"slider":null,"value":null,"display":null},{"text":"resolution limit = light wavelength / (2 * numerical aperture) // nm @hero","label":null,"prefix":null,"suffix":"nm","section":"Abbe Resolution Limit: d = lambda / (2 * NA)","hidden":false,"hero":true,"slider":null,"value":220,"display":"220"},{"text":"# Theoretical Limits","label":null,"prefix":null,"suffix":null,"section":"Theoretical Limits","hero":false,"slider":null,"value":null,"display":null},{"text":"resolution in microns = resolution limit / 1000","label":null,"prefix":null,"suffix":null,"section":"Theoretical 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-100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"x3 = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"x4 = 7 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":7,"display":"7"},{"text":"x5 = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Data points","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"# Most-frequent value via count comparisons","label":null,"prefix":null,"suffix":null,"section":"Most-frequent value via count comparisons","hero":false,"slider":null,"value":null,"display":null},{"text":"count_x1 = (x1 == x1) + (x2 == x1) + (x3 == x1) + 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mass_of_solvent_kg // mol/kg @hero","label":null,"prefix":null,"suffix":"mol/kg","section":null,"hidden":false,"hero":true,"slider":null,"value":0.5,"display":"0.5"}]},{"id":"molarity-calculator","title":"Molarity Calculator","description":"Calculate solution molarity from moles of solute and volume in milliliters.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Solute and Solvent","label":null,"prefix":null,"suffix":null,"section":"Solute and Solvent","hero":false,"slider":null,"value":null,"display":null},{"text":"moles of solute = 0.5 // moles 0.01..10","label":null,"prefix":null,"suffix":"moles","section":"Solute and Solvent","hidden":false,"hero":false,"slider":{"min":0.01,"max":10,"step":0.1},"value":0.5,"display":"0.5"},{"text":"solution volume = 500 // milliliters 1..5k","label":null,"prefix":null,"suffix":"milliliters","section":"Solute and 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1000","label":null,"prefix":null,"suffix":null,"section":"Details","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"micromolarity = molarity * 1000000","label":null,"prefix":null,"suffix":null,"section":"Details","hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"moles per liter = molarity","label":null,"prefix":null,"suffix":null,"section":"Details","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"}]},{"id":"mole-fraction","title":"Mole Fraction","description":"Calculate mole fractions of three components in a mixture.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Components","label":null,"prefix":null,"suffix":null,"section":"Components","hero":false,"slider":null,"value":null,"display":null},{"text":"moles component a = 2.5 // moles 0..100","label":null,"prefix":null,"suffix":"moles","section":"Components","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":2.5,"display":"2.5"},{"text":"moles component b = 7.5 // moles 0..100","label":null,"prefix":null,"suffix":"moles","section":"Components","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":7.5,"display":"7.5"},{"text":"moles component c = 0.0 // moles 0..100","label":null,"prefix":null,"suffix":"moles","section":"Components","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":0,"display":"0"},{"text":"# Totals","label":null,"prefix":null,"suffix":null,"section":"Totals","hero":false,"slider":null,"value":null,"display":null},{"text":"total moles = moles component a + moles component b + moles component c","label":null,"prefix":null,"suffix":null,"section":"Totals","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"mole fraction a = moles component a / total moles // @hero","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":0.25,"display":"0.25"},{"text":"# Fractions","label":null,"prefix":null,"suffix":null,"section":"Fractions","hero":false,"slider":null,"value":null,"display":null},{"text":"mole fraction b = moles component b / total moles","label":null,"prefix":null,"suffix":null,"section":"Fractions","hidden":false,"hero":false,"slider":null,"value":0.75,"display":"0.75"},{"text":"mole fraction c = moles component c / total moles","label":null,"prefix":null,"suffix":null,"section":"Fractions","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"total check = mole fraction a + mole fraction b + mole fraction c","label":null,"prefix":null,"suffix":null,"section":"Fractions","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"percentage a = mole fraction a * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Fractions","hidden":false,"hero":false,"slider":null,"value":25,"display":"25"}]},{"id":"momentum","title":"Momentum","description":"p = m · v — linear momentum of a moving object.","category":"formulas","icon":"zap","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"mass = 10 // kg 0.001..10k","label":null,"prefix":null,"suffix":"kg","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000,"step":100},"value":10,"display":"10"},{"text":"velocity = 5 // m/s -1k..1k","label":null,"prefix":null,"suffix":"m/s","section":"Inputs","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"# Momentum","label":null,"prefix":null,"suffix":null,"section":"Momentum","hero":false,"slider":null,"value":null,"display":null},{"text":"momentum = mass * velocity // @label(p) @suffix(kg·m/s)","label":"p","prefix":null,"suffix":null,"section":"Momentum","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"}]},{"id":"moon-phase-percent-illumination","title":"Moon Phase Percent Illumination","description":"Calculate moon illumination percentage from days since the last new moon.","category":"science","icon":"moon","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"days_since_new_moon = 14.7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":14.7,"display":"14.7"},{"text":"lunar_cycle_days = 29.53","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":29.53,"display":"29.53"},{"text":"phase_angle = (days_since_new_moon / lunar_cycle_days) * 2 * pi","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3.1277624116335905,"display":"3.128"},{"text":"illumination_fraction = (1 - cos(phase_angle)) / 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.0007448252690752,"display":"0.0007448"},{"text":"illumination_percentage = illumination_fraction * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.07448252690752,"display":"0.0745"}]},{"id":"moon-weight-comparison","title":"Moon Weight 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counts.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"number_of_dots = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"number_of_dashes = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"dot_duration_ms = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"dash_duration_ms = dot_duration_ms * 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"total_duration_seconds = (number_of_dots * dot_duration_ms + number_of_dashes * dash_duration_ms) / 1000 // seconds @hero","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"mortgage-calculator","title":"Mortgage Calculator","description":"Calculate monthly payments, total interest, and lifetime cost for any home loan.","category":"finance","icon":"house","tags":["mortgage","loan","housing","interest"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Loan Details","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = 400000 // 50k..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Loan Details","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":5000},"value":400000,"display":"$400,000.00"},{"text":"interest rate = 6.5 // % 1..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.1},"value":6.5,"display":"6.5"},{"text":"loan term = 30 // years 5..40","label":null,"prefix":null,"suffix":"years","section":"Loan Details","hidden":false,"hero":false,"slider":{"min":5,"max":40,"step":1},"value":30,"display":"30"},{"text":"_monthly_rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"_num_payments = loan term * 12","label":null,"prefix":null,"suffix":null,"section":"Loan Details","hidden":true,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"# Monthly Costs","label":null,"prefix":null,"suffix":null,"section":"Monthly Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$principal and interest = loan amount * (monthly_rate * (1 + monthly_rate)^num_payments) / ((1 + monthly_rate)^num_payments - 1)","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":null,"value":2528.2720939718615,"display":"$2,528.27"},{"text":"$property tax = 500 // 0..2k by 25","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":{"min":0,"max":2000,"step":25},"value":500,"display":"$500.00"},{"text":"$insurance = 150 // 0..1k","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":{"min":0,"max":1000,"step":1},"value":150,"display":"$150.00"},{"text":"$total monthly payment = principal and interest + property tax + insurance // @hero","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":true,"slider":null,"value":3178.2720939718615,"display":"$3,178.27"},{"text":"# Lifetime Totals","label":null,"prefix":null,"suffix":null,"section":"Lifetime Totals","hero":false,"slider":null,"value":null,"display":null},{"text":"$total amount paid = total monthly payment * num_payments","label":null,"prefix":"$","suffix":null,"section":"Lifetime Totals","hidden":false,"hero":false,"slider":null,"value":1144177.95382987,"display":"$1,144,177.95"},{"text":"$total interest paid = total amount paid - loan amount","label":null,"prefix":"$","suffix":null,"section":"Lifetime Totals","hidden":false,"hero":false,"slider":null,"value":744177.95382987,"display":"$744,177.95"}]},{"id":"mortgage-insurance-pmi-cost","title":"Mortgage Insurance PMI Cost","description":"Estimate monthly private mortgage insurance costs for your loan.","category":"real-estate","icon":"shield","tags":["mortgage","insurance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"loanAmount = 400000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":400000,"display":"400,000"},{"text":"pmiRateAnnual = 0.5 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"annualPMICost = loanAmount * (pmiRateAnnual / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"monthlyPMICost = annualPMICost / 12 // @prefix($) @suffix(/mo) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":166.66666666666666,"display":"166.67"}]},{"id":"mortgage-interest-tax-deduction","title":"Mortgage Interest Tax Deduction","description":"Calculate income tax savings from the mortgage interest deduction.","category":"finance","icon":"home","tags":["mortgage","interest","tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"annual_interest_paid = 15000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"marginal_tax_rate = 0.24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.24,"display":"0.24"},{"text":"tax_savings = annual_interest_paid * marginal_tax_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3600,"display":"3,600"}]},{"id":"mortgage-payoff-acceleration","title":"Mortgage Payoff Acceleration","description":"Calculate years saved and interest saved by paying extra each month on a mortgage.","category":"finance","icon":"home","tags":["mortgage","payoff","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Mortgage Details","label":null,"prefix":null,"suffix":null,"section":"Mortgage Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$current balance = 350000 // 10k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":10000,"max":1000000,"step":5000},"value":350000,"display":"$350,000.00"},{"text":"interest rate = 6.5 // % 1..15 by 0.1","label":null,"prefix":null,"suffix":"%","section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":1,"max":15,"step":0.1},"value":6.5,"display":"6.5"},{"text":"years remaining = 25 // years 1..30","label":null,"prefix":null,"suffix":"years","section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":25,"display":"25"},{"text":"$extra monthly payment = 500 // 0..5k","label":null,"prefix":"$","suffix":null,"section":"Mortgage Details","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":50},"value":500,"display":"$500.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_monthly_rate = interest rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"$_standard_monthly_payment = current balance * (monthly_rate * (1 + monthly_rate)^(years remaining * 12)) / ((1 + monthly_rate)^(years remaining * 12) - 1)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2363.225064716746,"display":"$2,363.23"},{"text":"$_total_monthly_payment = standard_monthly_payment + extra monthly payment","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2863.225064716746,"display":"$2,863.23"},{"text":"# Approximation for months remaining","label":null,"prefix":null,"suffix":null,"section":"Approximation for months remaining","hero":false,"slider":null,"value":null,"display":null},{"text":"# n = -ln(1 - (r*PV)/P) / ln(1 + r)","label":null,"prefix":null,"suffix":null,"section":"n = -ln(1 - (r*PV)/P) / ln(1 + r)","hero":false,"slider":null,"value":null,"display":null},{"text":"_months_remaining_with_extra = -ln(1 - (monthly_rate * current balance) / total_monthly_payment) / ln(1 + monthly_rate)","label":null,"prefix":null,"suffix":null,"section":"n = -ln(1 - (r*PV)/P) / ln(1 + r)","hidden":true,"hero":false,"slider":null,"value":200.86828948804973,"display":"200.87"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"years saved = years remaining - (months_remaining_with_extra / 12) // @hero years","label":null,"prefix":null,"suffix":"years","section":"Result","hidden":false,"hero":true,"slider":null,"value":8.260975875995857,"display":"8.261"},{"text":"$total interest saved = (standard_monthly_payment * years remaining * 12) - (total_monthly_payment * months_remaining_with_extra)","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":133836.3982460606,"display":"$133,836.40"},{"text":"new payoff time = months_remaining_with_extra / 12 // years","label":null,"prefix":null,"suffix":"years","section":"Result","hidden":false,"hero":false,"slider":null,"value":16.739024124004143,"display":"16.74"}]},{"id":"mosquito-repellent-duration","title":"Mosquito Repellent Duration","description":"Estimate hours of mosquito protection from a repellent's DEET concentration.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"deet_concentration_percent = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"estimated_protection_hours = deet_concentration_percent / 5 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"motor-torque-from-hp-rpm","title":"Motor Torque from HP and RPM","description":"Convert between horsepower and torque at a given RPM.","category":"engineering","icon":"settings","tags":["engineering","mechanical"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"horsepower = 5 // HP","label":null,"prefix":null,"suffix":"HP","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"rpm = 1750 // RPM","label":null,"prefix":null,"suffix":"RPM","section":null,"hidden":false,"hero":false,"slider":null,"value":1750,"display":"1,750"},{"text":"torque_lb_ft = (horsepower * 5252) / rpm // lb-ft @hero","label":null,"prefix":null,"suffix":"lb-ft","section":null,"hidden":false,"hero":true,"slider":null,"value":15.005714285714285,"display":"15.01"},{"text":"torque_nm = torque_lb_ft * 1.3558","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20.344747428571427,"display":"20.34"}]},{"id":"movement-speed-multiplier","title":"Movement Speed Multiplier","description":"Calculate final movement speed with various buffs.","category":"math","icon":"fast-forward","tags":["gaming"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Speed Settings","label":null,"prefix":null,"suffix":null,"section":"Speed Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base speed = 300","label":null,"prefix":null,"suffix":null,"section":"Speed Settings","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"boots bonus percent = 15 // %","label":null,"prefix":null,"suffix":"%","section":"Speed Settings","hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"haste buff percent = 20 // %","label":null,"prefix":null,"suffix":"%","section":"Speed Settings","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_multiplier = 1 + (boots bonus percent / 100) + (haste buff percent / 100)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":1.35,"display":"1.35"},{"text":"final speed = base speed * total_multiplier","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":405,"display":"405"}]},{"id":"moving-cost","title":"Moving Cost","description":"Estimate the cost of a DIY or professional move.","category":"real-estate","icon":"truck","tags":["truck"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Move Details","label":null,"prefix":null,"suffix":null,"section":"Move Details","hero":false,"slider":null,"value":null,"display":null},{"text":"distance = 500 // miles 10..3k by 10","label":null,"prefix":null,"suffix":"miles","section":"Move Details","hidden":false,"hero":false,"slider":{"min":10,"max":3000,"step":10},"value":500,"display":"500"},{"text":"bedrooms = 2 // 1..6","label":null,"prefix":null,"suffix":null,"section":"Move Details","hidden":false,"hero":false,"slider":{"min":1,"max":6,"step":0.05},"value":2,"display":"2"},{"text":"is professional = 1 // dropdown({Professional: 1, DIY: 0}) @label(Moving Method)","label":"Moving Method","prefix":null,"suffix":null,"section":"Move Details","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# DIY Costs","label":null,"prefix":null,"suffix":null,"section":"DIY Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$truck rental = 40 + distance * 0.70 + bedrooms * 50","label":null,"prefix":"$","suffix":null,"section":"DIY Costs","hidden":false,"hero":false,"slider":null,"value":490,"display":"$490.00"},{"text":"$fuel for truck = distance * 2 / 10 * 3.89 // @label(Fuel (truck ~10mpg))","label":"Fuel (truck ~10mpg)","prefix":"$","suffix":null,"section":"DIY Costs","hidden":false,"hero":false,"slider":null,"value":389,"display":"$389.00"},{"text":"$diy total = truck rental + fuel for truck","label":null,"prefix":"$","suffix":null,"section":"DIY Costs","hidden":false,"hero":false,"slider":null,"value":879,"display":"$879.00"},{"text":"# Professional Costs","label":null,"prefix":null,"suffix":null,"section":"Professional Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$base labor = 800 + bedrooms * 400 // @label(Base Labor (crew + hours))","label":"Base Labor (crew + hours)","prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":1600,"display":"$1,600.00"},{"text":"$mileage charge = distance * 0.75 // @label(Long Distance Charge)","label":"Long Distance Charge","prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":375,"display":"$375.00"},{"text":"$packing materials = 100 + bedrooms * 75","label":null,"prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":250,"display":"$250.00"},{"text":"$pro total = base labor + mileage charge + packing materials","label":null,"prefix":"$","suffix":null,"section":"Professional Costs","hidden":false,"hero":false,"slider":null,"value":2225,"display":"$2,225.00"},{"text":"# Your Estimate","label":null,"prefix":null,"suffix":null,"section":"Your Estimate","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated cost = is professional * pro total + (1 - is professional) * diy total // @hero","label":null,"prefix":"$","suffix":null,"section":"Your Estimate","hidden":false,"hero":true,"slider":null,"value":2225,"display":"$2,225.00"},{"text":"$per bedroom = round(estimated cost / bedrooms) // @label(Cost Per Bedroom)","label":"Cost Per Bedroom","prefix":"$","suffix":null,"section":"Your Estimate","hidden":false,"hero":false,"slider":null,"value":1113,"display":"$1,113.00"}]},{"id":"mtu-overhead-overhead-percent","title":"Mtu Overhead Overhead Percent","description":"Calculate the network overhead percentage of headers within an MTU.","category":"other","icon":"percent","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"mtu_size_bytes = 1500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"header_size_bytes = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"overhead_percentage = (header_size_bytes / mtu_size_bytes) * 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.666666666666667,"display":"2.667"}]},{"id":"mulch-volume-calculator","title":"Mulch Volume Calculator","description":"Estimate mulch in cubic yards and bags needed from area and depth.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Landscape Area","label":null,"prefix":null,"suffix":null,"section":"Landscape Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = 500 // square feet 1..5k","label":null,"prefix":null,"suffix":"square feet","section":"Landscape Area","hidden":false,"hero":false,"slider":{"min":1,"max":5000,"step":50},"value":500,"display":"500"},{"text":"depth = 3 // inches 1..12","label":null,"prefix":null,"suffix":"inches","section":"Landscape Area","hidden":false,"hero":false,"slider":{"min":1,"max":12,"step":0.2},"value":3,"display":"3"},{"text":"# Volume Calculations","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_depth_feet = depth / 12","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":0.25,"display":"0.25"},{"text":"_volume_cubic_feet = area * depth_feet","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":true,"hero":false,"slider":null,"value":125,"display":"125"},{"text":"volume cubic yards = round(volume_cubic_feet / 27, 2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Volume Calculations","hidden":false,"hero":true,"slider":null,"value":4.63,"display":"4.63"},{"text":"# Bags","label":null,"prefix":null,"suffix":null,"section":"Bags","hero":false,"slider":null,"value":null,"display":null},{"text":"# Small bag is typically 2 cubic feet","label":null,"prefix":null,"suffix":null,"section":"Small bag is typically 2 cubic feet","hero":false,"slider":null,"value":null,"display":null},{"text":"small bags needed = roundup(volume_cubic_feet / 2)","label":null,"prefix":null,"suffix":null,"section":"Small bag is typically 2 cubic feet","hidden":false,"hero":false,"slider":null,"value":63,"display":"63"},{"text":"# Large bag is typically 3 cubic feet","label":null,"prefix":null,"suffix":null,"section":"Large bag is typically 3 cubic feet","hero":false,"slider":null,"value":null,"display":null},{"text":"large bags needed = roundup(volume_cubic_feet / 3)","label":null,"prefix":null,"suffix":null,"section":"Large bag is typically 3 cubic feet","hidden":false,"hero":false,"slider":null,"value":42,"display":"42"}]},{"id":"music-chord-semitone-intervals","title":"Music Chord Semitone Intervals","description":"Calculate the semitone intervals between chord notes.","category":"design","icon":"palette","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"root_note = 0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"third_note = 4 // major third","label":null,"prefix":null,"suffix":"major third","section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"fifth_note = 7 // perfect fifth","label":null,"prefix":null,"suffix":"perfect fifth","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"interval_root_to_third = third_note - root_note // semitones @hero","label":null,"prefix":null,"suffix":"semitones","section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"},{"text":"interval_third_to_fifth = fifth_note - third_note // semitones @hero","label":null,"prefix":null,"suffix":"semitones","section":null,"hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"named-points-demo","title":"Named Points on Graph","description":"Mark and label specific points on a graph — intersections, maxima, reference levels. Each `point(x, y, \"name\")` renders as a labeled circle next to the curve. Mix as many as you need with any combination of curves.","category":"math","icon":"target","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# A parabola with three named points","label":null,"prefix":null,"suffix":null,"section":"A parabola with three named points","hero":false,"slider":null,"value":null,"display":null},{"text":"# Sine wave with key landmarks","label":null,"prefix":null,"suffix":null,"section":"Sine wave with key landmarks","hero":false,"slider":null,"value":null,"display":null},{"text":"# Linear function with the y-intercept and the point where it crosses x = 5","label":null,"prefix":null,"suffix":null,"section":"Linear function with the y-intercept and the point where it crosses x = 5","hero":false,"slider":null,"value":null,"display":null},{"text":"# Multiple curves with shared landmarks","label":null,"prefix":null,"suffix":null,"section":"Multiple curves with shared landmarks","hero":false,"slider":null,"value":null,"display":null},{"text":"# Styled points — pass {color, size, icon} for emphasis","label":null,"prefix":null,"suffix":null,"section":"Styled points — pass {color, size, icon} for emphasis","hero":false,"slider":null,"value":null,"display":null},{"text":"plot x^2, point(0, 0, {label: \"min\", color: \"info\"}), point(2, 4, {label: \"peak\", color: \"success\", size: \"lg\", icon: \"star\"}) from -3 to 3","label":null,"prefix":null,"suffix":null,"section":"Styled points — pass {color, size, icon} for emphasis","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null}]},{"id":"natural-logarithm","title":"Natural Logarithm","description":"Calculate the natural logarithm (ln) of a number.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"number = 2.71828","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.71828,"display":"2.718"},{"text":"result = log(number)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.4342941897738881,"display":"0.4343"}]},{"id":"nautical-mile-to-statute","title":"Nautical Mile To Statute","description":"Convert nautical miles to statute miles.","category":"other","icon":"calculator","tags":["statute"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"nautical_miles = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"statute_miles = nautical_miles * 1.15078 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11.5078,"display":"11.51"}]},{"id":"nda-breach-cost-estimate","title":"NDA Breach Cost","description":"Estimate the potential financial impact of an NDA violation.","category":"other","icon":"alert-triangle","tags":["breach"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"liquidatedDamages = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"estimatedLegalFees = 25000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":25000,"display":"25,000"},{"text":"potentialMarketLoss = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"totalBreachCost = liquidatedDamages + estimatedLegalFees + potentialMarketLoss // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":175000,"display":"175,000"}]},{"id":"net-operating-income","title":"Net Operating Income","description":"Calculate the annual profit of a property before taxes and debt.","category":"real-estate","icon":"briefcase","tags":["income"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"grossRentalIncome = 50000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"otherIncome = 2000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"vacancyLoss = 2500 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":2500,"display":"2,500"},{"text":"operatingExpenses = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"noi = (grossRentalIncome + otherIncome - vacancyLoss) - operatingExpenses // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":34500,"display":"34,500"}]},{"id":"net-present-value","title":"Net Present Value","description":"Calculate net present value (NPV) of a 5-year investment from cash flows and discount rate.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# NPV Project Analysis","label":null,"prefix":null,"suffix":null,"section":"NPV Project Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"$initial investment = 50000 // 1k..1M","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":1000,"max":1000000,"step":10000},"value":50000,"display":"$50,000.00"},{"text":"discount rate = 10 // % 1..25","label":null,"prefix":null,"suffix":"%","section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":1,"max":25,"step":1},"value":10,"display":"10"},{"text":"$year one cash flow = 15000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":15000,"display":"$15,000.00"},{"text":"$year two cash flow = 18000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":18000,"display":"$18,000.00"},{"text":"$year three cash flow = 22000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":22000,"display":"$22,000.00"},{"text":"$year four cash flow = 25000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":25000,"display":"$25,000.00"},{"text":"$year five cash flow = 30000 // 0..500k","label":null,"prefix":"$","suffix":null,"section":"NPV Project Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":5000},"value":30000,"display":"$30,000.00"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_r = discount rate / 100","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"$_pv1 = year one cash flow / (1 + r)^1","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":13636.363636363636,"display":"$13,636.36"},{"text":"$_pv2 = year two cash flow / (1 + r)^2","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":14876.033057851237,"display":"$14,876.03"},{"text":"$_pv3 = year three cash flow / (1 + r)^3","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":16528.925619834707,"display":"$16,528.93"},{"text":"$_pv4 = year four cash flow / (1 + r)^4","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":17075.33638412676,"display":"$17,075.34"},{"text":"$_pv5 = year five cash flow / (1 + r)^5","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":18627.63969177465,"display":"$18,627.64"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$net present value = pv1 + pv2 + pv3 + pv4 + pv5 - initial investment // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":30744.29838995099,"display":"$30,744.30"},{"text":"$total nominal cash flow = year one cash flow + year two cash flow + year three cash flow + year four cash flow + year five cash flow","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":110000,"display":"$110,000.00"},{"text":"profitability index = (net present value + initial investment) / initial investment","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":1.6148859677990197,"display":"1.615"}]},{"id":"net-promoter-score","title":"Net Promoter Score","description":"Calculate Net Promoter Score (NPS) from promoter, passive, and detractor counts.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Survey Results","label":null,"prefix":null,"suffix":null,"section":"Survey Results","hero":false,"slider":null,"value":null,"display":null},{"text":"total responses = 500 // 10..10k","label":null,"prefix":null,"suffix":null,"section":"Survey Results","hidden":false,"hero":false,"slider":{"min":10,"max":10000,"step":100},"value":500,"display":"500"},{"text":"number of promoters = 300 // 9-10 score 0..10000 by 1","label":null,"prefix":null,"suffix":"9-10 score","section":"Survey Results","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":1},"value":300,"display":"300"},{"text":"number of detractors = 50 // 0-6 score 0..10000 by 1","label":null,"prefix":null,"suffix":"0-6 score","section":"Survey Results","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":1},"value":50,"display":"50"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"_percent_promoters = (number of promoters / total responses) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"_percent_detractors = (number of detractors / total responses) * 100","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"_number_of_passives = total responses - number of promoters - number of detractors","label":null,"prefix":null,"suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":150,"display":"150"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"net promoter score = percent_promoters - percent_detractors // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":50,"display":"50"},{"text":"rating = if(net promoter score > 70, \"World Class\", if(net promoter score > 30, \"Good\", \"Needs Improvement\"))","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Good","display":"Good"},{"text":"percent passives = (number_of_passives / total responses) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"}]},{"id":"net-worth-growth-projection","title":"Net Worth Growth Projection","description":"Project future net worth from current value, annual contributions, and growth rate.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"current_net_worth = 100000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"annual_contribution = 12000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12000,"display":"12,000"},{"text":"years = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"expected_growth = 0.06","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.06,"display":"0.06"},{"text":"future_value = current_net_worth * (1 + expected_growth) ** years + annual_contribution * (((1 + expected_growth) ** years - 1) / expected_growth)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":337254.30896285636,"display":"337,254.31"}]},{"id":"net-worth","title":"Net Worth","description":"Track your assets minus liabilities to see your net worth.","category":"finance","icon":"wallet","tags":["finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Assets","label":null,"prefix":null,"suffix":null,"section":"Assets","hero":false,"slider":null,"value":null,"display":null},{"text":"$cash and savings = 15000 // 0..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":1000},"value":15000,"display":"$15,000.00"},{"text":"$investments = 50000 // 0..2M","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":20000},"value":50000,"display":"$50,000.00"},{"text":"$retirement accounts = 75000 // 0..3M","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":3000000,"step":50000},"value":75000,"display":"$75,000.00"},{"text":"$home value = 350000 // 0..2M by 10k","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":10000},"value":350000,"display":"$350,000.00"},{"text":"$other assets = 10000 // 0..500k by 1k","label":null,"prefix":"$","suffix":null,"section":"Assets","hidden":false,"hero":false,"slider":{"min":0,"max":500000,"step":1000},"value":10000,"display":"$10,000.00"},{"text":"# Liabilities","label":null,"prefix":null,"suffix":null,"section":"Liabilities","hero":false,"slider":null,"value":null,"display":null},{"text":"$mortgage balance = 280000 // 0..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":2000000,"step":5000},"value":280000,"display":"$280,000.00"},{"text":"$car loans = 12000 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":12000,"display":"$12,000.00"},{"text":"$student loans = 25000 // 0..200k by 1k","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":200000,"step":1000},"value":25000,"display":"$25,000.00"},{"text":"$credit card debt = 3000 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":3000,"display":"$3,000.00"},{"text":"$other debts = 0 // 0..100k by 500","label":null,"prefix":"$","suffix":null,"section":"Liabilities","hidden":false,"hero":false,"slider":{"min":0,"max":100000,"step":500},"value":0,"display":"$0.00"},{"text":"# Summary","label":null,"prefix":null,"suffix":null,"section":"Summary","hero":false,"slider":null,"value":null,"display":null},{"text":"$total assets = cash and savings + investments + retirement accounts + home value + other assets","label":null,"prefix":"$","suffix":null,"section":"Summary","hidden":false,"hero":false,"slider":null,"value":500000,"display":"$500,000.00"},{"text":"$total liabilities = mortgage balance + car loans + student loans + credit card debt + other debts","label":null,"prefix":"$","suffix":null,"section":"Summary","hidden":false,"hero":false,"slider":null,"value":320000,"display":"$320,000.00"},{"text":"$net worth = total assets - total liabilities","label":null,"prefix":"$","suffix":null,"section":"Summary","hidden":false,"hero":true,"slider":null,"value":180000,"display":"$180,000.00"}]},{"id":"network-latency-delay","title":"Network Latency Delay","description":"Calculate one-way and round-trip latency over fiber optic cable.","category":"other","icon":"calculator","tags":["delay"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Journey","label":null,"prefix":null,"suffix":null,"section":"Journey","hero":false,"slider":null,"value":null,"display":null},{"text":"distance kilometers = 1000 // km","label":null,"prefix":null,"suffix":"km","section":"Journey","hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"refraction index of fiber = 1.467 // speed of light is c/n","label":null,"prefix":null,"suffix":"speed of light is c/n","section":"Journey","hidden":false,"hero":false,"slider":null,"value":1.467,"display":"1.467"},{"text":"# Speed of light in vacuum (approx)","label":null,"prefix":null,"suffix":null,"section":"Speed of light in vacuum (approx)","hero":false,"slider":null,"value":null,"display":null},{"text":"_c_vacuum = 299792 // km/s","label":null,"prefix":null,"suffix":"km/s","section":"Speed of light in vacuum (approx)","hidden":true,"hero":false,"slider":null,"value":299792,"display":"299,792"},{"text":"_speed_in_fiber = c_vacuum / refraction index of fiber // km/s","label":null,"prefix":null,"suffix":"km/s","section":"Speed of light in vacuum (approx)","hidden":true,"hero":false,"slider":null,"value":204357.1915473756,"display":"204,357.19"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"one way delay milliseconds = (distance kilometers / speed_in_fiber) * 1000 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":4.893392752308267,"display":"4.893"},{"text":"roundtrip_time_milliseconds = one way delay milliseconds * 2 // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":9.786785504616534,"display":"9.787"}]},{"id":"newsletter-subscriber-valuation","title":"Newsletter Subscriber Valuation","description":"Calculate the total valuation of a newsletter from subscriber count and revenue.","category":"business","icon":"briefcase","tags":["valuation","business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"total_subscribers = 5000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"average_monthly_revenue_per_subscriber = 0.50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"churn_rate_percentage = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"subscriber_lifetime_months = 1 / churn_rate_percentage","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":33.333333333333336,"display":"33.33"},{"text":"total_newsletter_valuation = total_subscribers * average_monthly_revenue_per_subscriber * subscriber_lifetime_months","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":83333.33333333334,"display":"83,333.33"}]},{"id":"newtons-second-law-acceleration","title":"Newtons Second Law Acceleration","description":"Calculate acceleration from force and mass using Newton's Second Law.","category":"education","icon":"book-open","tags":["education"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"force = 100 // Newtons","label":null,"prefix":null,"suffix":"Newtons","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"mass = 20 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"acceleration = force / mass // meters per second squared @hero","label":null,"prefix":null,"suffix":"meters per second squared","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"newtons-second-law","title":"Newton's Second Law","description":"F = m · a — force equals mass times acceleration.","category":"formulas","icon":"zap","tags":["physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Inputs","label":null,"prefix":null,"suffix":null,"section":"Inputs","hero":false,"slider":null,"value":null,"display":null},{"text":"mass = 10 // kg 0.001..10k","label":null,"prefix":null,"suffix":"kg","section":"Inputs","hidden":false,"hero":false,"slider":{"min":0.001,"max":10000,"step":100},"value":10,"display":"10"},{"text":"acceleration = 9.8 // m/s² -100..100 by 0.01","label":null,"prefix":null,"suffix":"m/s²","section":"Inputs","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":0.01},"value":9.8,"display":"9.8"},{"text":"# Force","label":null,"prefix":null,"suffix":null,"section":"Force","hero":false,"slider":null,"value":null,"display":null},{"text":"force = mass * acceleration // @label(Force) @suffix(N)","label":"Force","prefix":null,"suffix":null,"section":"Force","hidden":false,"hero":true,"slider":null,"value":98,"display":"98"}]},{"id":"nitro-gas-mix-ppo2","title":"Nitro Gas Mix Ppo2","description":"Calculate partial pressure of oxygen (ppO2) for a nitrox mix at depth.","category":"everyday","icon":"home","tags":["gas","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"nitrox_oxygen_percent = 32","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":32,"display":"32"},{"text":"depth_feet = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"ata_pressure = (depth_feet / 33) + 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4.03030303030303,"display":"4.03"},{"text":"partial_pressure_oxygen = (nitrox_oxygen_percent / 100) * ata_pressure // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.2896969696969696,"display":"1.29"}]},{"id":"noise-exposure-limit-osha","title":"Noise Exposure Limit Osha","description":"Calculate permissible OSHA noise exposure hours from decibel level.","category":"math","icon":"infinity","tags":["exposure","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"noise_level_decibels = 95","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":95,"display":"95"},{"text":"permissible_exposure_hours = 8 / (2^((noise_level_decibels - 90) / 5)) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4,"display":"4"}]},{"id":"normal-distribution-probability","title":"Normal Distribution Density","description":"Probability density of a normal distribution: f(x) = (1 / (σ√(2π))) · exp(−(x−μ)²/(2σ²)).","category":"formulas","icon":"sigma","tags":["statistics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Distribution parameters","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"mean = 0 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":0,"display":"0"},{"text":"standard_deviation = 1 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":1,"display":"1"},{"text":"x = 0 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Distribution parameters","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":0,"display":"0"},{"text":"# PDF value at x","label":null,"prefix":null,"suffix":null,"section":"PDF value at x","hero":false,"slider":null,"value":null,"display":null},{"text":"_exponent = -(((x - mean)^2)) / (2 * (standard_deviation^2))","label":null,"prefix":null,"suffix":null,"section":"PDF value at x","hidden":true,"hero":false,"slider":null,"value":0,"display":"-0"},{"text":"density = (1 / (standard_deviation * sqrt(2 * pi))) * exp(exponent) // @label(f(x))","label":"f(x)","prefix":null,"suffix":null,"section":"PDF value at x","hidden":false,"hero":true,"slider":null,"value":0.3989422804014327,"display":"0.3989"}]},{"id":"notary-public-fee-limit","title":"Notary Fee Limit","description":"Calculate the maximum legal fee for notary services.","category":"other","icon":"file-check","tags":["fee"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"numberOfSignatures = 3 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"maxFeePerSignature = 10 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"totalMaxNotaryFee = numberOfSignatures * maxFeePerSignature // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"numerology-destiny-number","title":"Numerology Destiny Number","description":"Reduce a name's numeric sum to a single-digit numerology destiny number.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"name_value_sum = 42","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":42,"display":"42"},{"text":"destiny_number = mod(name_value_sum - 1, 9) + 1 // number @hero","label":null,"prefix":null,"suffix":"number","section":null,"hidden":false,"hero":true,"slider":null,"value":6,"display":"6"}]},{"id":"nyquist-sampling-rate","title":"Nyquist Sampling Rate","description":"Calculate minimum sampling frequency to avoid aliasing.","category":"engineering","icon":"activity","tags":["engineering","electronics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"max_signal_frequency_hz = 20000 // Hz (audio)","label":null,"prefix":null,"suffix":"Hz (audio)","section":null,"hidden":false,"hero":false,"slider":null,"value":20000,"display":"20,000"},{"text":"minimum_sampling_rate_hz = 2 * max_signal_frequency_hz // Hz @hero","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":true,"slider":null,"value":40000,"display":"40,000"},{"text":"standard_cd_quality_rate = 44100 // Hz","label":null,"prefix":null,"suffix":"Hz","section":null,"hidden":false,"hero":false,"slider":null,"value":44100,"display":"44,100"}]},{"id":"ocean-acidification-ph-change","title":"Ocean Acidification pH Change","description":"Predict pH change based on atmospheric CO2 increases.","category":"science","icon":"droplet","tags":["science","ocean","eco"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"initial_ph = 8.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8.1,"display":"8.1"},{"text":"carbon_dioxide_increase_percent = 20 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"ph_sensitivity_factor = 0.002 // change in pH per percent CO2 increase","label":null,"prefix":null,"suffix":"change in pH per percent CO2 increase","section":null,"hidden":false,"hero":false,"slider":null,"value":0.002,"display":"0.002"},{"text":"predicted_new_ph = initial_ph - (carbon_dioxide_increase_percent * ph_sensitivity_factor) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":8.06,"display":"8.06"}]},{"id":"ocean-tide-height-estimate","title":"Ocean Tide Height Estimate","description":"Estimate relative tidal force on Earth from the Moon's mass and distance.","category":"science","icon":"globe","tags":["ocean"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"moon_distance_km = 384400","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":384400,"display":"384,400"},{"text":"moon_mass_kg = 7.34e22","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7.34e+22,"display":"7.34e22"},{"text":"earth_radius_km = 6371","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371,"display":"6,371"},{"text":"tide_force_relative = (moon_mass_kg / moon_distance_km^3) * earth_radius_km // relative units @hero","label":null,"prefix":null,"suffix":"relative units","section":null,"hidden":false,"hero":true,"slider":null,"value":8232913036.222099,"display":"8,232,913,036.22"}]},{"id":"offshore-wind-farm-capacity","title":"Offshore Wind Farm Capacity","description":"Calculate energy generation and homes powered by offshore wind.","category":"engineering","icon":"fan","tags":["engineering","wind"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"number_of_turbines = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"turbine_capacity_mw = 8 // MW","label":null,"prefix":null,"suffix":"MW","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"capacity_factor = 40 // percent (efficiency in real conditions)","label":null,"prefix":null,"suffix":"percent (efficiency in real conditions)","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"total_annual_generation_gwh = number_of_turbines * turbine_capacity_mw * (capacity_factor / 100) * 8760 / 1000 // GWh @hero","label":null,"prefix":null,"suffix":"GWh","section":null,"hidden":false,"hero":true,"slider":null,"value":1401.6,"display":"1,401.6"},{"text":"homes_powered = total_annual_generation_gwh * 1000000 / 3500 // 3500 kWh per home","label":null,"prefix":null,"suffix":"3500 kWh per home","section":null,"hidden":false,"hero":false,"slider":null,"value":400457.14285714284,"display":"400,457.14"}]},{"id":"ohms-law","title":"Ohm's Law","description":"Calculate voltage, current, resistance, and power for electrical circuits.","category":"science","icon":"zap","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Circuit Values","label":null,"prefix":null,"suffix":null,"section":"Circuit Values","hero":false,"slider":null,"value":null,"display":null},{"text":"voltage = 12 // V 0.1..240","label":null,"prefix":null,"suffix":"V","section":"Circuit Values","hidden":false,"hero":false,"slider":{"min":0.1,"max":240,"step":5},"value":12,"display":"12"},{"text":"resistance = 6 // Ω 0.1..1000 by 0.1","label":null,"prefix":null,"suffix":"Ω","section":"Circuit Values","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":0.1},"value":6,"display":"6"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"current = voltage / resistance // A @hero @label(Current (I = V/R))","label":"Current (I = V/R)","prefix":null,"suffix":"A","section":"Results","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"},{"text":"power = voltage * current // W @label(Power (P = V × I))","label":"Power (P = V × I)","prefix":null,"suffix":"W","section":"Results","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"power check = current^2 * resistance // W @label(Power (P = I²R))","label":"Power (P = I²R)","prefix":null,"suffix":"W","section":"Results","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"energy per hour = power * 1 // Wh","label":null,"prefix":null,"suffix":"Wh","section":"Results","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"}]},{"id":"oil-change-interval-recommendation","title":"Oil Change Interval Recommendation","description":"Estimate oil change interval based on driving conditions.","category":"engineering","icon":"settings","tags":["automotive","maintenance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Driving Conditions","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hero":false,"slider":null,"value":null,"display":null},{"text":"base interval miles = 7500","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":7500,"display":"7,500"},{"text":"short trips factor = 0.8","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"towing factor = 0.7","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":0.7,"display":"0.7"},{"text":"dusty conditions factor = 0.9","label":null,"prefix":null,"suffix":null,"section":"Driving Conditions","hidden":false,"hero":false,"slider":null,"value":0.9,"display":"0.9"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"recommended interval miles = base interval miles * short trips factor * towing factor * dusty conditions factor","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":3780,"display":"3,780"}]},{"id":"on-time-delivery-rate","title":"On-Time Delivery Rate","description":"Monitor the percentage of orders delivered by the promised date.","category":"business","icon":"calendar","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"ordersDeliveredOnTime = 950 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":950,"display":"950"},{"text":"totalOrdersDelivered = 1000 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"onTimeDeliveryRatePercent = (ordersDeliveredOnTime / totalOrdersDelivered) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":95,"display":"95"}]},{"id":"one-rep-max-epley","title":"One Rep Max Epley","description":"Calculate one-rep max (1RM) using the Epley formula and training percentages.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Lift Details","label":null,"prefix":null,"suffix":null,"section":"Lift Details","hero":false,"slider":null,"value":null,"display":null},{"text":"weight lifted = 225 // lbs 5..1k","label":null,"prefix":null,"suffix":"lbs","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":5,"max":1000,"step":1},"value":225,"display":"225"},{"text":"reps performed = 5 // reps 1..30","label":null,"prefix":null,"suffix":"reps","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":5,"display":"5"},{"text":"# Epley Formula","label":null,"prefix":null,"suffix":null,"section":"Epley Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"one rep max = weight lifted * (1 + reps performed / 30) // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":"Epley Formula","hidden":false,"hero":true,"slider":null,"value":262.50000000000006,"display":"262.5"},{"text":"# Training Percentages","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hero":false,"slider":null,"value":null,"display":null},{"text":"ninety percent = one rep max * 0.9","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hidden":false,"hero":false,"slider":null,"value":236.25000000000003,"display":"236.25"},{"text":"eighty percent = one rep max * 0.8","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hidden":false,"hero":false,"slider":null,"value":210.00000000000003,"display":"210"},{"text":"seventy percent = one rep max * 0.7","label":null,"prefix":null,"suffix":null,"section":"Training Percentages","hidden":false,"hero":false,"slider":null,"value":183.75000000000003,"display":"183.75"}]},{"id":"one-rep-max","title":"One Rep Max","description":"Estimate your 1RM and training maxes from a submaximal lift.","category":"health","icon":"dumbbell","tags":["training"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Lift Details","label":null,"prefix":null,"suffix":null,"section":"Lift Details","hero":false,"slider":null,"value":null,"display":null},{"text":"weight lifted = 185 // lbs 5..1k by 5","label":null,"prefix":null,"suffix":"lbs","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":5,"max":1000,"step":5},"value":185,"display":"185"},{"text":"reps done = 5 // reps 1..30","label":null,"prefix":null,"suffix":"reps","section":"Lift Details","hidden":false,"hero":false,"slider":{"min":1,"max":30,"step":1},"value":5,"display":"5"},{"text":"# Estimated 1RM (Epley Formula)","label":null,"prefix":null,"suffix":null,"section":"Estimated 1RM (Epley Formula)","hero":false,"slider":null,"value":null,"display":null},{"text":"estimated 1rm = round(weight lifted * (1 + reps done / 30)) // lbs @hero","label":null,"prefix":null,"suffix":"lbs","section":"Estimated 1RM (Epley Formula)","hidden":false,"hero":true,"slider":null,"value":216,"display":"216"},{"text":"# Training Maxes","label":null,"prefix":null,"suffix":null,"section":"Training Maxes","hero":false,"slider":null,"value":null,"display":null},{"text":"ninety pct = round(estimated 1rm * 0.90) // lbs @label(90% Training Max)","label":"90% Training Max","prefix":null,"suffix":"lbs","section":"Training Maxes","hidden":false,"hero":false,"slider":null,"value":194,"display":"194"},{"text":"eighty five pct = round(estimated 1rm * 0.85) // lbs @label(85% Training Max)","label":"85% Training Max","prefix":null,"suffix":"lbs","section":"Training Maxes","hidden":false,"hero":false,"slider":null,"value":184,"display":"184"},{"text":"eighty pct = round(estimated 1rm * 0.80) // lbs @label(80% Training Max)","label":"80% Training Max","prefix":null,"suffix":"lbs","section":"Training Maxes","hidden":false,"hero":false,"slider":null,"value":173,"display":"173"}]},{"id":"op-amp-gain-non-inverting","title":"Op-Amp Gain Non-Inverting","description":"Calculate voltage gain for a non-inverting amplifier.","category":"engineering","icon":"activity","tags":["engineering","electronics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"resistor_feedback_ohms = 10000 // Rf","label":null,"prefix":null,"suffix":"Rf","section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"resistor_ground_ohms = 1000 // Rg","label":null,"prefix":null,"suffix":"Rg","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"voltage_gain = 1 + (resistor_feedback_ohms / resistor_ground_ohms) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11,"display":"11"},{"text":"input_voltage = 0.1 // volts","label":null,"prefix":null,"suffix":"volts","section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"output_voltage = input_voltage * voltage_gain // volts","label":null,"prefix":null,"suffix":"volts","section":null,"hidden":false,"hero":false,"slider":null,"value":1.1,"display":"1.1"}]},{"id":"openstax-algebra-trig-unit-circle","title":"OpenStax · Degrees, Radians & the Pythagorean Identity (Algebra and Trigonometry)","description":"Worked example in the style of OpenStax Algebra and Trigonometry 2e — evaluating unit-circle values and confirming sin²θ + cos²θ = 1, with a note on the degrees-vs-radians trap.","category":"education","icon":"book-open","tags":["trigonometry","unit-circle","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.441Z"},"rows":[{"text":"# Angle mode matters","label":null,"prefix":null,"suffix":null,"section":"Angle mode matters","hero":false,"slider":null,"value":null,"display":null},{"text":"sin_30 = sin(30) // @label(sin 30°)","label":"sin 30°","prefix":null,"suffix":null,"section":"Angle mode matters","hidden":false,"hero":false,"slider":null,"value":0.49999999999999994,"display":"0.5"},{"text":"sin_pi_6 = sin(pi/6 rad) // @label(sin(π/6), radians)","label":"sin(π/6), radians","prefix":null,"suffix":null,"section":"Angle mode matters","hidden":false,"hero":false,"slider":null,"value":0.49999999999999994,"display":"0.5"},{"text":"# Common unit-circle values (degrees)","label":null,"prefix":null,"suffix":null,"section":"Common unit-circle values (degrees)","hero":false,"slider":null,"value":null,"display":null},{"text":"cos_60 = cos(60) // @label(cos 60°)","label":"cos 60°","prefix":null,"suffix":null,"section":"Common unit-circle values (degrees)","hidden":false,"hero":false,"slider":null,"value":0.5000000000000001,"display":"0.5"},{"text":"tan_45 = tan(45) // @label(tan 45°)","label":"tan 45°","prefix":null,"suffix":null,"section":"Common unit-circle values (degrees)","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Pythagorean identity","label":null,"prefix":null,"suffix":null,"section":"Pythagorean identity","hero":false,"slider":null,"value":null,"display":null},{"text":"identity = sin(45)^2 + cos(45)^2 // @hero @formula @label(sin²45° + cos²45°)","label":"sin²45° + cos²45°","prefix":null,"suffix":null,"section":"Pythagorean identity","hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"openstax-calculus-definite-integral-ftc","title":"OpenStax · Definite Integral via the FTC (Calculus I)","description":"Worked example in the style of OpenStax Calculus Volume 1 — evaluating a definite integral with the Fundamental Theorem of Calculus.","category":"education","icon":"book-open","tags":["calculus","integrals","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.261Z"},"rows":[{"text":"# Find an antiderivative","label":null,"prefix":null,"suffix":null,"section":"Find an antiderivative","hero":false,"slider":null,"value":null,"display":null},{"text":"# Evaluate F at the bounds","label":null,"prefix":null,"suffix":null,"section":"Evaluate F at the bounds","hero":false,"slider":null,"value":null,"display":null},{"text":"F_upper = 3^3 - 3^2 // @label(F(3))","label":"F(3)","prefix":null,"suffix":null,"section":"Evaluate F at the bounds","hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"F_lower = 1^3 - 1^2 // @label(F(1))","label":"F(1)","prefix":null,"suffix":null,"section":"Evaluate F at the bounds","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# Apply the FTC","label":null,"prefix":null,"suffix":null,"section":"Apply the FTC","hero":false,"slider":null,"value":null,"display":null},{"text":"integral = F_upper - F_lower // @hero @formula @label(integral from 1 to 3)","label":"integral from 1 to 3","prefix":null,"suffix":null,"section":"Apply the FTC","hidden":false,"hero":true,"slider":null,"value":18,"display":"18"}]},{"id":"openstax-college-algebra-change-of-base","title":"OpenStax · Change-of-Base Formula (College Algebra)","description":"Worked example in the style of OpenStax College Algebra 2e — evaluating a logarithm to an unusual base with the change-of-base formula.","category":"education","icon":"book-open","tags":["algebra","logarithms","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.441Z"},"rows":[{"text":"# Change of base","label":null,"prefix":null,"suffix":null,"section":"Change of base","hero":false,"slider":null,"value":null,"display":null},{"text":"result = log(100)/log(5) // @hero @formula @label(log base 5 of 100)","label":"log base 5 of 100","prefix":null,"suffix":null,"section":"Change of base","hidden":false,"hero":true,"slider":null,"value":2.8613531161467867,"display":"2.861"},{"text":"# Verify by exponentiating","label":null,"prefix":null,"suffix":null,"section":"Verify by exponentiating","hero":false,"slider":null,"value":null,"display":null},{"text":"check = 5^result // @label(5 ^ result)","label":"5 ^ result","prefix":null,"suffix":null,"section":"Verify by exponentiating","hidden":false,"hero":false,"slider":null,"value":100.00000000000009,"display":"100"}]},{"id":"openstax-college-algebra-compound-interest","title":"OpenStax · Compound Interest (College Algebra)","description":"Worked example in the style of OpenStax College Algebra 2e — the compound-interest formula A = P(1 + r/n)^(nt), evaluated end to end.","category":"education","icon":"book-open","tags":["algebra","finance","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.261Z"},"rows":[{"text":"# Given values","label":null,"prefix":null,"suffix":null,"section":"Given values","hero":false,"slider":null,"value":null,"display":null},{"text":"P = 3000 // @label(principal) @prefix($)","label":"principal","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"r = 0.03 // @label(annual rate)","label":"annual rate","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"n = 4 // @label(compounds per year)","label":"compounds per year","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"t = 10 // @label(years)","label":"years","prefix":null,"suffix":null,"section":"Given values","hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"# Apply the compound-interest formula","label":null,"prefix":null,"suffix":null,"section":"Apply the compound-interest formula","hero":false,"slider":null,"value":null,"display":null},{"text":"amount = P*(1 + r/n)^(n*t) // @hero @prefix($) @formula @label(balance after 10 years)","label":"balance after 10 years","prefix":null,"suffix":null,"section":"Apply the compound-interest formula","hidden":false,"hero":true,"slider":null,"value":4045.045837009249,"display":"4,045.05"}]},{"id":"openstax-college-algebra-log-laws","title":"OpenStax · The Laws of Logarithms (College Algebra)","description":"Worked example in the style of OpenStax College Algebra 2e — verifying the product, inverse, and change-of-base log laws numerically.","category":"education","icon":"book-open","tags":["logarithms","college-algebra","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.629Z"},"rows":[{"text":"# Product law: log(ab) = log a + log b","label":null,"prefix":null,"suffix":null,"section":"Product law: log(ab) = log a + log b","hero":false,"slider":null,"value":null,"display":null},{"text":"product_law = log(2) + log(50) // @hero @label(log 2 + log 50)","label":"log 2 + log 50","prefix":null,"suffix":null,"section":"Product law: log(ab) = log a + log b","hidden":false,"hero":true,"slider":null,"value":1.9999999999999998,"display":"2"},{"text":"# Logs and exponentials are inverses","label":null,"prefix":null,"suffix":null,"section":"Logs and exponentials are inverses","hero":false,"slider":null,"value":null,"display":null},{"text":"inverse_check = e^(ln(5)) // @label(e^(ln 5))","label":"e^(ln 5)","prefix":null,"suffix":null,"section":"Logs and exponentials are inverses","hidden":false,"hero":false,"slider":null,"value":4.999999999999999,"display":"5"},{"text":"# Change of base / power law: log_b(a) = log a / log b","label":null,"prefix":null,"suffix":null,"section":"Change of base / power law: log_b(a) = log a / log b","hero":false,"slider":null,"value":null,"display":null},{"text":"power_law = log(8) / log(2) // @label(log 8 / log 2)","label":"log 8 / log 2","prefix":null,"suffix":null,"section":"Change of base / power law: log_b(a) = log a / log b","hidden":false,"hero":false,"slider":null,"value":2.9999999999999996,"display":"3"}]},{"id":"openstax-elementary-algebra-mixture","title":"OpenStax · Mixture Problem (Elementary Algebra)","description":"Worked example in the style of OpenStax Elementary Algebra 2e — mixing two acid solutions to hit a target concentration, solved two ways that agree.","category":"education","icon":"book-open","tags":["algebra","openstax","worked-example"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.441Z"},"rows":[{"text":"# Set up the equation","label":null,"prefix":null,"suffix":null,"section":"Set up the equation","hero":false,"slider":null,"value":null,"display":null},{"text":"# Method 1 — let the engine solve it","label":null,"prefix":null,"suffix":null,"section":"Method 1 — let the engine solve it","hero":false,"slider":null,"value":null,"display":null},{"text":"# Method 2 — isolate x by hand","label":null,"prefix":null,"suffix":null,"section":"Method 2 — isolate x by hand","hero":false,"slider":null,"value":null,"display":null},{"text":"liters_40 = (0.25*10 - 0.10*10) / (0.40 - 0.10) // @hero @label(liters of 40% solution)","label":"liters of 40% solution","prefix":null,"suffix":null,"section":"Method 2 — isolate x by hand","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"openstax-intermediate-algebra-factoring","title":"OpenStax · Factoring & Quadratic Roots (Intermediate Algebra)","description":"Worked example in the style of OpenStax Intermediate Algebra 2e — factor a trinomial, expand to check, solve the quadratic, and confirm the roots with Vieta's formulas.","category":"education","icon":"book-open","tags":["algebra","factoring","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.441Z"},"rows":[{"text":"# Factor the trinomial","label":null,"prefix":null,"suffix":null,"section":"Factor the trinomial","hero":false,"slider":null,"value":null,"display":null},{"text":"# Expand to check","label":null,"prefix":null,"suffix":null,"section":"Expand to check","hero":false,"slider":null,"value":null,"display":null},{"text":"# Solve for the roots","label":null,"prefix":null,"suffix":null,"section":"Solve for the roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# A quadratic with no real roots","label":null,"prefix":null,"suffix":null,"section":"A quadratic with no real roots","hero":false,"slider":null,"value":null,"display":null},{"text":"# Confirm with Vieta's formulas","label":null,"prefix":null,"suffix":null,"section":"Confirm with Vieta's formulas","hero":false,"slider":null,"value":null,"display":null},{"text":"product_of_roots = 2 * 3 // @hero @label(product of the roots)","label":"product of the roots","prefix":null,"suffix":null,"section":"Confirm with Vieta's formulas","hidden":false,"hero":true,"slider":null,"value":6,"display":"6"}]},{"id":"openstax-linear-algebra-matrices","title":"OpenStax · Matrices: Determinant, Inverse & a 2×2 System (Linear Algebra)","description":"Worked example in the style of OpenStax — matrix literals with [[...]] notation, the determinant and inverse, then solving a linear system as a matrix equation.","category":"education","icon":"book-open","tags":["linear-algebra","matrices","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.629Z"},"rows":[{"text":"# Define a matrix","label":null,"prefix":null,"suffix":null,"section":"Define a matrix","hero":false,"slider":null,"value":null,"display":null},{"text":"A = [[2, 1], [1, 3]] // @label(matrix A)","label":"matrix A","prefix":null,"suffix":null,"section":"Define a matrix","hidden":false,"hero":false,"slider":null,"value":[[2,1],[1,3]],"display":null},{"text":"# Determinant and inverse","label":null,"prefix":null,"suffix":null,"section":"Determinant and inverse","hero":false,"slider":null,"value":null,"display":null},{"text":"detA = det(A) // @hero @label(det(A))","label":"det(A)","prefix":null,"suffix":null,"section":"Determinant and inverse","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"invA = inverse(A) // @label(A⁻¹)","label":"A⁻¹","prefix":null,"suffix":null,"section":"Determinant and inverse","hidden":false,"hero":false,"slider":null,"value":[[0.6,-0.2],[-0.2,0.4]],"display":null},{"text":"# Solve a system Bx = c via the inverse","label":null,"prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hero":false,"slider":null,"value":null,"display":null},{"text":"B = [[1, 1], [1, -1]] // @label(coefficient matrix)","label":"coefficient matrix","prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hidden":false,"hero":false,"slider":null,"value":[[1,1],[1,-1]],"display":null},{"text":"c = [[10], [2]] // @label(constants)","label":"constants","prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hidden":false,"hero":false,"slider":null,"value":[[10],[2]],"display":null},{"text":"solution = inverse(B) * c // @label(solution [x; y])","label":"solution [x; y]","prefix":null,"suffix":null,"section":"Solve a system Bx = c via the inverse","hidden":false,"hero":false,"slider":null,"value":[[6],[4]],"display":null}]},{"id":"openstax-prealgebra-prime-factorization","title":"OpenStax · Prime Factorization, GCD & LCM (Prealgebra)","description":"Worked example in the style of OpenStax Prealgebra 2e — break a number into primes, then read off the greatest common divisor and least common multiple.","category":"education","icon":"book-open","tags":["prealgebra","number-theory","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.441Z"},"rows":[{"text":"# Prime factorization of 360","label":null,"prefix":null,"suffix":null,"section":"Prime factorization of 360","hero":false,"slider":null,"value":null,"display":null},{"text":"prime_factors = factor(360) // @label(360 as primes)","label":"360 as primes","prefix":null,"suffix":null,"section":"Prime factorization of 360","hidden":false,"hero":false,"slider":null,"value":"2^3*3^2*5","display":"2^3*3^2*5"},{"text":"# Greatest common divisor of 48 and 180","label":null,"prefix":null,"suffix":null,"section":"Greatest common divisor of 48 and 180","hero":false,"slider":null,"value":null,"display":null},{"text":"gcd_value = gcd(48, 180) // @label(GCD)","label":"GCD","prefix":null,"suffix":null,"section":"Greatest common divisor of 48 and 180","hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"# Least common multiple of 48 and 180","label":null,"prefix":null,"suffix":null,"section":"Least common multiple of 48 and 180","hero":false,"slider":null,"value":null,"display":null},{"text":"lcm_value = lcm(48, 180) // @hero @label(LCM)","label":"LCM","prefix":null,"suffix":null,"section":"Least common multiple of 48 and 180","hidden":false,"hero":true,"slider":null,"value":720,"display":"720"},{"text":"# Bonus: all divisors and a primality check","label":null,"prefix":null,"suffix":null,"section":"Bonus: all divisors and a primality check","hero":false,"slider":null,"value":null,"display":null},{"text":"all_divisors = divisors(36) // @label(divisors of 36)","label":"divisors of 36","prefix":null,"suffix":null,"section":"Bonus: all divisors and a primality check","hidden":false,"hero":false,"slider":null,"value":[1,2,3,4,6,9,12,18,36],"display":null},{"text":"is_97_prime = isprime(97) // @label(is 97 prime?)","label":"is 97 prime?","prefix":null,"suffix":null,"section":"Bonus: all divisors and a primality check","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"}]},{"id":"openstax-precalculus-complex-euler","title":"OpenStax · Complex Numbers & Euler's Identity (Precalculus)","description":"Worked example in the style of OpenStax Precalculus 2e — the imaginary unit, complex arithmetic and modulus, and Euler's identity e^(iπ) = −1.","category":"education","icon":"book-open","tags":["complex-numbers","precalculus","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.629Z"},"rows":[{"text":"# The imaginary unit","label":null,"prefix":null,"suffix":null,"section":"The imaginary unit","hero":false,"slider":null,"value":null,"display":null},{"text":"i_squared = i^2 // @label(i²)","label":"i²","prefix":null,"suffix":null,"section":"The imaginary unit","hidden":false,"hero":false,"slider":null,"value":-1,"display":"-1"},{"text":"# Modulus and conjugate","label":null,"prefix":null,"suffix":null,"section":"Modulus and conjugate","hero":false,"slider":null,"value":null,"display":null},{"text":"modulus = abs(3 + 4i) // @hero @label(|3 + 4i|)","label":"|3 + 4i|","prefix":null,"suffix":null,"section":"Modulus and conjugate","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"# Euler's identity","label":null,"prefix":null,"suffix":null,"section":"Euler's identity","hero":false,"slider":null,"value":null,"display":null},{"text":"euler = e^(i*pi) // @label(e^(iπ))","label":"e^(iπ)","prefix":null,"suffix":null,"section":"Euler's identity","hidden":false,"hero":false,"slider":null,"value":-1,"display":"-1"}]},{"id":"openstax-precalculus-geometric-series","title":"OpenStax · Geometric Series Sum (Precalculus)","description":"Worked example in the style of OpenStax Precalculus 2e — summing a finite geometric series with the closed form, then checking term by term.","category":"education","icon":"book-open","tags":["precalculus","sequences","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.261Z"},"rows":[{"text":"# Given","label":null,"prefix":null,"suffix":null,"section":"Given","hero":false,"slider":null,"value":null,"display":null},{"text":"a1 = 3 // @label(first term)","label":"first term","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"r = 2 // @label(common ratio)","label":"common ratio","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"n = 8 // @label(number of terms)","label":"number of terms","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Closed form for the sum","label":null,"prefix":null,"suffix":null,"section":"Closed form for the sum","hero":false,"slider":null,"value":null,"display":null},{"text":"sum = a1*(1 - r^n)/(1 - r) // @hero @formula @label(sum of first 8 terms)","label":"sum of first 8 terms","prefix":null,"suffix":null,"section":"Closed form for the sum","hidden":false,"hero":true,"slider":null,"value":765,"display":"765"},{"text":"# Sanity check: add the terms directly","label":null,"prefix":null,"suffix":null,"section":"Sanity check: add the terms directly","hero":false,"slider":null,"value":null,"display":null},{"text":"check = 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 // @label(term-by-term)","label":"term-by-term","prefix":null,"suffix":null,"section":"Sanity check: add the terms directly","hidden":false,"hero":false,"slider":null,"value":765,"display":"765"}]},{"id":"openstax-precalculus-vectors","title":"OpenStax · Vectors: Dot Product, Cross Product & Angle (Precalculus)","description":"Worked example in the style of OpenStax Precalculus 2e — vector magnitude, dot product, the angle between two vectors, and the cross product, all in natural [x, y, z] notation.","category":"education","icon":"book-open","tags":["vectors","precalculus","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.629Z"},"rows":[{"text":"# Define the vectors","label":null,"prefix":null,"suffix":null,"section":"Define the vectors","hero":false,"slider":null,"value":null,"display":null},{"text":"u = [1, 2, 2] // @label(vector u)","label":"vector u","prefix":null,"suffix":null,"section":"Define the vectors","hidden":false,"hero":false,"slider":null,"value":[1,2,2],"display":null},{"text":"v = [2, 0, 1] // @label(vector v)","label":"vector v","prefix":null,"suffix":null,"section":"Define the vectors","hidden":false,"hero":false,"slider":null,"value":[2,0,1],"display":null},{"text":"# Magnitudes","label":null,"prefix":null,"suffix":null,"section":"Magnitudes","hero":false,"slider":null,"value":null,"display":null},{"text":"mag_u = norm(u) // @label(|u|)","label":"|u|","prefix":null,"suffix":null,"section":"Magnitudes","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"mag_v = norm(v) // @label(|v|)","label":"|v|","prefix":null,"suffix":null,"section":"Magnitudes","hidden":false,"hero":false,"slider":null,"value":2.2360679775,"display":"2.236"},{"text":"# Dot product and the angle between","label":null,"prefix":null,"suffix":null,"section":"Dot product and the angle between","hero":false,"slider":null,"value":null,"display":null},{"text":"u_dot_v = dot(u, v) // @label(u · v)","label":"u · v","prefix":null,"suffix":null,"section":"Dot product and the angle between","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"angle_uv = angle(u, v) // @hero @label(angle between u and v)","label":"angle between u and v","prefix":null,"suffix":null,"section":"Dot product and the angle between","hidden":false,"hero":true,"slider":null,"value":53.39572355729035,"display":"53.3957"},{"text":"# Cross product (perpendicular to both)","label":null,"prefix":null,"suffix":null,"section":"Cross product (perpendicular to both)","hero":false,"slider":null,"value":null,"display":null},{"text":"u_cross_v = cross(u, v) // @label(u × v)","label":"u × v","prefix":null,"suffix":null,"section":"Cross product (perpendicular to both)","hidden":false,"hero":false,"slider":null,"value":[2,3,-4],"display":null}]},{"id":"openstax-statistics-normal-probability","title":"OpenStax · Normal Distribution Probability (Statistics)","description":"Worked example in the style of OpenStax Introductory Statistics 2e — a z-score and a normal-curve probability, with no printed Z-table needed.","category":"education","icon":"book-open","tags":["statistics","normal","openstax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T17:15:58.261Z"},"rows":[{"text":"# Given","label":null,"prefix":null,"suffix":null,"section":"Given","hero":false,"slider":null,"value":null,"display":null},{"text":"mu = 170 // @label(mean μ) @suffix(cm)","label":"mean μ","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":170,"display":"170"},{"text":"sigma = 8 // @label(std dev σ) @suffix(cm)","label":"std dev σ","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"x = 182 // @label(height of interest) @suffix(cm)","label":"height of interest","prefix":null,"suffix":null,"section":"Given","hidden":false,"hero":false,"slider":null,"value":182,"display":"182"},{"text":"# Standardize to a z-score","label":null,"prefix":null,"suffix":null,"section":"Standardize to a z-score","hero":false,"slider":null,"value":null,"display":null},{"text":"z = (x - mu)/sigma // @formula @label(z-score)","label":"z-score","prefix":null,"suffix":null,"section":"Standardize to a z-score","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"# Probability from the standard normal CDF","label":null,"prefix":null,"suffix":null,"section":"Probability from the standard normal CDF","hero":false,"slider":null,"value":null,"display":null},{"text":"probability = normDist(x, mu, sigma, true) // @hero @formula @label(P(height < 182 cm))","label":"P(height < 182 cm)","prefix":null,"suffix":null,"section":"Probability from the standard normal CDF","hidden":false,"hero":true,"slider":null,"value":0.9331927690234977,"display":"0.9332"}]},{"id":"operant-conditioning-ratio","title":"Operant Conditioning Ratio","description":"Calculate the response-to-reward ratio in operant conditioning.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"responses = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"rewards = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"ratio = responses / rewards // responses per reward @hero","label":null,"prefix":null,"suffix":"responses per reward","section":null,"hidden":false,"hero":true,"slider":null,"value":10,"display":"10"}]},{"id":"operating-expense-ratio","title":"Operating Expense Ratio","description":"Compare operating expenses against effective gross income.","category":"real-estate","icon":"pie-chart","tags":["real-estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"operatingExpenses = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"effectiveGrossIncome = 40000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":40000,"display":"40,000"},{"text":"oerPercent = (operatingExpenses / effectiveGrossIncome) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":37.5,"display":"37.5"}]},{"id":"operating-leverage-degree","title":"Operating Leverage Degree","description":"Calculate the degree of operating leverage from contribution margin and operating income.","category":"health","icon":"activity","tags":["leverage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"contribution_margin = 1000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"operating_income = 400000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":400000,"display":"400,000"},{"text":"degree_of_operating_leverage = contribution_margin / operating_income","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"}]},{"id":"opportunity-zone-investment-gain","title":"Opportunity Zone Gain","description":"Estimate potential tax savings from Opportunity Zone investments.","category":"real-estate","icon":"map","tags":["investment"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"capitalGainAmount = 100000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100000,"display":"100,000"},{"text":"taxRatePercentage = 20 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"deferralYears = 5 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"taxSavings = (capitalGainAmount * (taxRatePercentage / 100)) // dollars deferred @hero","label":null,"prefix":null,"suffix":"dollars deferred","section":null,"hidden":false,"hero":true,"slider":null,"value":20000,"display":"20,000"}]},{"id":"optimism-bias-margin","title":"Optimism Bias Margin","description":"Calculate the optimism bias margin between predicted and average success rates.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"predicted_success_rate = 0.8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.8,"display":"0.8"},{"text":"average_success_rate = 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"bias_margin = predicted_success_rate - average_success_rate // percentage points @hero","label":null,"prefix":null,"suffix":"percentage points","section":null,"hidden":false,"hero":true,"slider":null,"value":0.3,"display":"0.3"}]},{"id":"orbital-period","title":"Orbital Period","description":"Calculate orbital period in hours from semi-major axis and central body mass.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"semi_major_axis_kilometers = 42164 // Geostationary","label":null,"prefix":null,"suffix":"Geostationary","section":null,"hidden":false,"hero":false,"slider":null,"value":42164,"display":"42,164"},{"text":"planetary_mass_kilograms = 5.97e24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5.97e+24,"display":"5.97e24"},{"text":"gravitational_constant = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"period_seconds = 2 * pi * sqrt( (semi_major_axis_kilometers * 1000)^3 / (gravitational_constant * planetary_mass_kilograms) )","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":86181.15468591503,"display":"86,181.15"},{"text":"period_hours = period_seconds / 3600 // hours @hero","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":true,"slider":null,"value":23.939209634976397,"display":"23.94"}]},{"id":"orbital-velocity","title":"Orbital Velocity","description":"Circular-orbit speed and period for any altitude around any body.","category":"science","icon":"orbit","tags":["orbit","physics","space"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"# Orbit","label":null,"prefix":null,"suffix":null,"section":"Orbit","hero":false,"slider":null,"value":null,"display":null},{"text":"body mass kg = 5.972e24 // kg 1e20..2e30","label":null,"prefix":null,"suffix":"kg","section":"Orbit","hidden":false,"hero":false,"slider":{"min":100000000000000000000,"max":2e+30,"step":2e+28},"value":5.972e+24,"display":"5.972e24"},{"text":"altitude km = 408 // km 100..400k","label":null,"prefix":null,"suffix":"km","section":"Orbit","hidden":false,"hero":false,"slider":{"min":100,"max":400000,"step":5000},"value":408,"display":"408"},{"text":"body radius km = 6371 // km 100..70k","label":null,"prefix":null,"suffix":"km","section":"Orbit","hidden":false,"hero":false,"slider":{"min":100,"max":70000,"step":1000},"value":6371,"display":"6,371"},{"text":"# Circular Orbit Math","label":null,"prefix":null,"suffix":null,"section":"Circular Orbit Math","hero":false,"slider":null,"value":null,"display":null},{"text":"_G = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":"Circular Orbit Math","hidden":true,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"_orbit_radius_m = (body radius km + altitude km) * 1000 // m","label":null,"prefix":null,"suffix":"m","section":"Circular Orbit Math","hidden":true,"hero":false,"slider":null,"value":6779000,"display":"6,779,000"},{"text":"velocity m per s = sqrt(G * body mass kg / orbit_radius_m) // m/s @label(Orbital velocity) @suffix(m/s)","label":"Orbital velocity","prefix":null,"suffix":"m/s","section":"Circular Orbit Math","hidden":false,"hero":false,"slider":null,"value":7667.789532332016,"display":"7,667.79"},{"text":"velocity km per s = velocity m per s / 1000 // km/s @hero @label(Orbital velocity (km/s))","label":"Orbital velocity (km/s)","prefix":null,"suffix":"km/s","section":"Circular Orbit Math","hidden":false,"hero":true,"slider":null,"value":7.667789532332016,"display":"7.668"},{"text":"# Orbital Period","label":null,"prefix":null,"suffix":null,"section":"Orbital Period","hero":false,"slider":null,"value":null,"display":null},{"text":"_period_seconds = 2 * pi * orbit_radius_m / velocity m per s // s","label":null,"prefix":null,"suffix":"s","section":"Orbital Period","hidden":true,"hero":false,"slider":null,"value":5554.8881483730975,"display":"5,554.89"},{"text":"period minutes = round(period_seconds / 60, 1) // min @label(Orbital period) @suffix(min)","label":"Orbital period","prefix":null,"suffix":"min","section":"Orbital Period","hidden":false,"hero":false,"slider":null,"value":92.6,"display":"92.6"},{"text":"orbits per day = round(1440 / period minutes, 1)","label":null,"prefix":null,"suffix":null,"section":"Orbital Period","hidden":false,"hero":false,"slider":null,"value":15.6,"display":"15.6"}]},{"id":"order-picking-accuracy","title":"Order Picking Accuracy","description":"Track the percentage of orders picked without any errors.","category":"business","icon":"check-circle","tags":["order"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"totalOrdersPicked = 1000 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"incorrectOrders = 5 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"accuracyRate = ((totalOrdersPicked - incorrectOrders) / totalOrdersPicked) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":99.5,"display":"99.5"}]},{"id":"origami-fold-thickness","title":"Origami Fold Thickness","description":"Calculate the thickness in millimeters of paper after N folds.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"initial_thickness_mm = 0.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"number_of_folds = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"final_thickness_mm = initial_thickness_mm * 2^number_of_folds // millimeters @hero","label":null,"prefix":null,"suffix":"millimeters","section":null,"hidden":false,"hero":true,"slider":null,"value":12.8,"display":"12.8"}]},{"id":"osha-incident-rate","title":"OSHA Incident Rate","description":"Calculate your company's safety incident rate per 100 employees.","category":"other","icon":"shield","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"numberOfIncidents = 5 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"totalHoursWorked = 200000 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"incidentRate = (numberOfIncidents * 200000) / totalHoursWorked // per 100 employees @hero","label":null,"prefix":null,"suffix":"per 100 employees","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"outbound-shipping-cost","title":"Outbound Shipping Cost","description":"Calculate the average cost to ship orders to your customers.","category":"business","icon":"send","tags":["shipping"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.712Z"},"rows":[{"text":"totalOutboundFreight = 15000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":15000,"display":"15,000"},{"text":"totalOutboundOrders = 3000 // orders","label":null,"prefix":null,"suffix":"orders","section":null,"hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"averageOutboundCost = totalOutboundFreight / totalOutboundOrders // dollars per order @hero","label":null,"prefix":null,"suffix":"dollars per order","section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"ovulation-calculator","title":"Ovulation Calculator","description":"Calculate days until ovulation and the fertile window from cycle 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@hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":23.264388374233185,"display":"23.26"}]},{"id":"p-e-ratio","title":"P E Ratio","description":"Calculate price-to-earnings ratio and earnings yield from stock price and EPS.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Stock Data","label":null,"prefix":null,"suffix":null,"section":"Stock Data","hero":false,"slider":null,"value":null,"display":null},{"text":"$share_price = 150 // dollars 1..5k","label":null,"prefix":"$","suffix":"dollars","section":"Stock Data","hidden":false,"hero":false,"slider":{"min":1,"max":5000,"step":50},"value":150,"display":"$150.00"},{"text":"$earnings_per_share = 7.50 // dollars 0.01..500","label":null,"prefix":"$","suffix":"dollars","section":"Stock 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0.01","label":null,"prefix":null,"suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":0,"max":5,"step":0.01},"value":1.96,"display":"1.96"},{"text":"# Approximation for one-tailed p-value","label":null,"prefix":null,"suffix":null,"section":"Approximation for one-tailed p-value","hero":false,"slider":null,"value":null,"display":null},{"text":"# Using a simple approximation for the area under the normal curve","label":null,"prefix":null,"suffix":null,"section":"Using a simple approximation for the area under the normal curve","hero":false,"slider":null,"value":null,"display":null},{"text":"p value approx = 0.5 * exp(-0.717 * z score - 0.416 * z score^2) // @hero","label":null,"prefix":null,"suffix":null,"section":"Using a simple approximation for the area under the normal curve","hidden":false,"hero":true,"slider":null,"value":0.024808404786111647,"display":"0.0248"},{"text":"confidence level = (1 - p value approx) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Using a simple approximation for the area under the normal curve","hidden":false,"hero":false,"slider":null,"value":97.51915952138884,"display":"97.52"}]},{"id":"packet-loss-impact-tcp-throughput","title":"Packet Loss Impact Tcp Throughput","description":"Calculate maximum TCP throughput as constrained by RTT and packet loss.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"bandwidth_mbps = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"round_trip_time_ms = 50","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"packet_loss_rate = 0.001","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.001,"display":"0.001"},{"text":"max_throughput = (1460 * 8) / (round_trip_time_ms * 0.001 * (packet_loss_rate ** 0.5))","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":7387080.614153335,"display":"7,387,080.61"}]},{"id":"paint-coverage","title":"Paint Coverage","description":"Calculate how many gallons of paint you need for any room, minus doors and windows.","category":"construction","icon":"paintbrush","tags":["coverage"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Room Dimensions","label":null,"prefix":null,"suffix":null,"section":"Room Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"room length = 15 // ft 5..50","label":null,"prefix":null,"suffix":"ft","section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":15,"display":"15"},{"text":"room width = 12 // ft 5..50","label":null,"prefix":null,"suffix":"ft","section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":5,"max":50,"step":1},"value":12,"display":"12"},{"text":"wall height = 9 // ft 7..20","label":null,"prefix":null,"suffix":"ft","section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":7,"max":20,"step":0.2},"value":9,"display":"9"},{"text":"number of doors = 1 // 0..6","label":null,"prefix":null,"suffix":null,"section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":0,"max":6,"step":0.1},"value":1,"display":"1"},{"text":"number of windows = 2 // 0..10","label":null,"prefix":null,"suffix":null,"section":"Room Dimensions","hidden":false,"hero":false,"slider":{"min":0,"max":10,"step":0.1},"value":2,"display":"2"},{"text":"# Wall Area","label":null,"prefix":null,"suffix":null,"section":"Wall 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Needed","hidden":false,"hero":false,"slider":null,"value":3,"display":"3"}]},{"id":"painting-coverage-gallons-required","title":"Painting Coverage Gallons Required","description":"Calculate gallons of paint needed from wall area, coverage rate, and coat count.","category":"design","icon":"palette","tags":["coverage"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"wall_area_square_feet = 400 // square feet","label":null,"prefix":null,"suffix":"square feet","section":null,"hidden":false,"hero":false,"slider":null,"value":400,"display":"400"},{"text":"paint_coverage_per_gallon = 350 // square feet per gallon","label":null,"prefix":null,"suffix":"square feet per gallon","section":null,"hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"number_of_coats = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"total_gallons_required = (wall_area_square_feet / paint_coverage_per_gallon) * number_of_coats // gallons @hero","label":null,"prefix":null,"suffix":"gallons","section":null,"hidden":false,"hero":true,"slider":null,"value":2.2857142857142856,"display":"2.286"}]},{"id":"pallet-stack-height","title":"Pallet Stack Height","description":"Determine the total height of a pallet stack including the base.","category":"business","icon":"layers","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"palletBaseHeight = 0.15 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.15,"display":"0.15"},{"text":"boxHeight = 0.3 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"boxesPerStack = 5 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"totalStackHeight = palletBaseHeight + (boxHeight * boxesPerStack) // meters @hero","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":true,"slider":null,"value":1.65,"display":"1.65"}]},{"id":"paper-airplane-flight-time","title":"Paper Airplane Flight Time","description":"Estimate paper airplane flight time from launch height and glide ratio.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"launch_height_meters = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"glide_ratio = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"horizontal_distance = launch_height_meters * glide_ratio","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"flight_speed_m_s = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"flight_time_seconds = horizontal_distance / flight_speed_m_s // seconds @hero","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":true,"slider":null,"value":3.3333333333333335,"display":"3.333"}]},{"id":"paper-recycling-water-saved","title":"Paper Recycling Water Saved","description":"Calculate water saved by recycling paper instead of using virgin pulp.","category":"science","icon":"file-text","tags":["eco","water"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"paper_weight_kg = 50 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"water_saved_per_kg_recycled = 26 // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":26,"display":"26"},{"text":"total_water_saved_liters = paper_weight_kg * water_saved_per_kg_recycled // liters @hero","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":1300,"display":"1,300"}]},{"id":"parallelogram-area","title":"Parallelogram Area","description":"Find the area of a parallelogram: A = base × height.","category":"formulas","icon":"square","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Base and height","label":null,"prefix":null,"suffix":null,"section":"Base and height","hero":false,"slider":null,"value":null,"display":null},{"text":"base = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Base and height","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"height = 6 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Base and height","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":6,"display":"6"},{"text":"# Area","label":null,"prefix":null,"suffix":null,"section":"Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = base * height","label":null,"prefix":null,"suffix":null,"section":"Area","hidden":false,"hero":true,"slider":null,"value":60,"display":"60"}]},{"id":"parsec-to-lightyear","title":"Parsec To Lightyear","description":"Convert parsecs to light years.","category":"science","icon":"globe","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"parsecs = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"light_years = parsecs * 3.26156 // light years @hero","label":null,"prefix":null,"suffix":"light years","section":null,"hidden":false,"hero":true,"slider":null,"value":3.26156,"display":"3.262"}]},{"id":"password-entropy-bits","title":"Password Entropy Bits","description":"Calculate password entropy in bits from length and character set 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@hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":78.65506622013164,"display":"78.66"},{"text":"combinations = charset size ^ password length // @hero","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":4.7592031481425336e+23,"display":"4.7592e23"}]},{"id":"pasture-grazing-capacity","title":"Pasture Grazing Capacity","description":"Calculate animal grazing capacity from pasture area, forage yield, and daily intake.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"pasture_area_acres = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"forage_yield_pounds_per_acre = 2000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"animal_daily_intake_pounds = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"grazing_days = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"total_forage_available = pasture_area_acres * forage_yield_pounds_per_acre","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20000,"display":"20,000"},{"text":"grazing_capacity_animal_count = total_forage_available / (animal_daily_intake_pounds * grazing_days) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":22.22222222222222,"display":"22.22"}]},{"id":"patent-expiration-timeline","title":"Patent 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500","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"paypal_standard_percentage_fee = 0.0299","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.0299,"display":"0.0299"},{"text":"paypal_fixed_fee = 0.49","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.49,"display":"0.49"},{"text":"total_paypal_fees = (invoice_amount * paypal_standard_percentage_fee) + paypal_fixed_fee","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15.44,"display":"15.44"},{"text":"final_received_amount = invoice_amount - total_paypal_fees","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":484.56,"display":"484.56"}]},{"id":"payroll-tax","title":"Payroll Tax","description":"Calculate total employer and 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%","label":null,"prefix":null,"suffix":"%","section":"Payroll Details","hidden":false,"hero":false,"slider":null,"value":0.6,"display":"0.6"},{"text":"state unemployment rate = 3.4 // %","label":null,"prefix":null,"suffix":"%","section":"Payroll Details","hidden":false,"hero":false,"slider":null,"value":3.4,"display":"3.4"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_social_security_tax = gross pay * (social security rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":310,"display":"$310.00"},{"text":"$_medicare_tax = gross pay * (medicare rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":72.5,"display":"$72.50"},{"text":"$_futa_tax = gross pay * (federal unemployment rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":30,"display":"$30.00"},{"text":"$_suta_tax = gross pay * (state unemployment rate / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":170,"display":"$170.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$total employer payroll tax = social_security_tax + medicare_tax + futa_tax + suta_tax // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":582.5,"display":"$582.50"},{"text":"$total employee payroll tax = social_security_tax + medicare_tax","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":382.5,"display":"$382.50"},{"text":"$net employee pay = gross pay - total employee payroll 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C","label":null,"prefix":null,"suffix":"C","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"copper_thickness_oz = 1 // oz/ft2","label":null,"prefix":null,"suffix":"oz/ft2","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"required_trace_width_mils = (current_amperes / (0.048 * (temp_rise_celsius^0.44)))^(1/0.725) // mils @hero","label":null,"prefix":null,"suffix":"mils","section":null,"hidden":false,"hero":true,"slider":null,"value":42.39306714892737,"display":"42.39"}]},{"id":"pencil-writing-distance","title":"Pencil Writing Distance","description":"Calculate the total writing distance possible from a pencil's length.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"pencil_length_cm = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"km_per_cm = 2.4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.4,"display":"2.4"},{"text":"total_distance_km = pencil_length_cm * km_per_cm // kilometers @hero","label":null,"prefix":null,"suffix":"kilometers","section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"pendulum-period-large-angle","title":"Pendulum Period Large Angle","description":"Calculate pendulum period corrected for large swing amplitudes.","category":"education","icon":"book-open","tags":["pendulum","angle"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"length = 1 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"gravity = 9.80665 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@hero","label":null,"prefix":null,"suffix":"seconds","section":null,"hidden":false,"hero":true,"slider":null,"value":2.0407885738121707,"display":"2.041"}]},{"id":"pendulum-period","title":"Pendulum Period","description":"Find the period and frequency of a simple pendulum at any length.","category":"science","icon":"timer","tags":["pendulum","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Pendulum Properties","label":null,"prefix":null,"suffix":null,"section":"Pendulum Properties","hero":false,"slider":null,"value":null,"display":null},{"text":"pendulum length = 1.5 // m 0.1..10","label":null,"prefix":null,"suffix":"m","section":"Pendulum Properties","hidden":false,"hero":false,"slider":{"min":0.1,"max":10,"step":0.1},"value":1.5,"display":"1.5"},{"text":"gravitational acceleration = 9.81 // m/s² 1..25 by 0.01","label":null,"prefix":null,"suffix":"m/s²","section":"Pendulum Properties","hidden":false,"hero":false,"slider":{"min":1,"max":25,"step":0.01},"value":9.81,"display":"9.81"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"period = 2 * PI * sqrt(pendulum_length / gravitational_acceleration) // s @hero @label(Period (T = 2π√(L/g)))","label":"Period (T = 2π√(L/g))","prefix":null,"suffix":"s","section":"Results","hidden":false,"hero":true,"slider":null,"value":2.4569198788699134,"display":"2.457"},{"text":"frequency = 1 / period // Hz","label":null,"prefix":null,"suffix":"Hz","section":"Results","hidden":false,"hero":false,"slider":null,"value":0.4070136794448343,"display":"0.407"},{"text":"angular frequency = 2 * PI * frequency // rad/s","label":null,"prefix":null,"suffix":"rad/s","section":"Results","hidden":false,"hero":false,"slider":null,"value":2.557342370508885,"display":"2.557"},{"text":"# Different Lengths","label":null,"prefix":null,"suffix":null,"section":"Different Lengths","hero":false,"slider":null,"value":null,"display":null},{"text":"period at 1m = 2 * PI * sqrt(1 / gravitational_acceleration) // s","label":null,"prefix":null,"suffix":"s","section":"Different Lengths","hidden":false,"hero":false,"slider":null,"value":2.0060666807106475,"display":"2.006"},{"text":"period at 0.5m = 2 * PI * sqrt(0.5 / gravitational_acceleration) // s","label":null,"prefix":null,"suffix":"s","section":"Different Lengths","hidden":false,"hero":false,"slider":null,"value":1.4185033534428872,"display":"1.419"},{"text":"period at 2m = 2 * PI * sqrt(2 / gravitational_acceleration) // s","label":null,"prefix":null,"suffix":"s","section":"Different Lengths","hidden":false,"hero":false,"slider":null,"value":2.8370067068857745,"display":"2.837"}]},{"id":"percentage-change","title":"Percentage Change","description":"Calculate percentage increase or decrease between two 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value","label":null,"prefix":null,"suffix":null,"section":"Change","hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"percentage change = round((change amount / old value) * 100 * 100) / 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Change","hidden":false,"hero":true,"slider":null,"value":24,"display":"24"},{"text":"# Ratios","label":null,"prefix":null,"suffix":null,"section":"Ratios","hero":false,"slider":null,"value":null,"display":null},{"text":"multiplication factor = round(new value / old value * 10000) / 10000 // @label(Multiplier (new/old))","label":"Multiplier (new/old)","prefix":null,"suffix":null,"section":"Ratios","hidden":false,"hero":false,"slider":null,"value":1.24,"display":"1.24"},{"text":"inverse factor = round(old value / new value * 10000) / 10000 // @label(Inverse (old/new))","label":"Inverse (old/new)","prefix":null,"suffix":null,"section":"Ratios","hidden":false,"hero":false,"slider":null,"value":0.8065,"display":"0.8065"},{"text":"# Reverse","label":null,"prefix":null,"suffix":null,"section":"Reverse","hero":false,"slider":null,"value":null,"display":null},{"text":"reverse pct = round(((old value - new value) / new value) * 100 * 100) / 100 // % @label(% change back to original)","label":"% change back to original","prefix":null,"suffix":"%","section":"Reverse","hidden":false,"hero":false,"slider":null,"value":-19.35,"display":"-19.35"}]},{"id":"perfect-order-rate","title":"Perfect Order Rate","description":"Measure the percentage of orders that meet all requirements perfectly.","category":"business","icon":"award","tags":["order"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"ordersOnTime = 980 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":980,"display":"980"},{"text":"ordersComplete = 990 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":990,"display":"990"},{"text":"ordersDamageFree = 995 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":995,"display":"995"},{"text":"ordersWithCorrectInvoice = 990 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":990,"display":"990"},{"text":"totalOrders = 1000 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"perfectOrderRate = (ordersOnTime/totalOrders) * (ordersComplete/totalOrders) * (ordersDamageFree/totalOrders) * (ordersWithCorrectInvoice/totalOrders) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":95.569551,"display":"95.57"}]},{"id":"period-tracker","title":"Period Tracker","description":"Calculate days until the next menstrual period from cycle history.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# History","label":null,"prefix":null,"suffix":null,"section":"History","hero":false,"slider":null,"value":null,"display":null},{"text":"days since last period start = 20 // days 0..60","label":null,"prefix":null,"suffix":"days","section":"History","hidden":false,"hero":false,"slider":{"min":0,"max":60,"step":1},"value":20,"display":"20"},{"text":"average cycle length = 28 // days 20..45","label":null,"prefix":null,"suffix":"days","section":"History","hidden":false,"hero":false,"slider":{"min":20,"max":45,"step":1},"value":28,"display":"28"},{"text":"# Projections","label":null,"prefix":null,"suffix":null,"section":"Projections","hero":false,"slider":null,"value":null,"display":null},{"text":"days until next period = average cycle length - days since last period start // @hero","label":null,"prefix":null,"suffix":null,"section":"Projections","hidden":false,"hero":true,"slider":null,"value":8,"display":"8"},{"text":"period status = days until next period","label":null,"prefix":null,"suffix":null,"section":"Projections","hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"# Timeline","label":null,"prefix":null,"suffix":null,"section":"Timeline","hero":false,"slider":null,"value":null,"display":null},{"text":"next period start = average cycle length","label":null,"prefix":null,"suffix":null,"section":"Timeline","hidden":false,"hero":false,"slider":null,"value":28,"display":"28"},{"text":"expected duration = 5 // days","label":null,"prefix":null,"suffix":"days","section":"Timeline","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"late after = average cycle length + 2","label":null,"prefix":null,"suffix":null,"section":"Timeline","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"}]},{"id":"permutation-calculator","title":"Permutation Calculator","description":"Calculate n-permute-k permutations from a set of items.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"n = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"k = 3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"result = permutation(n, k)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":720,"display":"720"}]},{"id":"perpetuity-value-calculator","title":"Perpetuity Value Calculator","description":"Calculate the present value of a perpetuity from annual cash flow and discount rate.","category":"everyday","icon":"home","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"annual_cash_flow = 5000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"discount_rate = 0.08","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.08,"display":"0.08"},{"text":"present_value = annual_cash_flow / discount_rate","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":62500,"display":"62,500"}]},{"id":"personality-trait-percentile","title":"Personality Trait Percentile","description":"Calculate a z-score for a personality trait from population mean and standard deviation.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"raw_score = 35","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"population_mean = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"standard_deviation = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"z_score = (raw_score - population_mean) / standard_deviation // standard deviations from mean @hero","label":null,"prefix":null,"suffix":"standard deviations from mean","section":null,"hidden":false,"hero":true,"slider":null,"value":1,"display":"1"}]},{"id":"pet-age","title":"Pet Age","description":"Convert dog years to human years by size.","category":"everyday","icon":"heart","tags":["dog","pet","age"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Your Dog","label":null,"prefix":null,"suffix":null,"section":"Your Dog","hero":false,"slider":null,"value":null,"display":null},{"text":"dog age = 5 // years 1..20","label":null,"prefix":null,"suffix":"years","section":"Your Dog","hidden":false,"hero":false,"slider":{"min":1,"max":20,"step":0.2},"value":5,"display":"5"},{"text":"size factor = 1.0 // 0.8..1.3 by 0.1 @label(Size Factor (0.8=small, 1.0=medium, 1.3=large))","label":"Size Factor (0.8=small, 1.0=medium, 1.3=large)","prefix":null,"suffix":null,"section":"Your Dog","hidden":false,"hero":false,"slider":{"min":0.8,"max":1.3,"step":0.1},"value":1,"display":"1"},{"text":"# Modern Dog Age Formula","label":null,"prefix":null,"suffix":null,"section":"Modern Dog Age Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"# First 2 years age faster, then ~5 human years per dog year","label":null,"prefix":null,"suffix":null,"section":"First 2 years age faster, then ~5 human years per dog year","hero":false,"slider":null,"value":null,"display":null},{"text":"_base_years = min(dog age, 2) * 12","label":null,"prefix":null,"suffix":null,"section":"First 2 years age faster, then ~5 human years per dog year","hidden":true,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"_extra_years = max(dog age - 2, 0) * 5 * size factor","label":null,"prefix":null,"suffix":null,"section":"First 2 years age faster, then ~5 human years per dog year","hidden":true,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"human equivalent = round(base_years + extra_years) // years @hero @label(Human Equivalent Age)","label":"Human Equivalent Age","prefix":null,"suffix":"years","section":"Results","hidden":false,"hero":true,"slider":null,"value":39,"display":"39"},{"text":"simple 7x estimate = dog age * 7 // years","label":null,"prefix":null,"suffix":"years","section":"Results","hidden":false,"hero":false,"slider":null,"value":35,"display":"35"},{"text":"# Life Stage","label":null,"prefix":null,"suffix":null,"section":"Life Stage","hero":false,"slider":null,"value":null,"display":null},{"text":"is senior = max(0, dog age - 7 * (1.3 - size factor + 0.7)) // @label(Senior Years (large dogs age faster))","label":"Senior Years (large dogs age faster)","prefix":null,"suffix":null,"section":"Life Stage","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"}]},{"id":"pet-food-serving-size","title":"Pet Food Serving Size","description":"Calculate daily pet food cups from weight, calorie needs, and food density.","category":"everyday","icon":"utensils","tags":["pet","food","everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"pet_weight_pounds = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"calories_per_cup = 350","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"resting_energy_requirement = 70 * (pet_weight_pounds / 2.2) ** 0.75","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":366.48274031429713,"display":"366.48"},{"text":"daily_calorie_needs = resting_energy_requirement * 1.6","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":586.3723845028754,"display":"586.37"},{"text":"cups_per_day = daily_calorie_needs / calories_per_cup","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.6753496700082153,"display":"1.675"}]},{"id":"pet-human-age-cat","title":"Pet Human Age Cat","description":"Convert cat years to equivalent human years.","category":"everyday","icon":"smile","tags":["pet","human","age"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"cat_years = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"human_equivalent_years = 24 + (cat_years - 2) * 4 // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"pet-human-age-dog","title":"Pet Human Age Dog","description":"Convert dog years to equivalent human years using a size factor.","category":"everyday","icon":"smile","tags":["pet","human","age","dog"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"dog_years = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"dog_size_factor = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"human_equivalent_years = dog_years * dog_size_factor // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":35,"display":"35"}]},{"id":"pet-human-age-hamster","title":"Pet Human Age Hamster","description":"Convert hamster months to equivalent human years.","category":"everyday","icon":"smile","tags":["pet","human","age"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"hamster_months = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"human_equivalent_years = (hamster_months / 24) * 80 // years @hero","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":true,"slider":null,"value":40,"display":"40"}]},{"id":"ph-calculator","title":"Ph Calculator","description":"Calculate pH from hydrogen ion concentration, with acidity classification.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Concentration","label":null,"prefix":null,"suffix":null,"section":"Concentration","hero":false,"slider":null,"value":null,"display":null},{"text":"hydrogen ion concentration = 0.00001 // mol/l 1e-14..1","label":null,"prefix":null,"suffix":"mol/l","section":"Concentration","hidden":false,"hero":false,"slider":{"min":1e-14,"max":1,"step":0.01},"value":0.00001,"display":"0.00001"},{"text":"# Formula: -log10[H+]","label":null,"prefix":null,"suffix":null,"section":"Formula: -log10[H+]","hero":false,"slider":null,"value":null,"display":null},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"ph level = -log10(hydrogen ion concentration) // @hero","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"},{"text":"# Status","label":null,"prefix":null,"suffix":null,"section":"Status","hero":false,"slider":null,"value":null,"display":null},{"text":"acidity = ph level","label":null,"prefix":null,"suffix":null,"section":"Status","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"is acidic = ph level < 7","label":null,"prefix":null,"suffix":null,"section":"Status","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"},{"text":"is neutral = ph level == 7","label":null,"prefix":null,"suffix":null,"section":"Status","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"is basic = ph level > 7","label":null,"prefix":null,"suffix":null,"section":"Status","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"# Reference","label":null,"prefix":null,"suffix":null,"section":"Reference","hero":false,"slider":null,"value":null,"display":null},{"text":"poh = 14 - ph level","label":null,"prefix":null,"suffix":null,"section":"Reference","hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"hydroxide concentration = 10^-poh","label":null,"prefix":null,"suffix":null,"section":"Reference","hidden":false,"hero":false,"slider":null,"value":1e-9,"display":"1e-9"}]},{"id":"photography-exposure-value-ev","title":"Photography Exposure Value Ev","description":"Calculate photographic exposure value (EV) corrected for ISO.","category":"design","icon":"palette","tags":["exposure","ev"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"aperture_f_stop = 2.8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2.8,"display":"2.8"},{"text":"shutter_speed = 0.01 // seconds (1/100)","label":null,"prefix":null,"suffix":"seconds (1/100)","section":null,"hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"iso = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"exposure_value_at_iso_100 = log2(aperture_f_stop^2 / shutter_speed) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":9.614709844115207,"display":"9.615"},{"text":"exposure_value_corrected = exposure_value_at_iso_100 + log2(iso / 100) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":9.614709844115207,"display":"9.615"}]},{"id":"photography-print-resolution","title":"Photography Print Resolution","description":"Calculate maximum print dimensions and megapixels from image pixel dimensions.","category":"other","icon":"calculator","tags":["print"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Image Stats","label":null,"prefix":null,"suffix":null,"section":"Image 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@hero","label":null,"prefix":null,"suffix":"inches","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":20,"display":"20"},{"text":"max print height = height pixels / desired dpi // inches @hero","label":null,"prefix":null,"suffix":"inches","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":13.333333333333334,"display":"13.33"},{"text":"megapixels = (width pixels * height pixels) / 1000000 // MP @hero","label":null,"prefix":null,"suffix":"MP","section":"Calculation","hidden":false,"hero":true,"slider":null,"value":24,"display":"24"}]},{"id":"picking-productivity-lines-per-hour","title":"Picking Productivity","description":"Measure how many order lines are picked per labor hour.","category":"business","icon":"list","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"totalLinesPicked = 1200 // lines","label":null,"prefix":null,"suffix":"lines","section":null,"hidden":false,"hero":false,"slider":null,"value":1200,"display":"1,200"},{"text":"totalHoursWorked = 40 // hours","label":null,"prefix":null,"suffix":"hours","section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"pickingProductivity = totalLinesPicked / totalHoursWorked // lines per hour @hero","label":null,"prefix":null,"suffix":"lines per hour","section":null,"hidden":false,"hero":true,"slider":null,"value":30,"display":"30"}]},{"id":"pickling-vinegar-ratio","title":"Pickling Vinegar Ratio","description":"Calculate final acidity percentage of a pickling brine from vinegar and water ratio.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"vinegar_volume_cups = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"water_volume_cups = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"vinegar_acidity_percent = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"total_volume_cups = vinegar_volume_cups + water_volume_cups","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"final_acidity_percent = (vinegar_volume_cups * vinegar_acidity_percent) / total_volume_cups // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":3.3333333333333335,"display":"3.333"}]},{"id":"picture-frame-mat-size","title":"Picture Frame Mat Size","description":"Calculate mat and frame dimensions for a photo.","category":"design","icon":"frame","tags":["design"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"photo_width_inches = 8 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"photo_height_inches = 10 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"mat_border_inches = 2 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"frame_opening_width = photo_width_inches + (2 * mat_border_inches) // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":12,"display":"12"},{"text":"frame_opening_height = photo_height_inches + (2 * mat_border_inches) // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":14,"display":"14"}]},{"id":"pilot-crosswind-component","title":"Pilot Crosswind Component","description":"Calculate crosswind component in knots from wind speed and angle to runway.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"wind_speed_knots = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"wind_angle_degrees = 45","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"crosswind_component_knots = wind_speed_knots * sin(wind_angle_degrees) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":14.142135623730951,"display":"14.14"}]},{"id":"piotroski-f-score","title":"Piotroski F Score","description":"Calculate the Piotroski F-Score from nine financial-health checks.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"net_income_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"operating_cash_flow_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"return_on_assets_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"accruals_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"leverage_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"liquidity_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"equity_issuance_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"gross_margin_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"asset_turnover_score = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"total_f_score = net_income_score + operating_cash_flow_score + return_on_assets_score + accruals_score + leverage_score + liquidity_score + equity_issuance_score + gross_margin_score + asset_turnover_score","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":9,"display":"9"}]},{"id":"pipe-flow","title":"Pipe Flow","description":"Calculate flow velocity, Reynolds number, and pressure drop through pipes.","category":"engineering","icon":"droplet","tags":["flow"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Pipe Dimensions","label":null,"prefix":null,"suffix":null,"section":"Pipe Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"pipe inner diameter = 4 // in 0.5..24","label":null,"prefix":null,"suffix":"in","section":"Pipe Dimensions","hidden":false,"hero":false,"slider":{"min":0.5,"max":24,"step":0.5},"value":4,"display":"4"},{"text":"pipe length = 100 // ft 10..5k by 10","label":null,"prefix":null,"suffix":"ft","section":"Pipe Dimensions","hidden":false,"hero":false,"slider":{"min":10,"max":5000,"step":10},"value":100,"display":"100"},{"text":"pipe_roughness = 0.00015 // ft 0.00001..0.01","label":null,"prefix":null,"suffix":"ft","section":"Pipe Dimensions","hidden":false,"hero":false,"slider":{"min":0.00001,"max":0.01,"step":0.00009999999999999999},"value":0.00015,"display":"0.00015"},{"text":"# Flow","label":null,"prefix":null,"suffix":null,"section":"Flow","hero":false,"slider":null,"value":null,"display":null},{"text":"flow rate = 100 // GPM 1..2k","label":null,"prefix":null,"suffix":"GPM","section":"Flow","hidden":false,"hero":false,"slider":{"min":1,"max":2000,"step":20},"value":100,"display":"100"},{"text":"diameter ft = pipe_inner_diameter / 12","label":null,"prefix":null,"suffix":null,"section":"Flow","hidden":false,"hero":false,"slider":null,"value":0.3333333333333333,"display":"0.3333"},{"text":"cross section area = PI * (diameter_ft / 2)^2 // ft²","label":null,"prefix":null,"suffix":"ft²","section":"Flow","hidden":false,"hero":false,"slider":null,"value":0.08726646259971647,"display":"0.0873"},{"text":"flow cfs = flow_rate / 449","label":null,"prefix":null,"suffix":null,"section":"Flow","hidden":false,"hero":false,"slider":null,"value":0.22271714922049,"display":"0.2227"},{"text":"flow velocity = flow_cfs / cross_section_area // ft/s @hero","label":null,"prefix":null,"suffix":"ft/s","section":"Flow","hidden":false,"hero":true,"slider":null,"value":2.5521505351038902,"display":"2.552"},{"text":"# Head Loss (Darcy-Weisbach approx)","label":null,"prefix":null,"suffix":null,"section":"Head Loss (Darcy-Weisbach approx)","hero":false,"slider":null,"value":null,"display":null},{"text":"reynolds number = flow_velocity * diameter_ft / 0.0000141","label":null,"prefix":null,"suffix":null,"section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":null,"value":60334.52801664043,"display":"60,334.53"},{"text":"friction factor approx = 0.025 // 0.005..0.1","label":null,"prefix":null,"suffix":null,"section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":{"min":0.005,"max":0.1,"step":0.001},"value":0.025,"display":"0.025"},{"text":"head loss = friction_factor_approx * (pipe_length / diameter_ft) * (flow_velocity^2) / (2 * 32.2) // ft","label":null,"prefix":null,"suffix":"ft","section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":null,"value":0.7585565629461652,"display":"0.7586"},{"text":"pressure drop = head_loss * 0.433 // psi","label":null,"prefix":null,"suffix":"psi","section":"Head Loss (Darcy-Weisbach approx)","hidden":false,"hero":false,"slider":null,"value":0.32845499175568954,"display":"0.3285"}]},{"id":"pipe-pressure-drop-hazen-williams","title":"Pipe Pressure Drop","description":"Calculate pressure loss in pipes using Hazen-Williams.","category":"engineering","icon":"droplet","tags":["engineering","plumbing","fluids"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"flow_rate_gpm = 50 // gallons per minute","label":null,"prefix":null,"suffix":"gallons per minute","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"pipe_diameter_inches = 2 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"pipe_length_feet = 100 // feet","label":null,"prefix":null,"suffix":"feet","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"roughness_coefficient_c = 140 // for PVC","label":null,"prefix":null,"suffix":"for PVC","section":null,"hidden":false,"hero":false,"slider":null,"value":140,"display":"140"},{"text":"pressure_drop_psi = 4.52 * pipe_length_feet * (flow_rate_gpm^1.85) / (roughness_coefficient_c^1.85 * pipe_diameter_inches^4.87) // psi @hero","label":null,"prefix":null,"suffix":"psi","section":null,"hidden":false,"hero":true,"slider":null,"value":2.300805982491716,"display":"2.301"}]},{"id":"pixel-converter","title":"Pixel Converter","description":"Convert between px, rem, em, and pt units.","category":"design","icon":"type","tags":["pixel","font"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Base Settings","label":null,"prefix":null,"suffix":null,"section":"Base Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"base font size = 16 // px 8..32","label":null,"prefix":null,"suffix":"px","section":"Base Settings","hidden":false,"hero":false,"slider":{"min":8,"max":32,"step":1},"value":16,"display":"16"},{"text":"pixel value = 24 // px 1..200","label":null,"prefix":null,"suffix":"px","section":"Base Settings","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":24,"display":"24"},{"text":"# Conversions","label":null,"prefix":null,"suffix":null,"section":"Conversions","hero":false,"slider":null,"value":null,"display":null},{"text":"rem value = round(pixel value / base font size * 10000) / 10000 // rem @hero","label":null,"prefix":null,"suffix":"rem","section":"Conversions","hidden":false,"hero":true,"slider":null,"value":1.5,"display":"1.5"},{"text":"em value = round(pixel value / base font size * 10000) / 10000 // em @label(em (same as rem at root))","label":"em (same as rem at root)","prefix":null,"suffix":"em","section":"Conversions","hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"pt value = round(pixel value * 0.75 * 100) / 100 // pt","label":null,"prefix":null,"suffix":"pt","section":"Conversions","hidden":false,"hero":false,"slider":null,"value":18,"display":"18"},{"text":"# Reverse: rem to px","label":null,"prefix":null,"suffix":null,"section":"Reverse: rem to px","hero":false,"slider":null,"value":null,"display":null},{"text":"rem input = 1.5 // rem 0.1..20 by 0.1","label":null,"prefix":null,"suffix":"rem","section":"Reverse: rem to px","hidden":false,"hero":false,"slider":{"min":0.1,"max":20,"step":0.1},"value":1.5,"display":"1.5"},{"text":"px from rem = round(rem input * base font size * 10) / 10 // px","label":null,"prefix":null,"suffix":"px","section":"Reverse: rem to px","hidden":false,"hero":false,"slider":null,"value":24,"display":"24"},{"text":"# Common Sizes","label":null,"prefix":null,"suffix":null,"section":"Common Sizes","hero":false,"slider":null,"value":null,"display":null},{"text":"px for 1rem = base font size // px","label":null,"prefix":null,"suffix":"px","section":"Common Sizes","hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"px for 0.875rem = round(0.875 * base font size * 10) / 10 // px @label(0.875rem in px (small text))","label":"0.875rem in px (small text)","prefix":null,"suffix":"px","section":"Common Sizes","hidden":false,"hero":false,"slider":null,"value":14,"display":"14"},{"text":"px for 1.25rem = round(1.25 * base font size * 10) / 10 // px @label(1.25rem in px (large text))","label":"1.25rem in px (large text)","prefix":null,"suffix":"px","section":"Common Sizes","hidden":false,"hero":false,"slider":null,"value":20,"display":"20"}]},{"id":"pizza-slice-angle","title":"Pizza Slice Angle","description":"Calculate the angle in degrees of each slice in a divided pizza.","category":"everyday","icon":"smile","tags":["angle"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"number_of_slices = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"angle_degrees = 360 / number_of_slices // degrees per slice @hero","label":null,"prefix":null,"suffix":"degrees per slice","section":null,"hidden":false,"hero":true,"slider":null,"value":45,"display":"45"}]},{"id":"pizza-value","title":"Pizza Value","description":"Compare pizza sizes to find the best deal per square inch.","category":"everyday","icon":"pizza","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Small Pizza","label":null,"prefix":null,"suffix":null,"section":"Small Pizza","hero":false,"slider":null,"value":null,"display":null},{"text":"small diameter = 10 // inches 6..16","label":null,"prefix":null,"suffix":"inches","section":"Small Pizza","hidden":false,"hero":false,"slider":{"min":6,"max":16,"step":0.1},"value":10,"display":"10"},{"text":"$small price = 9.99 // 4..30","label":null,"prefix":"$","suffix":null,"section":"Small Pizza","hidden":false,"hero":false,"slider":{"min":4,"max":30,"step":1},"value":9.99,"display":"$9.99"},{"text":"small area = round(3.14159 * (small diameter / 2)^2 * 10) / 10 // sq in","label":null,"prefix":null,"suffix":"sq in","section":"Small Pizza","hidden":false,"hero":false,"slider":null,"value":78.5,"display":"78.5"},{"text":"# Large Pizza","label":null,"prefix":null,"suffix":null,"section":"Large Pizza","hero":false,"slider":null,"value":null,"display":null},{"text":"large diameter = 16 // inches 10..24","label":null,"prefix":null,"suffix":"inches","section":"Large Pizza","hidden":false,"hero":false,"slider":{"min":10,"max":24,"step":0.2},"value":16,"display":"16"},{"text":"$large price = 16.99 // 8..40","label":null,"prefix":"$","suffix":null,"section":"Large Pizza","hidden":false,"hero":false,"slider":{"min":8,"max":40,"step":1},"value":16.99,"display":"$16.99"},{"text":"large area = round(3.14159 * (large diameter / 2)^2 * 10) / 10 // sq in","label":null,"prefix":null,"suffix":"sq in","section":"Large Pizza","hidden":false,"hero":false,"slider":null,"value":201.1,"display":"201.1"},{"text":"# Value Comparison","label":null,"prefix":null,"suffix":null,"section":"Value Comparison","hero":false,"slider":null,"value":null,"display":null},{"text":"$small price per sq in = round(small price / small area * 1000) / 1000 // @label(Small: Price Per Sq Inch)","label":"Small: Price Per Sq Inch","prefix":"$","suffix":null,"section":"Value Comparison","hidden":false,"hero":false,"slider":null,"value":0.127,"display":"$0.13"},{"text":"$large price per sq in = round(large price / large area * 1000) / 1000 // @label(Large: Price Per Sq Inch)","label":"Large: Price Per Sq Inch","prefix":"$","suffix":null,"section":"Value Comparison","hidden":false,"hero":false,"slider":null,"value":0.084,"display":"$0.08"},{"text":"large vs small area = round(large area / small area * 10) / 10 // x more pizza @hero @label(Large Has X Times More Pizza)","label":"Large Has X Times More Pizza","prefix":null,"suffix":"x more pizza","section":"Value Comparison","hidden":false,"hero":true,"slider":null,"value":2.6,"display":"2.6"},{"text":"$savings per sq in = round((small price per sq in - large price per sq in) * 1000) / 1000 // @label(You Save Per Sq Inch With Large)","label":"You Save Per Sq Inch With Large","prefix":"$","suffix":null,"section":"Value Comparison","hidden":false,"hero":false,"slider":null,"value":0.043,"display":"$0.04"}]},{"id":"planetary-equilibrium-temperature","title":"Planetary Equilibrium Temperature","description":"Calculate a planet's equilibrium temperature from distance, albedo, and star luminosity.","category":"science","icon":"globe","tags":["planetary","temperature"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"distance_au = 1.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"albedo = 0.3","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"star_luminosity_solar = 1.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"temperature_kelvin = 278 * (star_luminosity_solar^0.25) * sqrt((1 - albedo) / distance_au) // Kelvin @hero","label":null,"prefix":null,"suffix":"Kelvin","section":null,"hidden":false,"hero":true,"slider":null,"value":232.59148737647303,"display":"232.59"}]},{"id":"planetary-periods","title":"Planetary Periods","description":"Compare a planet's rotation and orbital period — when a day exceeds a year.","category":"science","icon":"globe","tags":["orbit"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Planet (default: Venus)","label":null,"prefix":null,"suffix":null,"section":"Planet (default: Venus)","hero":false,"slider":null,"value":null,"display":null},{"text":"rotation days = 243 // Earth days 0.1..10k","label":null,"prefix":null,"suffix":"Earth days","section":"Planet (default: Venus)","hidden":false,"hero":false,"slider":{"min":0.1,"max":10000,"step":100},"value":243,"display":"243"},{"text":"orbital days = 224.7 // Earth days 0.1..100k","label":null,"prefix":null,"suffix":"Earth days","section":"Planet (default: Venus)","hidden":false,"hero":false,"slider":{"min":0.1,"max":100000,"step":1000},"value":224.7,"display":"224.7"},{"text":"# Comparison","label":null,"prefix":null,"suffix":null,"section":"Comparison","hero":false,"slider":null,"value":null,"display":null},{"text":"day longer than year = rotation days - orbital days // days @hero @label(Day minus year (Earth days))","label":"Day minus year (Earth days)","prefix":null,"suffix":"days","section":"Comparison","hidden":false,"hero":true,"slider":null,"value":18.3,"display":"18.3"},{"text":"ratio day to year = round(rotation days / orbital days, 3) // @label(Rotation ÷ orbit)","label":"Rotation ÷ orbit","prefix":null,"suffix":null,"section":"Comparison","hidden":false,"hero":false,"slider":null,"value":1.081,"display":"1.081"},{"text":"# How Many \"Years\" in One \"Day\"","label":null,"prefix":null,"suffix":null,"section":"How Many \"Years\" in One \"Day\"","hero":false,"slider":null,"value":null,"display":null},{"text":"years per day = round(rotation days / orbital days, 3) // @label(Years per rotation)","label":"Years per rotation","prefix":null,"suffix":null,"section":"How Many \"Years\" in One \"Day\"","hidden":false,"hero":false,"slider":null,"value":1.081,"display":"1.081"},{"text":"# Reference: Earth","label":null,"prefix":null,"suffix":null,"section":"Reference: Earth","hero":false,"slider":null,"value":null,"display":null},{"text":"earth rotation hours = 23.93 // hr @label(Earth sidereal day) @suffix(hr)","label":"Earth sidereal day","prefix":null,"suffix":"hr","section":"Reference: Earth","hidden":false,"hero":false,"slider":null,"value":23.93,"display":"23.93"},{"text":"earth orbit days = 365.25 // days @label(Earth orbit (days))","label":"Earth orbit (days)","prefix":null,"suffix":"days","section":"Reference: Earth","hidden":false,"hero":false,"slider":null,"value":365.25,"display":"365.25"}]},{"id":"planetary-surface-gravity","title":"Planetary Surface Gravity","description":"Calculate surface gravity of a planet from its mass and radius.","category":"science","icon":"globe","tags":["planetary","gravity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"planetary_mass_kilograms = 5.97e24","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5.97e+24,"display":"5.97e24"},{"text":"planetary_radius_meters = 6371000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6371000,"display":"6,371,000"},{"text":"gravitational_constant = 6.674e-11","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":6.674e-11,"display":"6.674e-11"},{"text":"surface_gravity = (gravitational_constant * planetary_mass_kilograms) / planetary_radius_meters^2 // m/s^2 @hero","label":null,"prefix":null,"suffix":"m/s^2","section":null,"hidden":false,"hero":true,"slider":null,"value":9.816243509027343,"display":"9.816"}]},{"id":"plant-population-density","title":"Plant Population Density","description":"Calculate total plants needed for a field or garden bed.","category":"everyday","icon":"sprout","tags":["garden"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"field_width_meters = 20 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"field_length_meters = 50 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"row_spacing_meters = 0.5 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"plant_spacing_in_row_meters = 0.3 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":0.3,"display":"0.3"},{"text":"total_plants = (field_width_meters / row_spacing_meters) * (field_length_meters / plant_spacing_in_row_meters) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":6666.666666666666,"display":"6,666.67"}]},{"id":"plant-watering-frequency-estimator","title":"Plant Watering Frequency Estimator","description":"Estimate days between waterings based on temperature and humidity.","category":"health","icon":"leaf","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"container_size_liters = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"ambient_temperature_celsius = 25","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"humidity_percentage = 40","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"base_watering_interval_days = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"temperature_factor = (ambient_temperature_celsius - 20) * 0.2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"humidity_factor = (60 - humidity_percentage) * 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"estimated_watering_interval_days = base_watering_interval_days - temperature_factor - humidity_factor","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"plastic-bottle-waste-reduction","title":"Plastic Bottle Waste Reduction","description":"Calculate weight of plastic waste avoided by using reusables.","category":"everyday","icon":"cup-soda","tags":["eco","waste"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"bottles_per_week = 7 // count","label":null,"prefix":null,"suffix":"count","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"bottle_weight_grams = 15 // grams","label":null,"prefix":null,"suffix":"grams","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"weeks_per_year = 52 // weeks","label":null,"prefix":null,"suffix":"weeks","section":null,"hidden":false,"hero":false,"slider":null,"value":52,"display":"52"},{"text":"annual_plastic_waste_avoided_kg = bottles_per_week * bottle_weight_grams * weeks_per_year / 1000 // kg @hero","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":true,"slider":null,"value":5.46,"display":"5.46"}]},{"id":"podcast-hosting-cost-growth","title":"Podcast Hosting Cost 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(monthly_storage_increase_gigabytes * months_of_growth * cost_per_extra_gigabyte)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":140,"display":"140"}]},{"id":"point-break-even-mortgage","title":"Point Break Even Mortgage","description":"Calculate months to break even when buying mortgage discount points.","category":"finance","icon":"home","tags":["mortgage","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Points Analysis","label":null,"prefix":null,"suffix":null,"section":"Points Analysis","hero":false,"slider":null,"value":null,"display":null},{"text":"$loan amount = 400000 // 50k..1M by 5k","label":null,"prefix":"$","suffix":null,"section":"Points Analysis","hidden":false,"hero":false,"slider":{"min":50000,"max":1000000,"step":5000},"value":400000,"display":"$400,000.00"},{"text":"interest rate without points = 7.0 // %","label":null,"prefix":null,"suffix":"%","section":"Points Analysis","hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"interest rate with points = 6.75 // %","label":null,"prefix":null,"suffix":"%","section":"Points Analysis","hidden":false,"hero":false,"slider":null,"value":6.75,"display":"6.75"},{"text":"number of points = 1 // 0..4 by 0.25","label":null,"prefix":null,"suffix":null,"section":"Points Analysis","hidden":false,"hero":false,"slider":{"min":0,"max":4,"step":0.25},"value":1,"display":"1"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_cost_of_points = loan amount * (number of points / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":4000,"display":"$4,000.00"},{"text":"$_monthly_payment_no_points = loan amount * (7.0/1200 * (1+7.0/1200)^360) / ((1+7.0/1200)^360 - 1)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2661.2099807167297,"display":"$2,661.21"},{"text":"$_monthly_payment_with_points = loan amount * (6.75/1200 * (1+6.75/1200)^360) / ((1+6.75/1200)^360 - 1)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":2594.392386272862,"display":"$2,594.39"},{"text":"$_monthly_savings = monthly_payment_no_points - monthly_payment_with_points","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":66.8175944438676,"display":"$66.82"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"break even months = cost_of_points / monthly_savings // @hero months","label":null,"prefix":null,"suffix":"months","section":"Result","hidden":false,"hero":true,"slider":null,"value":59.864471825012146,"display":"59.86"},{"text":"break even years = break even months / 12","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":4.9887059854176785,"display":"4.989"},{"text":"$total savings over 30 years = (monthly_savings * 360) - cost_of_points","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":20054.333999792336,"display":"$20,054.33"}]},{"id":"point-distance-2d","title":"Point Distance 2d","description":"Calculate Euclidean distance between two 2D points.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Point 1","label":null,"prefix":null,"suffix":null,"section":"Point 1","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 0 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 1","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":0,"display":"0"},{"text":"y1 = 0 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 1","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":0,"display":"0"},{"text":"# Point 2","label":null,"prefix":null,"suffix":null,"section":"Point 2","hero":false,"slider":null,"value":null,"display":null},{"text":"x2 = 3 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 2","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":3,"display":"3"},{"text":"y2 = 4 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Point 2","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":4,"display":"4"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"_dx = x2 - x1","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":3,"display":"3"},{"text":"_dy = y2 - y1","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":true,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"distance = sqrt(dx^2 + dy^2)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"point-slope-form","title":"Point-Slope Form","description":"Evaluate y from point-slope form: y - y₁ = m(x - x₁).","category":"formulas","icon":"trending-up","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Line through (x1, y1) with slope m","label":null,"prefix":null,"suffix":null,"section":"Line through (x1, y1) with slope m","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = 2 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Line through (x1, y1) with slope m","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":2,"display":"2"},{"text":"y1 = 3 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Line through (x1, y1) with slope m","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":3,"display":"3"},{"text":"m = 4 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Line through (x1, y1) with slope m","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":4,"display":"4"},{"text":"# Evaluate at x","label":null,"prefix":null,"suffix":null,"section":"Evaluate at x","hero":false,"slider":null,"value":null,"display":null},{"text":"x = 5 // -1k..1k","label":null,"prefix":null,"suffix":null,"section":"Evaluate at x","hidden":false,"hero":false,"slider":{"min":-1000,"max":1000,"step":20},"value":5,"display":"5"},{"text":"y = m * (x - x1) + y1","label":null,"prefix":null,"suffix":null,"section":"Evaluate at x","hidden":false,"hero":true,"slider":null,"value":15,"display":"15"}]},{"id":"poisson-distribution","title":"Poisson Distribution","description":"Probability of exactly k events: P(X = k) = (λᵏ · e^(−λ)) / k!.","category":"formulas","icon":"sigma","tags":["probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Parameters","label":null,"prefix":null,"suffix":null,"section":"Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"lambda_rate = 3 // 0.01..100","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0.01,"max":100,"step":1},"value":3,"display":"3"},{"text":"k = 2 // 0..50","label":null,"prefix":null,"suffix":null,"section":"Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":1},"value":2,"display":"2"},{"text":"# Probability","label":null,"prefix":null,"suffix":null,"section":"Probability","hero":false,"slider":null,"value":null,"display":null},{"text":"probability = (lambda_rate^k * exp(-lambda_rate)) / factorial(k) // @label(P(X = k))","label":"P(X = k)","prefix":null,"suffix":null,"section":"Probability","hidden":false,"hero":true,"slider":null,"value":0.22404180765538775,"display":"0.224"}]},{"id":"poker-hand-probability","title":"Poker Hand Probability","description":"Calculate probabilities of common 5-card poker hands from a 52-card deck.","category":"math","icon":"infinity","tags":["probability","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"# Deck Size","label":null,"prefix":null,"suffix":null,"section":"Deck Size","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 52 // cards","label":null,"prefix":null,"suffix":"cards","section":"Deck Size","hidden":false,"hero":false,"slider":null,"value":52,"display":"52"},{"text":"k = 5 // hand size","label":null,"prefix":null,"suffix":"hand size","section":"Deck Size","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"# Combinations of nCr","label":null,"prefix":null,"suffix":null,"section":"Combinations of nCr","hero":false,"slider":null,"value":null,"display":null},{"text":"_total_hands = 2598960","label":null,"prefix":null,"suffix":null,"section":"Combinations of nCr","hidden":true,"hero":false,"slider":null,"value":2598960,"display":"2,598,960"},{"text":"# Specific Hand Counts","label":null,"prefix":null,"suffix":null,"section":"Specific Hand Counts","hero":false,"slider":null,"value":null,"display":null},{"text":"royal flush count = 4","label":null,"prefix":null,"suffix":null,"section":"Specific Hand Counts","hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"straight flush count = 36","label":null,"prefix":null,"suffix":null,"section":"Specific Hand Counts","hidden":false,"hero":false,"slider":null,"value":36,"display":"36"},{"text":"four of a kind count = 624","label":null,"prefix":null,"suffix":null,"section":"Specific Hand Counts","hidden":false,"hero":false,"slider":null,"value":624,"display":"624"},{"text":"full house count = 3744","label":null,"prefix":null,"suffix":null,"section":"Specific Hand Counts","hidden":false,"hero":false,"slider":null,"value":3744,"display":"3,744"},{"text":"flush count = 5108","label":null,"prefix":null,"suffix":null,"section":"Specific Hand Counts","hidden":false,"hero":false,"slider":null,"value":5108,"display":"5,108"},{"text":"straight count = 10200","label":null,"prefix":null,"suffix":null,"section":"Specific Hand Counts","hidden":false,"hero":false,"slider":null,"value":10200,"display":"10,200"},{"text":"# Calculation (Choose one)","label":null,"prefix":null,"suffix":null,"section":"Calculation (Choose one)","hero":false,"slider":null,"value":null,"display":null},{"text":"prob of flush = (flush count / total_hands) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation (Choose one)","hidden":false,"hero":true,"slider":null,"value":0.1965401545233478,"display":"0.1965"},{"text":"prob of straight = (straight count / total_hands) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Calculation (Choose one)","hidden":false,"hero":true,"slider":null,"value":0.3924646781789639,"display":"0.3925"}]},{"id":"polar-ice-melt-sea-level-rise","title":"Polar Ice Melt Sea Level Rise","description":"Calculate sea level rise from melting ice sheets.","category":"science","icon":"mountain","tags":["science","eco","ocean"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"ice_melt_gigatonnes = 300 // gigatonnes","label":null,"prefix":null,"suffix":"gigatonnes","section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"ocean_surface_area_square_km = 361800000 // sq km","label":null,"prefix":null,"suffix":"sq km","section":null,"hidden":false,"hero":false,"slider":null,"value":361800000,"display":"361,800,000"},{"text":"water_density_kg_m3 = 1000 // kg/m3","label":null,"prefix":null,"suffix":"kg/m3","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"sea_level_rise_mm_per_gigatonne = 1 / 361.8 // mm","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":false,"slider":null,"value":0.002763957987838585,"display":"0.002764"},{"text":"total_sea_level_rise_mm = ice_melt_gigatonnes * sea_level_rise_mm_per_gigatonne // mm @hero","label":null,"prefix":null,"suffix":"mm","section":null,"hidden":false,"hero":true,"slider":null,"value":0.8291873963515756,"display":"0.8292"}]},{"id":"pomodoro-session-cycles-timer","title":"Pomodoro Session Cycles Timer","description":"Calculate total elapsed time across pomodoro work-break cycles.","category":"productivity","icon":"clock","tags":["timer"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"work_session_minutes = 25 // minutes","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":false,"slider":null,"value":25,"display":"25"},{"text":"short_break_minutes = 5 // minutes","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"long_break_minutes = 15 // minutes","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"sessions_before_long_break = 4","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":4,"display":"4"},{"text":"cycles_completed = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"_total_work_minutes = cycles_completed * work_session_minutes","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"_total_break_minutes = (cycles_completed - 1) * short_break_minutes","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"total_elapsed_time = total_work_minutes + total_break_minutes // minutes @hero","label":null,"prefix":null,"suffix":"minutes","section":null,"hidden":false,"hero":true,"slider":null,"value":55,"display":"55"}]},{"id":"pond-volume-liters","title":"Pond Volume Liters","description":"Calculate pond volume in liters from length, width, and average depth.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"length = 10 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"width = 5 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"average_depth = 1.5 // meters","label":null,"prefix":null,"suffix":"meters","section":null,"hidden":false,"hero":false,"slider":null,"value":1.5,"display":"1.5"},{"text":"volume_cubic_meters = length * width * average_depth // cubic meters","label":null,"prefix":null,"suffix":"cubic meters","section":null,"hidden":false,"hero":false,"slider":null,"value":75,"display":"75"},{"text":"liters_per_cubic_meter = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"volume_liters = volume_cubic_meters * liters_per_cubic_meter // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":true,"slider":null,"value":75000,"display":"75,000"}]},{"id":"pool-acid-dosage","title":"Pool Acid Dosage","description":"Calculate ounces of acid needed to lower pool pH to a target.","category":"health","icon":"activity","tags":["pool","dosage","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"pool_volume_gallons = 10000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10000,"display":"10,000"},{"text":"current_ph = 8.0","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"target_ph = 7.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7.5,"display":"7.5"},{"text":"acid_strength_baume = 20","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"ph_drop_needed = current_ph - target_ph","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5,"display":"0.5"},{"text":"acid_dosage_ounces = (ph_drop_needed * pool_volume_gallons) / 1000 * (acid_strength_baume / 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10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"chlorine_increase_needed = target_chlorine_ppm - current_chlorine_ppm","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"chlorine_dosage_ounces = (chlorine_increase_needed * pool_volume_gallons) / (chlorine_strength_percent * 0.75)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2666.6666666666665,"display":"2,666.67"}]},{"id":"pool-volume-rectangle","title":"Pool Volume Rectangle","description":"Calculate rectangular pool volume in gallons from length, width, and depth.","category":"science","icon":"flask-conical","tags":["pool","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"length_feet = 30","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"width_feet = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"average_depth_feet = 5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"volume_cubic_feet = length_feet * width_feet * average_depth_feet","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2250,"display":"2,250"},{"text":"volume_gallons = volume_cubic_feet * 7.48 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":16830,"display":"16,830"}]},{"id":"pool-volume-round","title":"Pool Volume Round","description":"Calculate round pool volume in gallons from diameter and 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@hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":7613.7061968,"display":"7,613.71"}]},{"id":"popcorn-pop-rate","title":"Popcorn Pop Rate","description":"Calculate the average popping rate of popcorn kernels per second.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.716Z"},"rows":[{"text":"kernels = 200","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"pop_time_seconds = 120","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":120,"display":"120"},{"text":"avg_pops_per_second = kernels / pop_time_seconds // pops per second @hero","label":null,"prefix":null,"suffix":"pops per 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acos(target_power_factor)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":18.194872338766785,"display":"18.1949"},{"text":"required_reactive_power_kvar = real_power_kw * (tan(existing_phase_angle) - tan(target_phase_angle)) // kVAR @hero","label":null,"prefix":null,"suffix":"kVAR","section":null,"hidden":false,"hero":true,"slider":null,"value":34.575997802055234,"display":"34.58"}]},{"id":"powers-of-two","title":"Powers of Two","description":"2^n with binary storage labels and how many doublings reach a million.","category":"programming","icon":"hash","tags":["math","storage"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Exponent","label":null,"prefix":null,"suffix":null,"section":"Exponent","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 20 // 0..64","label":null,"prefix":null,"suffix":null,"section":"Exponent","hidden":false,"hero":false,"slider":{"min":0,"max":64,"step":1},"value":20,"display":"20"},{"text":"# Powers of Two","label":null,"prefix":null,"suffix":null,"section":"Powers of Two","hero":false,"slider":null,"value":null,"display":null},{"text":"two to the n = 2^n // @hero @label(2^n)","label":"2^n","prefix":null,"suffix":null,"section":"Powers of Two","hidden":false,"hero":true,"slider":null,"value":1048576,"display":"1,048,576"},{"text":"power of ten approx = round(n * log10(2), 2) // @label(≈ 10^x where x =)","label":"≈ 10^x where x =","prefix":null,"suffix":null,"section":"Powers of Two","hidden":false,"hero":false,"slider":null,"value":6.02,"display":"6.02"},{"text":"# Binary Storage Sizes","label":null,"prefix":null,"suffix":null,"section":"Binary Storage Sizes","hero":false,"slider":null,"value":null,"display":null},{"text":"bytes = two to the n // B","label":null,"prefix":null,"suffix":"B","section":"Binary Storage Sizes","hidden":false,"hero":false,"slider":null,"value":1048576,"display":"1,048,576"},{"text":"kilobytes = bytes / 1024 // KiB","label":null,"prefix":null,"suffix":"KiB","section":"Binary Storage Sizes","hidden":false,"hero":false,"slider":null,"value":1024,"display":"1,024"},{"text":"megabytes = bytes / 1048576 // MiB","label":null,"prefix":null,"suffix":"MiB","section":"Binary Storage Sizes","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"gigabytes = bytes / 1073741824 // GiB","label":null,"prefix":null,"suffix":"GiB","section":"Binary Storage Sizes","hidden":false,"hero":false,"slider":null,"value":0.0009765625,"display":"0.0009766"},{"text":"# Doublings to Reach 1 Million / Billion","label":null,"prefix":null,"suffix":null,"section":"Doublings to Reach 1 Million / Billion","hero":false,"slider":null,"value":null,"display":null},{"text":"doublings to million = round(log(1000000) / log(2), 2) // @label(2^n = 1 million when n ≈)","label":"2^n = 1 million when n ≈","prefix":null,"suffix":null,"section":"Doublings to Reach 1 Million / Billion","hidden":false,"hero":false,"slider":null,"value":19.93,"display":"19.93"},{"text":"doublings to billion = round(log(1000000000) / log(2), 2) // @label(2^n = 1 billion when n ≈)","label":"2^n = 1 billion when n ≈","prefix":null,"suffix":null,"section":"Doublings to Reach 1 Million / Billion","hidden":false,"hero":false,"slider":null,"value":29.9,"display":"29.9"}]},{"id":"pregnancy-due-date","title":"Pregnancy Timeline","description":"Track pregnancy progress, trimester, and weeks remaining.","category":"health","icon":"baby","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Pregnancy Timeline","label":null,"prefix":null,"suffix":null,"section":"Pregnancy Timeline","hero":false,"slider":null,"value":null,"display":null},{"text":"weeks since last period = 12 // weeks 1..42","label":null,"prefix":null,"suffix":"weeks","section":"Pregnancy Timeline","hidden":false,"hero":false,"slider":{"min":1,"max":42,"step":1},"value":12,"display":"12"},{"text":"# Due Date","label":null,"prefix":null,"suffix":null,"section":"Due Date","hero":false,"slider":null,"value":null,"display":null},{"text":"total weeks = 40","label":null,"prefix":null,"suffix":null,"section":"Due Date","hidden":false,"hero":false,"slider":null,"value":40,"display":"40"},{"text":"weeks remaining = total weeks - weeks since last period // weeks @hero","label":null,"prefix":null,"suffix":"weeks","section":"Due Date","hidden":false,"hero":true,"slider":null,"value":28,"display":"28"},{"text":"days remaining = weeks remaining * 7 // days","label":null,"prefix":null,"suffix":"days","section":"Due Date","hidden":false,"hero":false,"slider":null,"value":196,"display":"196"},{"text":"# Trimester","label":null,"prefix":null,"suffix":null,"section":"Trimester","hero":false,"slider":null,"value":null,"display":null},{"text":"trimester = ceil(weeks since last period / 13.33) // (1, 2, or 3)","label":null,"prefix":null,"suffix":"(1, 2, or 3)","section":"Trimester","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"current month = round(weeks since last period / 4.33 * 10) / 10 // month","label":null,"prefix":null,"suffix":"month","section":"Trimester","hidden":false,"hero":false,"slider":null,"value":2.8,"display":"2.8"},{"text":"# Baby Size","label":null,"prefix":null,"suffix":null,"section":"Baby Size","hero":false,"slider":null,"value":null,"display":null},{"text":"gestational days = weeks since last period * 7 // days","label":null,"prefix":null,"suffix":"days","section":"Baby Size","hidden":false,"hero":false,"slider":null,"value":84,"display":"84"},{"text":"percent complete = round(weeks since last period / total weeks * 100) // %","label":null,"prefix":null,"suffix":"%","section":"Baby Size","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"}]},{"id":"present-value-growing-perpetuity","title":"Present Value Growing Perpetuity","description":"Calculate present value of a growing perpetuity (Gordon growth model).","category":"everyday","icon":"home","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"initial_cash_flow = 5000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"discount_rate = 0.10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"growth_rate = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"present_value = initial_cash_flow / (discount_rate 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= 10 // 1..100","label":null,"prefix":"$","suffix":null,"section":"Inputs","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":10,"display":"$10.00"},{"text":"# Present value","label":null,"prefix":null,"suffix":null,"section":"Present value","hero":false,"slider":null,"value":null,"display":null},{"text":"$present_value = future_value / (1 + discount_rate / 100)^years","label":null,"prefix":"$","suffix":null,"section":"Present value","hidden":false,"hero":true,"slider":null,"value":6139.132535407591,"display":"$6,139.13"}]},{"id":"pressure-altitude","title":"Pressure Altitude","description":"Calculate pressure altitude from station pressure and field elevation.","category":"science","icon":"flask-conical","tags":["altitude","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Altimeter Settings","label":null,"prefix":null,"suffix":null,"section":"Altimeter Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"station pressure = 29.92 // inHg 25..31","label":null,"prefix":null,"suffix":"inHg","section":"Altimeter Settings","hidden":false,"hero":false,"slider":{"min":25,"max":31,"step":0.1},"value":29.92,"display":"29.92"},{"text":"field elevation = 0 // feet 0..10k","label":null,"prefix":null,"suffix":"feet","section":"Altimeter Settings","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":0,"display":"0"},{"text":"# Standard Atmosphere Formula","label":null,"prefix":null,"suffix":null,"section":"Standard Atmosphere Formula","hero":false,"slider":null,"value":null,"display":null},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"pressure altitude = ((1 - (station pressure / 29.921)^0.190284) * 145366.45) + field elevation // feet @hero","label":null,"prefix":null,"suffix":"feet","section":"Result","hidden":false,"hero":true,"slider":null,"value":0.9244772519580338,"display":"0.9245"},{"text":"# Flight Level","label":null,"prefix":null,"suffix":null,"section":"Flight Level","hero":false,"slider":null,"value":null,"display":null},{"text":"flight level = pressure altitude / 100","label":null,"prefix":null,"suffix":null,"section":"Flight Level","hidden":false,"hero":false,"slider":null,"value":0.009244772519580337,"display":"0.009245"},{"text":"standard pressure hpa = 1013.25","label":null,"prefix":null,"suffix":null,"section":"Flight Level","hidden":false,"hero":false,"slider":null,"value":1013.25,"display":"1,013.25"},{"text":"station pressure hpa = station pressure * 33.8639","label":null,"prefix":null,"suffix":null,"section":"Flight Level","hidden":false,"hero":false,"slider":null,"value":1013.207888,"display":"1,013.21"},{"text":"altimeter setting = 29.92","label":null,"prefix":null,"suffix":null,"section":"Flight Level","hidden":false,"hero":false,"slider":null,"value":29.92,"display":"29.92"},{"text":"pressure correction = (altimeter setting - station pressure) * 1000","label":null,"prefix":null,"suffix":null,"section":"Flight Level","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"}]},{"id":"pressure-cooker-altitude-adjustment","title":"Pressure Cooker Altitude Adjustment","description":"Adjust pressure cooker processing time for altitude above sea level.","category":"science","icon":"flask-conical","tags":["altitude","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"standard_processing_time_minutes = 60","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":60,"display":"60"},{"text":"altitude_feet = 5000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5000,"display":"5,000"},{"text":"adjustment_factor = 1 + (max(0, altitude_feet - 2000) / 1000 * 0.05)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.15,"display":"1.15"},{"text":"adjusted_processing_time_minutes = standard_processing_time_minutes * adjustment_factor // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":69,"display":"69"}]},{"id":"pressure-unit-converter","title":"Pressure Unit Converter","description":"Convert pressure between PSI, bars, pascals, atmospheres, kPa, and torr.","category":"science","icon":"flask-conical","tags":["unit","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Input Pressure","label":null,"prefix":null,"suffix":null,"section":"Input Pressure","hero":false,"slider":null,"value":null,"display":null},{"text":"pressure value = 32 // psi 0..10k","label":null,"prefix":null,"suffix":"psi","section":"Input Pressure","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":100},"value":32,"display":"32"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"bars = pressure value * 0.0689476 // bar @hero","label":null,"prefix":null,"suffix":"bar","section":"Result","hidden":false,"hero":true,"slider":null,"value":2.2063232,"display":"2.206"},{"text":"# Others","label":null,"prefix":null,"suffix":null,"section":"Others","hero":false,"slider":null,"value":null,"display":null},{"text":"pascals = pressure value * 6894.76","label":null,"prefix":null,"suffix":null,"section":"Others","hidden":false,"hero":false,"slider":null,"value":220632.32,"display":"220,632.32"},{"text":"atmospheres = pressure value * 0.068046","label":null,"prefix":null,"suffix":null,"section":"Others","hidden":false,"hero":false,"slider":null,"value":2.177472,"display":"2.177"},{"text":"kilopascals = pascals / 1000","label":null,"prefix":null,"suffix":null,"section":"Others","hidden":false,"hero":false,"slider":null,"value":220.63232,"display":"220.63"},{"text":"torr = pressure value * 51.7149","label":null,"prefix":null,"suffix":null,"section":"Others","hidden":false,"hero":false,"slider":null,"value":1654.8768,"display":"1,654.88"}]},{"id":"prime-factorization","title":"Prime Factor Check","description":"Check small-prime divisibility of an integer to begin its prime factorization. For full factorization, divide iteratively.","category":"formulas","icon":"sigma","tags":["number-theory"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Integer to factor","label":null,"prefix":null,"suffix":null,"section":"Integer to factor","hero":false,"slider":null,"value":null,"display":null},{"text":"n = 360 // 2..100k","label":null,"prefix":null,"suffix":null,"section":"Integer to factor","hidden":false,"hero":false,"slider":{"min":2,"max":100000,"step":1000},"value":360,"display":"360"},{"text":"# Test divisibility by small primes","label":null,"prefix":null,"suffix":null,"section":"Test divisibility by small primes","hero":false,"slider":null,"value":null,"display":null},{"text":"divisible_by_2 = (n mod 2 == 0) // @label(Divisible by 2?)","label":"Divisible by 2?","prefix":null,"suffix":null,"section":"Test divisibility by small primes","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"},{"text":"divisible_by_3 = (n mod 3 == 0) // @label(Divisible by 3?)","label":"Divisible by 3?","prefix":null,"suffix":null,"section":"Test divisibility by small primes","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"},{"text":"divisible_by_5 = (n mod 5 == 0) // @label(Divisible by 5?)","label":"Divisible by 5?","prefix":null,"suffix":null,"section":"Test divisibility by small primes","hidden":false,"hero":false,"slider":null,"value":true,"display":"true"},{"text":"divisible_by_7 = (n mod 7 == 0) // @label(Divisible by 7?)","label":"Divisible by 7?","prefix":null,"suffix":null,"section":"Test divisibility by small primes","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"divisible_by_11 = (n mod 11 == 0) // @label(Divisible by 11?)","label":"Divisible by 11?","prefix":null,"suffix":null,"section":"Test divisibility by small primes","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"divisible_by_13 = (n mod 13 == 0) // @label(Divisible by 13?)","label":"Divisible by 13?","prefix":null,"suffix":null,"section":"Test divisibility by small primes","hidden":false,"hero":false,"slider":null,"value":false,"display":"false"},{"text":"# Count of 2s in the factorization (max 20)","label":null,"prefix":null,"suffix":null,"section":"Count of 2s in the factorization (max 20)","hero":false,"slider":null,"value":null,"display":null},{"text":"power_of_2 = (n mod 2 == 0) + (n mod 4 == 0) + (n mod 8 == 0) + (n mod 16 == 0) + (n mod 32 == 0) + (n mod 64 == 0) + (n mod 128 == 0) + (n mod 256 == 0) + (n mod 512 == 0) + (n mod 1024 == 0) // @label(Power of 2 in n)","label":"Power of 2 in n","prefix":null,"suffix":null,"section":"Count of 2s in the factorization (max 20)","hidden":false,"hero":true,"slider":null,"value":3,"display":"3"}]},{"id":"prime-rib-roast-time","title":"Prime Rib Roast Time","description":"Estimate prime rib roasting time from weight and target internal temperature.","category":"math","icon":"infinity","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"roast_weight_pounds = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"desired_doneness_internal_temp = 130 // Rare: 125, Med-Rare: 135","label":null,"prefix":null,"suffix":"Rare: 125, Med-Rare: 135","section":null,"hidden":false,"hero":false,"slider":null,"value":130,"display":"130"},{"text":"oven_temperature_fahrenheit = 325","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":325,"display":"325"},{"text":"minutes_per_pound = 15 + (desired_doneness_internal_temp - 120) * 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"estimated_cooking_time_minutes = roast_weight_pounds * minutes_per_pound // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":160,"display":"160"}]},{"id":"print-bleed-margin-trim-size","title":"Print Bleed Margin Trim Size","description":"Calculate full print dimensions including bleed margins around a trim size.","category":"design","icon":"palette","tags":["print"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"trim_width = 8.5 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":8.5,"display":"8.5"},{"text":"trim_height = 11 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":11,"display":"11"},{"text":"bleed_size = 0.125 // inches","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":false,"slider":null,"value":0.125,"display":"0.125"},{"text":"bleed_width = trim_width + (2 * bleed_size) // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":8.75,"display":"8.75"},{"text":"bleed_height = trim_height + (2 * bleed_size) // inches @hero","label":null,"prefix":null,"suffix":"inches","section":null,"hidden":false,"hero":true,"slider":null,"value":11.25,"display":"11.25"}]},{"id":"procrastination-deadline-pressure","title":"Procrastination Deadline Pressure","description":"Calculate deadline pressure from task size and days remaining.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"days_until_deadline = 2","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"task_size_hours = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"pressure_index = task_size_hours / (days_until_deadline * 24) // pressure factor @hero","label":null,"prefix":null,"suffix":"pressure factor","section":null,"hidden":false,"hero":true,"slider":null,"value":0.16666666666666666,"display":"0.1667"}]},{"id":"profit-margin","title":"Profit Margin","description":"Calculate gross margin, operating margin, and markup from revenue and costs.","category":"business","icon":"chart-line","tags":["profit"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Sales Data","label":null,"prefix":null,"suffix":null,"section":"Sales Data","hero":false,"slider":null,"value":null,"display":null},{"text":"$revenue = 50000 // 1k..1M","label":null,"prefix":"$","suffix":null,"section":"Sales Data","hidden":false,"hero":false,"slider":{"min":1000,"max":1000000,"step":10000},"value":50000,"display":"$50,000.00"},{"text":"$cost of goods sold = 30000 // 0..800k","label":null,"prefix":"$","suffix":null,"section":"Sales Data","hidden":false,"hero":false,"slider":{"min":0,"max":800000,"step":10000},"value":30000,"display":"$30,000.00"},{"text":"$operating expenses = 12000 // 0..200k by 500","label":null,"prefix":"$","suffix":null,"section":"Sales Data","hidden":false,"hero":false,"slider":{"min":0,"max":200000,"step":500},"value":12000,"display":"$12,000.00"},{"text":"# Profit","label":null,"prefix":null,"suffix":null,"section":"Profit","hero":false,"slider":null,"value":null,"display":null},{"text":"$gross profit = revenue - cost of goods sold","label":null,"prefix":"$","suffix":null,"section":"Profit","hidden":false,"hero":false,"slider":null,"value":20000,"display":"$20,000.00"},{"text":"$operating profit = gross profit - operating expenses","label":null,"prefix":"$","suffix":null,"section":"Profit","hidden":false,"hero":false,"slider":null,"value":8000,"display":"$8,000.00"},{"text":"# Margins","label":null,"prefix":null,"suffix":null,"section":"Margins","hero":false,"slider":null,"value":null,"display":null},{"text":"gross margin = (gross profit / revenue) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Margins","hidden":false,"hero":true,"slider":null,"value":40,"display":"40"},{"text":"operating margin = (operating profit / revenue) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Margins","hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"markup on cost = (gross profit / cost of goods sold) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Margins","hidden":false,"hero":false,"slider":null,"value":66.66666666666666,"display":"66.67"},{"text":"# Per Unit","label":null,"prefix":null,"suffix":null,"section":"Per Unit","hero":false,"slider":null,"value":null,"display":null},{"text":"units sold = 500 // 1..10k","label":null,"prefix":null,"suffix":null,"section":"Per Unit","hidden":false,"hero":false,"slider":{"min":1,"max":10000,"step":100},"value":500,"display":"500"},{"text":"$revenue per unit = revenue / units sold","label":null,"prefix":"$","suffix":null,"section":"Per Unit","hidden":false,"hero":false,"slider":null,"value":100,"display":"$100.00"},{"text":"$profit per unit = operating profit / units sold","label":null,"prefix":"$","suffix":null,"section":"Per Unit","hidden":false,"hero":false,"slider":null,"value":16,"display":"$16.00"}]},{"id":"project-buffer-time-contingency","title":"Project Buffer Time Contingency","description":"Calculate recommended buffer days for a project from uncertainty percentage.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"estimated_project_duration_days = 30 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"uncertainty_percent = 20 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":20,"display":"20"},{"text":"recommended_buffer_days = estimated_project_duration_days * (uncertainty_percent / 100) // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":6,"display":"6"},{"text":"total_buffered_duration = estimated_project_duration_days + recommended_buffer_days // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":36,"display":"36"}]},{"id":"project-deadline-probability-estimator","title":"Project Deadline Probability Estimator","description":"Estimate project duration using PERT three-point estimation.","category":"productivity","icon":"clock","tags":["probability"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"optimistic_days = 10 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"most_likely_days = 15 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"pessimistic_days = 30 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"expected_duration_pert = (optimistic_days + 4 * most_likely_days + pessimistic_days) / 6 // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":16.666666666666668,"display":"16.67"},{"text":"standard_deviation = (pessimistic_days - optimistic_days) / 6 // days @hero","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":true,"slider":null,"value":3.3333333333333335,"display":"3.333"}]},{"id":"projectile-motion-air-resistance","title":"Projectile Motion Air Resistance","description":"Calculate terminal velocity for projectile motion with air resistance.","category":"education","icon":"book-open","tags":["motion","air"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"velocity = 50 // meters per second","label":null,"prefix":null,"suffix":"meters per second","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"angle_degrees = 45 // degrees","label":null,"prefix":null,"suffix":"degrees","section":null,"hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"mass = 1 // kg","label":null,"prefix":null,"suffix":"kg","section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"drag_coefficient = 0.47","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.47,"display":"0.47"},{"text":"air_density = 1.225 // kg/m^3","label":null,"prefix":null,"suffix":"kg/m^3","section":null,"hidden":false,"hero":false,"slider":null,"value":1.225,"display":"1.225"},{"text":"area = 0.01 // m^2","label":null,"prefix":null,"suffix":"m^2","section":null,"hidden":false,"hero":false,"slider":null,"value":0.01,"display":"0.01"},{"text":"_gravity = 9.81 // m/s^2","label":null,"prefix":null,"suffix":"m/s^2","section":null,"hidden":true,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"_v_x = velocity * cos(angle_degrees)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":35.35533905932738,"display":"35.36"},{"text":"_v_y = velocity * sin(angle_degrees)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":35.35533905932737,"display":"35.36"},{"text":"terminal_velocity = sqrt((2 * mass * gravity) / (air_density * area * drag_coefficient)) // meters per second @hero","label":null,"prefix":null,"suffix":"meters per second","section":null,"hidden":false,"hero":true,"slider":null,"value":58.375757374670826,"display":"58.38"}]},{"id":"projectile-motion","title":"Projectile Motion","description":"Calculate max height, range, and flight time for launched projectiles.","category":"science","icon":"target","tags":["motion","physics"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Launch Parameters","label":null,"prefix":null,"suffix":null,"section":"Launch Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"initial velocity = 50 // m/s 1..200","label":null,"prefix":null,"suffix":"m/s","section":"Launch Parameters","hidden":false,"hero":false,"slider":{"min":1,"max":200,"step":1},"value":50,"display":"50"},{"text":"launch angle = 45 // ° 1..89","label":null,"prefix":null,"suffix":"°","section":"Launch Parameters","hidden":false,"hero":false,"slider":{"min":1,"max":89,"step":1},"value":45,"display":"45"},{"text":"initial height = 0 // m 0..100","label":null,"prefix":null,"suffix":"m","section":"Launch Parameters","hidden":false,"hero":false,"slider":{"min":0,"max":100,"step":1},"value":0,"display":"0"},{"text":"_g = 9.81 // m/s²","label":null,"prefix":null,"suffix":"m/s²","section":"Launch Parameters","hidden":true,"hero":false,"slider":null,"value":9.81,"display":"9.81"},{"text":"_horizontal_velocity = initial velocity * cos(launch angle) // m/s","label":null,"prefix":null,"suffix":"m/s","section":"Launch Parameters","hidden":true,"hero":false,"slider":null,"value":35.35533905932738,"display":"35.36"},{"text":"_vertical_velocity = initial velocity * sin(launch angle) // m/s","label":null,"prefix":null,"suffix":"m/s","section":"Launch Parameters","hidden":true,"hero":false,"slider":null,"value":35.35533905932737,"display":"35.36"},{"text":"# Results","label":null,"prefix":null,"suffix":null,"section":"Results","hero":false,"slider":null,"value":null,"display":null},{"text":"maximum height = round(initial height + (vertical_velocity^2) / (2 * g), 1) // m @hero","label":null,"prefix":null,"suffix":"m","section":"Results","hidden":false,"hero":true,"slider":null,"value":63.7,"display":"63.7"},{"text":"time of flight = round((vertical_velocity + sqrt(vertical_velocity^2 + 2 * g * initial height)) / g, 2) // s","label":null,"prefix":null,"suffix":"s","section":"Results","hidden":false,"hero":false,"slider":null,"value":7.21,"display":"7.21"},{"text":"horizontal range = round(horizontal_velocity * time of flight, 1) // m","label":null,"prefix":null,"suffix":"m","section":"Results","hidden":false,"hero":false,"slider":null,"value":254.9,"display":"254.9"},{"text":"impact speed = round(sqrt(horizontal_velocity^2 + (vertical_velocity - g * time of flight)^2), 1) // m/s","label":null,"prefix":null,"suffix":"m/s","section":"Results","hidden":false,"hero":false,"slider":null,"value":50,"display":"50"}]},{"id":"projectile-range","title":"Projectile Range","description":"A projectile launched at angle θ with initial velocity v0 lands at horizontal range R = v0² sin(2θ) / g. Adjust the launch angle and see where it lands — or set a target distance and solve for the angle.","category":"physics","icon":"target","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Setup","label":null,"prefix":null,"suffix":null,"section":"Setup","hero":false,"slider":null,"value":null,"display":null},{"text":"v0 = 30 // 1..100 — initial speed (m/s)","label":null,"prefix":null,"suffix":"1..100 — initial speed (m/s)","section":"Setup","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"g = 9.81 // 9..10 — gravity (m/s²)","label":null,"prefix":null,"suffix":null,"section":"Setup","hidden":false,"hero":false,"slider":{"min":9,"max":0.2,"step":0.1},"value":9.81,"display":"9.81"},{"text":"theta = 45 // 0..90 — launch angle (degrees)","label":null,"prefix":null,"suffix":"0..90 — launch angle (degrees)","section":"Setup","hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"# Range — instacalc trig is in degrees by default, so sin(2θ) reads literally","label":null,"prefix":null,"suffix":null,"section":"Range — instacalc trig is in degrees by default, so sin(2θ) reads literally","hero":false,"slider":null,"value":null,"display":null},{"text":"range = v0^2 * sin(2 * theta) / g","label":null,"prefix":null,"suffix":null,"section":"Range — instacalc trig is in degrees by default, so sin(2θ) reads literally","hidden":false,"hero":true,"slider":null,"value":91.74311926605505,"display":"91.74"},{"text":"# Trajectory — height as a function of horizontal distance","label":null,"prefix":null,"suffix":null,"section":"Trajectory — height as a function of horizontal distance","hero":false,"slider":null,"value":null,"display":null},{"text":"# Want to hit a target? Uncomment the line below to solve for the","label":null,"prefix":null,"suffix":null,"section":"Want to hit a target? Uncomment the line below to solve for the","hero":false,"slider":null,"value":null,"display":null},{"text":"# launch angle that lands at target_distance:","label":null,"prefix":null,"suffix":null,"section":"launch angle that lands at target_distance:","hero":false,"slider":null,"value":null,"display":null},{"text":"target_distance = 80 // 1..200 — meters","label":null,"prefix":null,"suffix":null,"section":"launch angle that lands at target_distance:","hidden":false,"hero":false,"slider":{"min":1,"max":199,"step":1},"value":80,"display":"80"},{"text":"# set range = target_distance using theta","label":null,"prefix":null,"suffix":null,"section":"set range = target_distance using theta","hero":false,"slider":null,"value":null,"display":null}]},{"id":"property-tax-estimator","title":"Property Tax Estimator","description":"Estimate annual property tax from market value, assessment ratio, and mill rate.","category":"finance","icon":"dollar-sign","tags":["property","tax","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Property Value","label":null,"prefix":null,"suffix":null,"section":"Property Value","hero":false,"slider":null,"value":null,"display":null},{"text":"$fair market value = 450000 // 50k..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Property Value","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":5000},"value":450000,"display":"$450,000.00"},{"text":"assessment ratio = 80 // % 10..100","label":null,"prefix":null,"suffix":"%","section":"Property Value","hidden":false,"hero":false,"slider":{"min":10,"max":100,"step":1},"value":80,"display":"80"},{"text":"tax rate per 1000 = 12.5 // mills 1..50 by 0.1","label":null,"prefix":null,"suffix":"mills","section":"Property Value","hidden":false,"hero":false,"slider":{"min":1,"max":50,"step":0.1},"value":12.5,"display":"12.5"},{"text":"# Calculations","label":null,"prefix":null,"suffix":null,"section":"Calculations","hero":false,"slider":null,"value":null,"display":null},{"text":"$_assessed_value = fair market value * (assessment ratio / 100)","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":360000,"display":"$360,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"$estimated annual property tax = (assessed_value / 1000) * tax rate per 1000 // @hero","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":4500,"display":"$4,500.00"},{"text":"$monthly property tax = estimated annual property tax / 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":375,"display":"$375.00"},{"text":"effective tax rate = (estimated annual property tax / fair market value) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Result","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"}]},{"id":"protein-intake","title":"Protein Intake","description":"Calculate daily protein needs based on weight and fitness goals.","category":"health","icon":"dumbbell","tags":["protein"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.720Z"},"rows":[{"text":"# Your Stats","label":null,"prefix":null,"suffix":null,"section":"Your Stats","hero":false,"slider":null,"value":null,"display":null},{"text":"body weight = 170 // lbs 80..400","label":null,"prefix":null,"suffix":"lbs","section":"Your 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base_length^2","label":null,"prefix":null,"suffix":null,"section":"Volume","hidden":false,"hero":false,"slider":null,"value":64,"display":"64"},{"text":"volume = (1 / 3) * base_area * height","label":null,"prefix":null,"suffix":null,"section":"Volume","hidden":false,"hero":true,"slider":null,"value":213.33333333333331,"display":"213.33"}]},{"id":"pythagorean-theorem","title":"Pythagorean Theorem","description":"Find the hypotenuse of a right triangle from its two legs: c² = a² + b².","category":"formulas","icon":"triangle","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Pythagorean Theorem @formula","label":null,"prefix":null,"suffix":null,"section":"Pythagorean Theorem","hero":false,"slider":null,"value":null,"display":null},{"text":"# Legs of right triangle","label":null,"prefix":null,"suffix":null,"section":"Legs of right triangle","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 3 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Legs of right triangle","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":3,"display":"3"},{"text":"b = 4 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Legs of right triangle","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":4,"display":"4"},{"text":"# Hypotenuse","label":null,"prefix":null,"suffix":null,"section":"Hypotenuse","hero":false,"slider":null,"value":null,"display":null},{"text":"c = sqrt(a^2 + b^2) // @label(Hypotenuse c)","label":"Hypotenuse c","prefix":null,"suffix":null,"section":"Hypotenuse","hidden":false,"hero":true,"slider":null,"value":5,"display":"5"}]},{"id":"quadratic-explorer","title":"Quadratic Explorer","description":"Visualize y = ax² + bx + c. 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Or fix a target value and let the solver find the coefficient that hits it.","category":"math","icon":"trending-up","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Coefficients","label":null,"prefix":null,"suffix":null,"section":"Coefficients","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 1 // -5..5 — leading coefficient","label":null,"prefix":null,"suffix":"-5..5 — leading coefficient","section":"Coefficients","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"b = 0 // -10..10 — linear term","label":null,"prefix":null,"suffix":"-10..10 — linear term","section":"Coefficients","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"c = 0 // -20..20 — constant","label":null,"prefix":null,"suffix":"-20..20 — constant","section":"Coefficients","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# The parabola","label":null,"prefix":null,"suffix":null,"section":"The parabola","hero":false,"slider":null,"value":null,"display":null},{"text":"# Roots — where y = 0 (real if discriminant ≥ 0)","label":null,"prefix":null,"suffix":null,"section":"Roots — where y = 0 (real if discriminant ≥ 0)","hero":false,"slider":null,"value":null,"display":null},{"text":"disc = b^2 - 4*a*c","label":null,"prefix":null,"suffix":null,"section":"Roots — where y = 0 (real if discriminant ≥ 0)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"root_1 = (-b - sqrt(disc)) / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Roots — where y = 0 (real if discriminant ≥ 0)","hidden":false,"hero":false,"slider":null,"value":0,"display":"-0"},{"text":"root_2 = (-b + sqrt(disc)) / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Roots — where y = 0 (real if discriminant ≥ 0)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# Vertex of the parabola (minimum if a > 0, maximum if a < 0)","label":null,"prefix":null,"suffix":null,"section":"Vertex of the parabola (minimum if a > 0, maximum if a < 0)","hero":false,"slider":null,"value":null,"display":null},{"text":"vertex_x = -b / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Vertex of the parabola (minimum if a > 0, maximum if a < 0)","hidden":false,"hero":false,"slider":null,"value":0,"display":"-0"},{"text":"vertex_y = a*vertex_x^2 + b*vertex_x + c","label":null,"prefix":null,"suffix":null,"section":"Vertex of the parabola (minimum if a > 0, maximum if a < 0)","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# Want to find b that makes y(3) = 10? 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4 * a * c // @label(Discriminant b²−4ac)","label":"Discriminant b²−4ac","prefix":null,"suffix":null,"section":"Discriminant","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Roots","label":null,"prefix":null,"suffix":null,"section":"Roots","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = (-b + sqrt(abs(discriminant))) / (2 * a) // @hero @label(x₁)","label":"x₁","prefix":null,"suffix":null,"section":"Roots","hidden":false,"hero":true,"slider":null,"value":3,"display":"3"},{"text":"x2 = (-b - sqrt(abs(discriminant))) / (2 * a) // @hero @label(x₂)","label":"x₂","prefix":null,"suffix":null,"section":"Roots","hidden":false,"hero":true,"slider":null,"value":2,"display":"2"}]},{"id":"quadratic-solver","title":"Quadratic Solver","description":"Solve any quadratic equation ax² + bx + c = 0.","category":"science","icon":"function","tags":["equation","algebra","math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Coefficients (ax² + bx + c = 0)","label":null,"prefix":null,"suffix":null,"section":"Coefficients (ax² + bx + c = 0)","hero":false,"slider":null,"value":null,"display":null},{"text":"a = 1 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Coefficients (ax² + bx + c = 0)","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":1,"display":"1"},{"text":"b = -5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Coefficients (ax² + bx + c = 0)","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":-5,"display":"-5"},{"text":"c = 6 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Coefficients (ax² + bx + c = 0)","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":6,"display":"6"},{"text":"# Discriminant","label":null,"prefix":null,"suffix":null,"section":"Discriminant","hero":false,"slider":null,"value":null,"display":null},{"text":"discriminant = b^2 - 4 * a * c // @label(Discriminant (b²-4ac))","label":"Discriminant (b²-4ac)","prefix":null,"suffix":null,"section":"Discriminant","hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"# Solutions","label":null,"prefix":null,"suffix":null,"section":"Solutions","hero":false,"slider":null,"value":null,"display":null},{"text":"x1 = (-b + sqrt(abs(discriminant))) / (2 * a) // @hero @label(Solution x₁)","label":"Solution x₁","prefix":null,"suffix":null,"section":"Solutions","hidden":false,"hero":true,"slider":null,"value":3,"display":"3"},{"text":"x2 = (-b - sqrt(abs(discriminant))) / (2 * a) // @label(Solution x₂)","label":"Solution x₂","prefix":null,"suffix":null,"section":"Solutions","hidden":false,"hero":false,"slider":null,"value":2,"display":"2"},{"text":"# Verification","label":null,"prefix":null,"suffix":null,"section":"Verification","hero":false,"slider":null,"value":null,"display":null},{"text":"check x1 = a * x1^2 + b * x1 + c // @label(Verify: f(x₁) should = 0)","label":"Verify: f(x₁) should = 0","prefix":null,"suffix":null,"section":"Verification","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"check x2 = a * x2^2 + b * x2 + c // @label(Verify: f(x₂) should = 0)","label":"Verify: f(x₂) should = 0","prefix":null,"suffix":null,"section":"Verification","hidden":false,"hero":false,"slider":null,"value":0,"display":"0"},{"text":"# Vertex","label":null,"prefix":null,"suffix":null,"section":"Vertex","hero":false,"slider":null,"value":null,"display":null},{"text":"vertex x = -b / (2 * a)","label":null,"prefix":null,"suffix":null,"section":"Vertex","hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"vertex y = a * vertex x^2 + b * vertex x + c // @label(Vertex y (minimum/maximum))","label":"Vertex y (minimum/maximum)","prefix":null,"suffix":null,"section":"Vertex","hidden":false,"hero":false,"slider":null,"value":-0.25,"display":"-0.25"}]},{"id":"quadratic-vertex-form","title":"Quadratic Vertex Form","description":"Evaluate a quadratic in vertex form a(x-h)² + k at a given x value.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Vertex Parameters","label":null,"prefix":null,"suffix":null,"section":"Vertex Parameters","hero":false,"slider":null,"value":null,"display":null},{"text":"a coefficient = 1 // -10..10 by 0.1","label":null,"prefix":null,"suffix":null,"section":"Vertex Parameters","hidden":false,"hero":false,"slider":{"min":-10,"max":10,"step":0.1},"value":1,"display":"1"},{"text":"h vertex x = 0 // -50..50","label":null,"prefix":null,"suffix":null,"section":"Vertex Parameters","hidden":false,"hero":false,"slider":{"min":-50,"max":50,"step":1},"value":0,"display":"0"},{"text":"k vertex y = 0 // -50..50","label":null,"prefix":null,"suffix":null,"section":"Vertex Parameters","hidden":false,"hero":false,"slider":{"min":-50,"max":50,"step":1},"value":0,"display":"0"},{"text":"# Input","label":null,"prefix":null,"suffix":null,"section":"Input","hero":false,"slider":null,"value":null,"display":null},{"text":"x value = 5 // -100..100","label":null,"prefix":null,"suffix":null,"section":"Input","hidden":false,"hero":false,"slider":{"min":-100,"max":100,"step":1},"value":5,"display":"5"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"y value = a coefficient * (x value - h vertex x)^2 + k vertex y","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":25,"display":"25"}]},{"id":"quality-control-error-rate-percent","title":"Quality Control Error Rate Percent","description":"Calculate quality control error rate and yield percentage from production data.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"units_produced = 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"defective_units = 12","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":12,"display":"12"},{"text":"error_rate_percent = (defective_units / units_produced) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.2,"display":"1.2"},{"text":"yield_percent = 100 - error_rate_percent // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":98.8,"display":"98.8"}]},{"id":"quarter-mile-time-prediction","title":"Quarter Mile Time Prediction","description":"Estimate quarter mile time based on power and weight.","category":"engineering","icon":"settings","tags":["automotive"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Specs","label":null,"prefix":null,"suffix":null,"section":"Specs","hero":false,"slider":null,"value":null,"display":null},{"text":"horsepower = 350","label":null,"prefix":null,"suffix":null,"section":"Specs","hidden":false,"hero":false,"slider":null,"value":350,"display":"350"},{"text":"weight pounds = 3000","label":null,"prefix":null,"suffix":null,"section":"Specs","hidden":false,"hero":false,"slider":null,"value":3000,"display":"3,000"},{"text":"# Calculation","label":null,"prefix":null,"suffix":null,"section":"Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"estimated time seconds = 5.825 * ((weight pounds / horsepower) ^ 0.333)","label":null,"prefix":null,"suffix":null,"section":"Calculation","hidden":false,"hero":true,"slider":null,"value":11.912492734044125,"display":"11.91"}]},{"id":"quaternion-rotation","title":"Rotate a vector with a quaternion","description":"Drag the angle and watch a vector turn in 3-D. A unit quaternion is the machine that does the turning — change the inputs and see it move.","category":"education","icon":"box","tags":["vectors","quaternions","rotation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-23T08:34:24.057Z"},"rows":[{"text":"# Try it","label":null,"prefix":null,"suffix":null,"section":"Try it","hero":false,"slider":null,"value":null,"display":null},{"text":"angle = 90 // ° 0..360","label":null,"prefix":null,"suffix":"°","section":"Try it","hidden":false,"hero":false,"slider":{"min":0,"max":360,"step":1},"value":90,"display":"90"},{"text":"axis_x = 0 // -1..1","label":null,"prefix":null,"suffix":null,"section":"Try it","hidden":false,"hero":false,"slider":{"min":-1,"max":1,"step":0.02},"value":0,"display":"0"},{"text":"axis_y = 0 // -1..1","label":null,"prefix":null,"suffix":null,"section":"Try it","hidden":false,"hero":false,"slider":{"min":-1,"max":1,"step":0.02},"value":0,"display":"0"},{"text":"axis_z = 1 // -1..1","label":null,"prefix":null,"suffix":null,"section":"Try it","hidden":false,"hero":false,"slider":{"min":-1,"max":1,"step":0.02},"value":1,"display":"1"},{"text":"@hero turned = rotate([1,0,0], [axis_x, axis_y, axis_z], angle) // @label(rotated x̂)","label":"rotated x̂","prefix":null,"suffix":null,"section":"Try it","hidden":false,"hero":true,"slider":null,"value":[0,1,0],"display":null},{"text":"@hero diagram = svg(``)","label":null,"prefix":null,"suffix":null,"section":"Try it","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false},"display":null},{"text":"# Why a quaternion can do this","label":null,"prefix":null,"suffix":null,"section":"Why a quaternion can do this","hero":false,"slider":null,"value":null,"display":null},{"text":"ij = quat(0,1,0,0) * quat(0,0,1,0) // @label(i · j)","label":"i · j","prefix":null,"suffix":null,"section":"Why a quaternion can do this","hidden":false,"hero":false,"slider":null,"value":{"__quat":true,"w":0,"x":0,"y":0,"z":1},"display":"k"},{"text":"# The rotation as a quaternion","label":null,"prefix":null,"suffix":null,"section":"The rotation as a quaternion","hero":false,"slider":null,"value":null,"display":null},{"text":"half = angle / 2 // @label(θ/2)","label":"θ/2","prefix":null,"suffix":null,"section":"The rotation as a quaternion","hidden":false,"hero":false,"slider":null,"value":45,"display":"45"},{"text":"q = quat(cos(half), sin(half)*axis_x, sin(half)*axis_y, sin(half)*axis_z) // @label(rotation quaternion)","label":"rotation quaternion","prefix":null,"suffix":null,"section":"The rotation as a quaternion","hidden":false,"hero":false,"slider":null,"value":{"__quat":true,"w":0.707106781187,"x":0,"y":0,"z":0.707106781187},"display":"0.707107 + 0.707107k"}]},{"id":"quick-ratio-acid-test","title":"Quick Ratio Acid Test","description":"Calculate the quick ratio (acid test) from liquid assets and current liabilities.","category":"math","icon":"ratio","tags":["math"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Liquid Assets","label":null,"prefix":null,"suffix":null,"section":"Liquid Assets","hero":false,"slider":null,"value":null,"display":null},{"text":"$cash and equivalents = 50000 // 0..1M","label":null,"prefix":"$","suffix":null,"section":"Liquid Assets","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":50000,"display":"$50,000.00"},{"text":"$marketable securities = 25000 // 0..1M","label":null,"prefix":"$","suffix":null,"section":"Liquid Assets","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":25000,"display":"$25,000.00"},{"text":"$accounts receivable = 30000 // 0..1M","label":null,"prefix":"$","suffix":null,"section":"Liquid Assets","hidden":false,"hero":false,"slider":{"min":0,"max":1000000,"step":10000},"value":30000,"display":"$30,000.00"},{"text":"$current liabilities = 60000 // 1k..1M","label":null,"prefix":"$","suffix":null,"section":"Liquid Assets","hidden":false,"hero":false,"slider":{"min":1000,"max":1000000,"step":10000},"value":60000,"display":"$60,000.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"quick ratio = (cash and equivalents + marketable securities + accounts receivable) / current liabilities // @hero @suffix()","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":1.75,"display":"1.75"},{"text":"$total quick assets = cash and equivalents + marketable securities + accounts receivable","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":105000,"display":"$105,000.00"},{"text":"liquidity status = if(quick ratio >= 1, \"Strong\", \"Potential liquidity risk\")","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":"Strong","display":"Strong"}]},{"id":"radiation-dose-background-equiv","title":"Radiation Dose Background Equiv","description":"Calculate how many days of background radiation a given dose equals.","category":"health","icon":"activity","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"dose_millisieverts = 0.1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.1,"display":"0.1"},{"text":"background_equivalent_days = dose_millisieverts / 0.0085 // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":11.764705882352942,"display":"11.76"}]},{"id":"radiator-cooling-capacity","title":"Radiator Cooling Capacity","description":"Calculate estimated heat rejection needed.","category":"engineering","icon":"settings","tags":["automotive","cooling"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Engine Settings","label":null,"prefix":null,"suffix":null,"section":"Engine Settings","hero":false,"slider":null,"value":null,"display":null},{"text":"horsepower = 300","label":null,"prefix":null,"suffix":null,"section":"Engine Settings","hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"efficiency factor = 0.3 // percentage of fuel energy to mechanical","label":null,"prefix":null,"suffix":"percentage of fuel energy to mechanical","section":"Engine 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estimate","section":"Details","hidden":false,"hero":false,"slider":null,"value":286.5000746312461,"display":"286.5"},{"text":"calendar year = 1950 - estimated age // approx relative to 1950 baseline","label":null,"prefix":null,"suffix":"approx relative to 1950 baseline","section":"Details","hidden":false,"hero":false,"slider":null,"value":-3780.001492624922,"display":"-3,780"}]},{"id":"radioactive-decay-remaining-mass","title":"Radioactive Decay Remaining Mass","description":"Calculate remaining mass of a radioactive substance after time elapsed.","category":"education","icon":"book-open","tags":["radioactive","mass"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"initial_mass = 100 // grams","label":null,"prefix":null,"suffix":"grams","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"half_life = 5730 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":5730,"display":"5,730"},{"text":"time_elapsed = 1000 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":1000,"display":"1,000"},{"text":"_decay_constant = ln(2) / half_life","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":0.00012096809433855938,"display":"0.000121"},{"text":"remaining_mass = initial_mass * exp(-decay_constant * time_elapsed) // grams @hero","label":null,"prefix":null,"suffix":"grams","section":null,"hidden":false,"hero":true,"slider":null,"value":88.60622295433987,"display":"88.61"}]},{"id":"radioactive-decay","title":"Radioactive Decay","description":"Model exponential decay with half-life calculations and timeline 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Calculation","label":null,"prefix":null,"suffix":null,"section":"Decay Calculation","hero":false,"slider":null,"value":null,"display":null},{"text":"decay constant = ln(2) / half life","label":null,"prefix":null,"suffix":null,"section":"Decay Calculation","hidden":false,"hero":false,"slider":null,"value":0.00012096809433855938,"display":"0.000121"},{"text":"amount remaining = initial amount * E^(-decay constant * time elapsed) // g @hero","label":null,"prefix":null,"suffix":"g","section":"Decay Calculation","hidden":false,"hero":true,"slider":null,"value":29.829243642371445,"display":"29.83"},{"text":"amount decayed = initial amount - amount remaining // g","label":null,"prefix":null,"suffix":"g","section":"Decay Calculation","hidden":false,"hero":false,"slider":null,"value":70.17075635762856,"display":"70.17"},{"text":"percentage remaining = (amount remaining / initial amount) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Decay Calculation","hidden":false,"hero":false,"slider":null,"value":29.829243642371445,"display":"29.83"},{"text":"# Timeline","label":null,"prefix":null,"suffix":null,"section":"Timeline","hero":false,"slider":null,"value":null,"display":null},{"text":"number of half lives = time elapsed / half life","label":null,"prefix":null,"suffix":null,"section":"Timeline","hidden":false,"hero":false,"slider":null,"value":1.7452006980802792,"display":"1.745"},{"text":"time_until_1_percent_remains = -ln(0.01) / decay_constant // years","label":null,"prefix":null,"suffix":"years","section":"Timeline","hidden":false,"hero":false,"slider":null,"value":38069.29596740917,"display":"38,069.3"}]},{"id":"raid-rebuild-time-estimator","title":"Raid Rebuild Time Estimator","description":"Estimate RAID array rebuild time in hours from drive size and speed.","category":"productivity","icon":"clock","tags":["raid","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"drive_size_terabytes = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"rebuild_speed_megabytes_per_second = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"total_megabytes = drive_size_terabytes * 1000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8000000,"display":"8,000,000"},{"text":"rebuild_time_hours = total_megabytes / (rebuild_speed_megabytes_per_second * 3600) // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":22.22222222222222,"display":"22.22"}]},{"id":"rain-drop-count-on-roof","title":"Rain Drop Count On Roof","description":"Estimate the number of raindrops falling on a roof during rainfall.","category":"everyday","icon":"smile","tags":["everyday"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"roof_area_m2 = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"rainfall_mm = 10","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"drop_volume_ml = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"total_water_ml = roof_area_m2 * rainfall_mm * 1000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1000000,"display":"1,000,000"},{"text":"number_of_drops = total_water_ml / drop_volume_ml // estimated drops @hero","label":null,"prefix":null,"suffix":"estimated drops","section":null,"hidden":false,"hero":true,"slider":null,"value":20000000,"display":"20,000,000"}]},{"id":"rainfall-harvesting-volume","title":"Rainfall Harvesting Volume","description":"Calculate harvested rainwater in gallons from roof area and rainfall.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"roof_area_square_feet = 2000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":2000,"display":"2,000"},{"text":"rainfall_inches = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"runoff_coefficient = 0.9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.9,"display":"0.9"},{"text":"harvest_gallons = roof_area_square_feet * (rainfall_inches / 12) * 7.48 * runoff_coefficient // @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1122,"display":"1,122"}]},{"id":"rainwater-collection-savings","title":"Rainwater Collection Savings","description":"Estimate annual water and cost savings from rainwater harvesting.","category":"finance","icon":"cloud-rain","tags":["eco","water"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"roof_area_square_meters = 100 // square meters","label":null,"prefix":null,"suffix":"square meters","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"annual_rainfall_mm = 800 // millimeters","label":null,"prefix":null,"suffix":"millimeters","section":null,"hidden":false,"hero":false,"slider":null,"value":800,"display":"800"},{"text":"collection_efficiency = 80 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"total_liters_collected = roof_area_square_meters * annual_rainfall_mm * (collection_efficiency / 100) // liters","label":null,"prefix":null,"suffix":"liters","section":null,"hidden":false,"hero":false,"slider":null,"value":64000,"display":"64,000"},{"text":"cost_of_water_per_liter = 0.002 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":0.002,"display":"0.002"},{"text":"annual_water_savings_dollars = total_liters_collected * cost_of_water_per_liter // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":128,"display":"128"}]},{"id":"range","title":"Range","description":"Compute the range of a dataset: max − 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min_val","label":null,"prefix":null,"suffix":null,"section":"Range","hidden":false,"hero":true,"slider":null,"value":8,"display":"8"}]},{"id":"reaction-time-analysis","title":"Reaction Time Analysis","description":"Calculate average reaction time in milliseconds across three trials.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"trial_1_ms = 250","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"trial_2_ms = 230","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":230,"display":"230"},{"text":"trial_3_ms = 270","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":270,"display":"270"},{"text":"average_reaction_time = (trial_1_ms + trial_2_ms + trial_3_ms) / 3 // milliseconds @hero","label":null,"prefix":null,"suffix":"milliseconds","section":null,"hidden":false,"hero":true,"slider":null,"value":250,"display":"250"}]},{"id":"reading-time-estimator-page-count","title":"Reading Time Estimator Page Count","description":"Estimate reading time in minutes and hours from page count and reading speed.","category":"productivity","icon":"clock","tags":["productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"page_count = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"words_per_page = 250","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250,"display":"250"},{"text":"reading_speed_wpm = 200 // words per minute","label":null,"prefix":null,"suffix":"words per 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expenses.","category":"other","icon":"calculator","tags":["estate","cap"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Property Performance","label":null,"prefix":null,"suffix":null,"section":"Property Performance","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchase price = 450000 // 50k..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Property Performance","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":5000},"value":450000,"display":"$450,000.00"},{"text":"$monthly rental income = 3500 // 500..20k by 100","label":null,"prefix":"$","suffix":null,"section":"Property Performance","hidden":false,"hero":false,"slider":{"min":500,"max":20000,"step":100},"value":3500,"display":"$3,500.00"},{"text":"vacancy rate = 5 // % 0..20","label":null,"prefix":null,"suffix":"%","section":"Property 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expenses","label":null,"prefix":"$","suffix":null,"section":"Calculations","hidden":true,"hero":false,"slider":null,"value":27900,"display":"$27,900.00"},{"text":"# Result","label":null,"prefix":null,"suffix":null,"section":"Result","hero":false,"slider":null,"value":null,"display":null},{"text":"capitalization rate = (net_operating_income / purchase price) * 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":true,"slider":null,"value":6.2,"display":"6.2"},{"text":"$monthly net_operating_income = net_operating_income / 12","label":null,"prefix":"$","suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":2325,"display":"$2,325.00"},{"text":"estimated property value at 6 percent cap = net_operating_income / 0.06","label":null,"prefix":null,"suffix":null,"section":"Result","hidden":false,"hero":false,"slider":null,"value":465000,"display":"465,000"}]},{"id":"real-estate-commission-split","title":"Real Estate Commission Split","description":"Calculate the breakdown between broker and agent commissions.","category":"real-estate","icon":"handshake","tags":["estate"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"totalCommission = 18000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":18000,"display":"18,000"},{"text":"brokerSplitPercentage = 30 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"brokerShare = totalCommission * (brokerSplitPercentage / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":5400,"display":"5,400"},{"text":"agentShare = totalCommission - brokerShare // @prefix($) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":12600,"display":"12,600"}]},{"id":"real-estate-tax-assessment","title":"Real Estate Tax Assessment","description":"Calculate annual property taxes using assessed value and millage.","category":"real-estate","icon":"file-text","tags":["estate","tax"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"marketValue = 400000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":400000,"display":"400,000"},{"text":"assessmentRatio = 80 // percent","label":null,"prefix":null,"suffix":"percent","section":null,"hidden":false,"hero":false,"slider":null,"value":80,"display":"80"},{"text":"millageRate = 15 // mills","label":null,"prefix":null,"suffix":"mills","section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"_assessedValue = marketValue * (assessmentRatio / 100)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":true,"hero":false,"slider":null,"value":320000,"display":"320,000"},{"text":"annualPropertyTax = (assessedValue / 1000) * millageRate // @prefix($) @suffix(/yr) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4800,"display":"4,800"}]},{"id":"real-interest-rate-fisher-eq","title":"Real Interest Rate Fisher Eq","description":"Calculate real interest rate from nominal rate and inflation using the Fisher equation.","category":"finance","icon":"dollar-sign","tags":["interest","finance"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"nominal_rate = 0.05","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.05,"display":"0.05"},{"text":"inflation_rate = 0.03","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.03,"display":"0.03"},{"text":"real_rate = (1 + nominal_rate) / (1 + inflation_rate) - 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.0194174757281554,"display":"0.0194"}]},{"id":"recipe-scaler","title":"Recipe Scaler","description":"Scale any recipe up or down with automatic metric conversions.","category":"cooking","icon":"scale","tags":["recipe"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Original Recipe","label":null,"prefix":null,"suffix":null,"section":"Original Recipe","hero":false,"slider":null,"value":null,"display":null},{"text":"original servings = 4 // 1..24","label":null,"prefix":null,"suffix":null,"section":"Original Recipe","hidden":false,"hero":false,"slider":{"min":1,"max":24,"step":1},"value":4,"display":"4"},{"text":"desired servings = 10 // 1..100","label":null,"prefix":null,"suffix":null,"section":"Original Recipe","hidden":false,"hero":false,"slider":{"min":1,"max":100,"step":1},"value":10,"display":"10"},{"text":"# Scale Factor","label":null,"prefix":null,"suffix":null,"section":"Scale Factor","hero":false,"slider":null,"value":null,"display":null},{"text":"multiply everything by = desired servings / original servings // @hero","label":null,"prefix":null,"suffix":null,"section":"Scale Factor","hidden":false,"hero":true,"slider":null,"value":2.5,"display":"2.5"},{"text":"# Ingredients","label":null,"prefix":null,"suffix":null,"section":"Ingredients","hero":false,"slider":null,"value":null,"display":null},{"text":"flour = 2 * multiply everything by // cups","label":null,"prefix":null,"suffix":"cups","section":"Ingredients","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"sugar = 1 * multiply everything by // cups","label":null,"prefix":null,"suffix":"cups","section":"Ingredients","hidden":false,"hero":false,"slider":null,"value":2.5,"display":"2.5"},{"text":"butter = 0.5 * multiply everything by // cups","label":null,"prefix":null,"suffix":"cups","section":"Ingredients","hidden":false,"hero":false,"slider":null,"value":1.25,"display":"1.25"},{"text":"eggs = 2 * multiply everything by","label":null,"prefix":null,"suffix":null,"section":"Ingredients","hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"milk = 1.5 * multiply everything by // cups","label":null,"prefix":null,"suffix":"cups","section":"Ingredients","hidden":false,"hero":false,"slider":null,"value":3.75,"display":"3.75"},{"text":"# Metric Equivalents","label":null,"prefix":null,"suffix":null,"section":"Metric Equivalents","hero":false,"slider":null,"value":null,"display":null},{"text":"flour grams = flour * 120 // g","label":null,"prefix":null,"suffix":"g","section":"Metric Equivalents","hidden":false,"hero":false,"slider":null,"value":600,"display":"600"},{"text":"sugar grams = sugar * 200 // g","label":null,"prefix":null,"suffix":"g","section":"Metric Equivalents","hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"butter grams = butter * 227 // g","label":null,"prefix":null,"suffix":"g","section":"Metric Equivalents","hidden":false,"hero":false,"slider":null,"value":283.75,"display":"283.75"},{"text":"milk ml = milk * 237 // mL","label":null,"prefix":null,"suffix":"mL","section":"Metric Equivalents","hidden":false,"hero":false,"slider":null,"value":888.75,"display":"888.75"}]},{"id":"rectangle-area","title":"Rectangle Area","description":"Find the area of a rectangle: A = length × width.","category":"formulas","icon":"square","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Dimensions","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"length = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"width = 6 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":6,"display":"6"},{"text":"# Area","label":null,"prefix":null,"suffix":null,"section":"Area","hero":false,"slider":null,"value":null,"display":null},{"text":"area = length * width","label":null,"prefix":null,"suffix":null,"section":"Area","hidden":false,"hero":true,"slider":null,"value":60,"display":"60"}]},{"id":"rectangle-perimeter","title":"Rectangle Perimeter","description":"Find the perimeter of a rectangle: P = 2 × (length + width).","category":"formulas","icon":"square","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Dimensions","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"length = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"width = 6 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":6,"display":"6"},{"text":"# Perimeter","label":null,"prefix":null,"suffix":null,"section":"Perimeter","hero":false,"slider":null,"value":null,"display":null},{"text":"perimeter = 2 * (length + width)","label":null,"prefix":null,"suffix":null,"section":"Perimeter","hidden":false,"hero":true,"slider":null,"value":32,"display":"32"}]},{"id":"rectangular-prism-volume","title":"Rectangular Prism Volume","description":"Find the volume and surface area of a rectangular prism (box).","category":"formulas","icon":"box","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.722Z"},"rows":[{"text":"# Dimensions","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hero":false,"slider":null,"value":null,"display":null},{"text":"length = 10 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":10,"display":"10"},{"text":"width = 6 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":6,"display":"6"},{"text":"height = 4 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Dimensions","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":4,"display":"4"},{"text":"# Volume and surface area","label":null,"prefix":null,"suffix":null,"section":"Volume and surface area","hero":false,"slider":null,"value":null,"display":null},{"text":"volume = length * width * height // @hero","label":null,"prefix":null,"suffix":null,"section":"Volume and surface area","hidden":false,"hero":true,"slider":null,"value":240,"display":"240"},{"text":"surface_area = 2 * (length * width + width * height + length * height)","label":null,"prefix":null,"suffix":null,"section":"Volume and surface area","hidden":false,"hero":false,"slider":null,"value":248,"display":"248"}]},{"id":"reference-lines","title":"Reference Lines on Graphs","description":"Annotate any plot with reference lines and shaded bands. `vline(x)` and `hline(y)` mark axis values; `vrect(x1, x2)` and `hrect(y1, y2)` highlight valid ranges or target bands. Mix and match — they compose with every other plot primitive.","category":"math","icon":"grid","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"# A parabola with axes lines and a \"valid input\" band","label":null,"prefix":null,"suffix":null,"section":"A parabola with axes lines and a \"valid input\" band","hero":false,"slider":null,"value":null,"display":null},{"text":"# Sine wave with a threshold line and a target tolerance band","label":null,"prefix":null,"suffix":null,"section":"Sine wave with a threshold line and a target tolerance band","hero":false,"slider":null,"value":null,"display":null},{"text":"# A control-engineering plot: response curve with reference setpoint","label":null,"prefix":null,"suffix":null,"section":"A control-engineering plot: response curve with reference setpoint","hero":false,"slider":null,"value":null,"display":null},{"text":"# Polynomial roots highlighted with vertical reference lines","label":null,"prefix":null,"suffix":null,"section":"Polynomial roots highlighted with vertical reference lines","hero":false,"slider":null,"value":null,"display":null},{"text":"plot x^3 - 3x, vline(-sqrt(3), \"root −√3\"), vline(0, \"root 0\"), vline(sqrt(3), \"root √3\") from -3 to 3","label":null,"prefix":null,"suffix":null,"section":"Polynomial roots highlighted with vertical reference lines","hidden":false,"hero":true,"slider":null,"value":{"type":"svg","source":"","isUrl":false,"refShapes":[{"kind":"vline","x":-1.7320508075688772,"label":"root −√3"},{"kind":"vline","x":0,"label":"root 0"},{"kind":"vline","x":1.7320508075688772,"label":"root √3"}],"curveExprs":["x^3-3x"]},"display":null}]},{"id":"regular-polygon-area","title":"Regular Polygon Area","description":"Find the area of a regular n-sided polygon from its side length.","category":"formulas","icon":"hexagon","tags":["geometry"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"# Polygon","label":null,"prefix":null,"suffix":null,"section":"Polygon","hero":false,"slider":null,"value":null,"display":null},{"text":"sides = 6 // 3..20","label":null,"prefix":null,"suffix":null,"section":"Polygon","hidden":false,"hero":false,"slider":{"min":3,"max":20,"step":0.2},"value":6,"display":"6"},{"text":"side_length = 5 // 0.1..1k","label":null,"prefix":null,"suffix":null,"section":"Polygon","hidden":false,"hero":false,"slider":{"min":0.1,"max":1000,"step":10},"value":5,"display":"5"},{"text":"# Area (use radians for tan)","label":null,"prefix":null,"suffix":null,"section":"Area (use radians for tan)","hero":false,"slider":null,"value":null,"display":null},{"text":"_interior_half_angle_deg = 180 / sides","label":null,"prefix":null,"suffix":null,"section":"Area (use radians for tan)","hidden":true,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"area = (sides * side_length^2) / (4 * tan(interior_half_angle_deg deg)) // @hero","label":null,"prefix":null,"suffix":null,"section":"Area (use radians for tan)","hidden":false,"hero":true,"slider":null,"value":64.9519052838329,"display":"64.95"},{"text":"perimeter = sides * side_length","label":null,"prefix":null,"suffix":null,"section":"Area (use radians for tan)","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"}]},{"id":"regulatory-change-impact-score","title":"Regulatory Change Impact","description":"Assess how new regulations will affect your operations.","category":"other","icon":"refresh-cw","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"operationalChangeScore = 7 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"financialCostScore = 5 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":5,"display":"5"},{"text":"timeToImplementScore = 8 // scale 1-10","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"overallImpactScore = (operationalChangeScore + financialCostScore + timeToImplementScore) / 3 // scale 1-10 @hero","label":null,"prefix":null,"suffix":"scale 1-10","section":null,"hidden":false,"hero":true,"slider":null,"value":6.666666666666667,"display":"6.667"}]},{"id":"reit-dividend-yield","title":"REIT Dividend Yield","description":"Calculate the annual dividend yield for REIT share investments.","category":"real-estate","icon":"pie-chart","tags":["dividend"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"annualDividend = 4.50 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":4.5,"display":"4.5"},{"text":"sharePrice = 100 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"dividendYield = (annualDividend / sharePrice) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":4.5,"display":"4.5"}]},{"id":"relative-worth-historic-currency","title":"Relative Worth Historic Currency","description":"Adjust a historic currency amount to today's purchasing power using CPI ratios.","category":"other","icon":"calculator","tags":[],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"historic_amount = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"historic_year_cpi = 15","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":15,"display":"15"},{"text":"current_cpi = 300","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300,"display":"300"},{"text":"current_worth = historic_amount * (current_cpi / historic_year_cpi)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":2000,"display":"2,000"}]},{"id":"relativistic-length-contraction","title":"Relativistic Length Contraction","description":"Calculate length contraction of an object moving near the speed of light.","category":"other","icon":"calculator","tags":["relativistic"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"proper_length_meters = 100","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":100,"display":"100"},{"text":"relative_velocity_meters_per_second = 250000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250000000,"display":"250,000,000"},{"text":"speed_of_light = 299792458","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"lorentz_factor_reciprocal = (1 - (relative_velocity_meters_per_second ** 2 / speed_of_light ** 2)) ** 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.5519000950955603,"display":"0.5519"},{"text":"contracted_length_meters = proper_length_meters * lorentz_factor_reciprocal","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":55.190009509556035,"display":"55.19"}]},{"id":"relativistic-mass-increase","title":"Relativistic Mass Increase","description":"Calculate the relativistic mass of an object moving near the speed of light.","category":"science","icon":"flask-conical","tags":["relativistic","mass","science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"rest_mass_kilograms = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"relative_velocity_meters_per_second = 250000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250000000,"display":"250,000,000"},{"text":"speed_of_light = 299792458","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"relativistic_mass_kilograms = rest_mass_kilograms / (1 - (relative_velocity_meters_per_second ** 2 / speed_of_light ** 2)) ** 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.8119221375144938,"display":"1.812"}]},{"id":"relativistic-time-dilation","title":"Relativistic Time Dilation","description":"Calculate time dilation experienced at relativistic velocities.","category":"productivity","icon":"clock","tags":["relativistic","productivity"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"proper_time_interval_seconds = 1","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1,"display":"1"},{"text":"relative_velocity_meters_per_second = 250000000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250000000,"display":"250,000,000"},{"text":"speed_of_light = 299792458","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":299792458,"display":"299,792,458"},{"text":"lorentz_factor = 1 / (1 - (relative_velocity_meters_per_second ** 2 / speed_of_light ** 2)) ** 0.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":1.8119221375144938,"display":"1.812"},{"text":"dilated_time_interval_seconds = proper_time_interval_seconds * lorentz_factor","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":1.811922137514494,"display":"1.812"}]},{"id":"rem-to-pixel-font-scaler","title":"Rem To Pixel Font Scaler","description":"Convert a CSS rem value to pixels using the root font size.","category":"design","icon":"palette","tags":["pixel","font"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"rem_value = 1.2 // rem","label":null,"prefix":null,"suffix":"rem","section":null,"hidden":false,"hero":false,"slider":null,"value":1.2,"display":"1.2"},{"text":"root_pixel_size = 16 // pixels","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":false,"slider":null,"value":16,"display":"16"},{"text":"calculated_pixel_size = rem_value * root_pixel_size // pixels @hero","label":null,"prefix":null,"suffix":"pixels","section":null,"hidden":false,"hero":true,"slider":null,"value":19.2,"display":"19.2"}]},{"id":"rent-affordability","title":"Rent Affordability","description":"Find your affordable rent using the 30% rule, 25% rule, and NYC 40x rule.","category":"everyday","icon":"building-2","tags":["rent","housing","budget","income"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"# Income","label":null,"prefix":null,"suffix":null,"section":"Income","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly take home pay = 5000 // 1k..30k by 100","label":null,"prefix":"$","suffix":null,"section":"Income","hidden":false,"hero":false,"slider":{"min":1000,"max":30000,"step":100},"value":5000,"display":"$5,000.00"},{"text":"$other monthly income = 0 // 0..10k by 50","label":null,"prefix":"$","suffix":null,"section":"Income","hidden":false,"hero":false,"slider":{"min":0,"max":10000,"step":50},"value":0,"display":"$0.00"},{"text":"$total monthly income = monthly take home pay + other monthly income","label":null,"prefix":"$","suffix":null,"section":"Income","hidden":false,"hero":false,"slider":null,"value":5000,"display":"$5,000.00"},{"text":"# Affordability Rules","label":null,"prefix":null,"suffix":null,"section":"Affordability Rules","hero":false,"slider":null,"value":null,"display":null},{"text":"$max rent 30 pct rule = total monthly income * 0.30 // @hero @label(Max Rent (30% Rule))","label":"Max Rent (30% Rule)","prefix":"$","suffix":null,"section":"Affordability Rules","hidden":false,"hero":true,"slider":null,"value":1500,"display":"$1,500.00"},{"text":"$conservative 25 pct rule = total monthly income * 0.25 // @label(Conservative (25% Rule))","label":"Conservative (25% Rule)","prefix":"$","suffix":null,"section":"Affordability Rules","hidden":false,"hero":false,"slider":null,"value":1250,"display":"$1,250.00"},{"text":"$nyc_standard_40x_rule = total monthly income * 12 / 40 // @label(NYC Standard (40x Rule))","label":"NYC Standard (40x Rule)","prefix":"$","suffix":null,"section":"Affordability Rules","hidden":false,"hero":false,"slider":null,"value":1500,"display":"$1,500.00"},{"text":"# With Expenses","label":null,"prefix":null,"suffix":null,"section":"With Expenses","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly debt payments = 300 // 0..5k by 25","label":null,"prefix":"$","suffix":null,"section":"With Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":5000,"step":25},"value":300,"display":"$300.00"},{"text":"$after debts = total monthly income - monthly debt payments","label":null,"prefix":"$","suffix":null,"section":"With Expenses","hidden":false,"hero":false,"slider":null,"value":4700,"display":"$4,700.00"},{"text":"$affordable rent after debts = after debts * 0.30 // @label(Affordable Rent (30% After Debts))","label":"Affordable Rent (30% After Debts)","prefix":"$","suffix":null,"section":"With Expenses","hidden":false,"hero":false,"slider":null,"value":1410,"display":"$1,410.00"},{"text":"# Annual Impact","label":null,"prefix":null,"suffix":null,"section":"Annual Impact","hero":false,"slider":null,"value":null,"display":null},{"text":"$rent you are considering = 1500 // 300..10k by 50","label":null,"prefix":"$","suffix":null,"section":"Annual Impact","hidden":false,"hero":false,"slider":{"min":300,"max":10000,"step":50},"value":1500,"display":"$1,500.00"},{"text":"rent as pct of income = (rent you are considering / total monthly income) * 100 // %","label":null,"prefix":null,"suffix":"%","section":"Annual Impact","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"$remaining after rent and debts = total monthly income - rent you are considering - monthly debt payments","label":null,"prefix":"$","suffix":null,"section":"Annual Impact","hidden":false,"hero":false,"slider":null,"value":3200,"display":"$3,200.00"}]},{"id":"rent-to-value-ratio","title":"Rent-to-Value Ratio","description":"Determine the relationship between monthly rent and property price.","category":"real-estate","icon":"percent","tags":["rent"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"monthlyRent = 1500 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"propertyValue = 200000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":200000,"display":"200,000"},{"text":"rentToValueRatio = (monthlyRent / propertyValue) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":0.75,"display":"0.75"}]},{"id":"rent-vs-buy","title":"Rent vs Buy","description":"Compare the monthly cost of renting versus buying a home.","category":"finance","icon":"home","tags":["rent","housing"],"featured":true,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"# Renting","label":null,"prefix":null,"suffix":null,"section":"Renting","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly rent = 2000 // 500..5k by 100","label":null,"prefix":"$","suffix":null,"section":"Renting","hidden":false,"hero":false,"slider":{"min":500,"max":5000,"step":100},"value":2000,"display":"$2,000.00"},{"text":"annual rent increase = 3 // % 0..10 by 0.5","label":null,"prefix":null,"suffix":"%","section":"Renting","hidden":false,"hero":false,"slider":{"min":0,"max":10,"step":0.5},"value":3,"display":"3"},{"text":"# Buying","label":null,"prefix":null,"suffix":null,"section":"Buying","hero":false,"slider":null,"value":null,"display":null},{"text":"$home price = 400000 // 50k..2M by 10k","label":null,"prefix":"$","suffix":null,"section":"Buying","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":10000},"value":400000,"display":"$400,000.00"},{"text":"down payment pct = 20 // % 0..50 by 5","label":null,"prefix":null,"suffix":"%","section":"Buying","hidden":false,"hero":false,"slider":{"min":0,"max":50,"step":5},"value":20,"display":"20"},{"text":"mortgage rate = 6.5 // % 2..10","label":null,"prefix":null,"suffix":"%","section":"Buying","hidden":false,"hero":false,"slider":{"min":2,"max":10,"step":0.1},"value":6.5,"display":"6.5"},{"text":"loan term = 30 // years","label":null,"prefix":null,"suffix":"years","section":"Buying","hidden":false,"hero":false,"slider":null,"value":30,"display":"30"},{"text":"# Monthly Costs","label":null,"prefix":null,"suffix":null,"section":"Monthly Costs","hero":false,"slider":null,"value":null,"display":null},{"text":"$down payment = home price * down payment pct / 100","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":null,"value":80000,"display":"$80,000.00"},{"text":"loan amount = home price - down payment","label":null,"prefix":null,"suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":null,"value":320000,"display":"320,000"},{"text":"monthly rate = mortgage rate / 100 / 12","label":null,"prefix":null,"suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":null,"value":0.005416666666666667,"display":"0.005417"},{"text":"num payments = loan term * 12","label":null,"prefix":null,"suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":null,"value":360,"display":"360"},{"text":"$mortgage payment = loan amount * (monthly rate * (1 + monthly rate)^num payments) / ((1 + monthly rate)^num payments - 1)","label":null,"prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":false,"slider":null,"value":2022.6176751774892,"display":"$2,022.62"},{"text":"$monthly ownership = mortgage payment + home price * 0.01 / 12 + 150 // @label(Monthly Buy Cost (mortgage + tax + insurance)) @hero","label":"Monthly Buy Cost (mortgage + tax + insurance)","prefix":"$","suffix":null,"section":"Monthly Costs","hidden":false,"hero":true,"slider":null,"value":2505.9510085108222,"display":"$2,505.95"},{"text":"# Comparison","label":null,"prefix":null,"suffix":null,"section":"Comparison","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly difference = monthly ownership - monthly rent // @label(Buy vs Rent Difference)","label":"Buy vs Rent Difference","prefix":"$","suffix":null,"section":"Comparison","hidden":false,"hero":false,"slider":null,"value":505.9510085108224,"display":"$505.95"}]},{"id":"rental-listing-roi","title":"Rental Listing ROI","description":"Measure the return on investment for paid rental advertisements.","category":"real-estate","icon":"activity","tags":["rental","roi"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"listingFee = 50 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"monthlyRentGain = 1500 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":1500,"display":"1,500"},{"text":"daysVacantSaved = 10 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"totalBenefit = (monthlyRentGain / 30) * daysVacantSaved","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"listingROI = ((totalBenefit - listingFee) / listingFee) * 100 // @suffix(%) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":900,"display":"900"}]},{"id":"rental-property-depreciation-schedule","title":"Rental Property Depreciation Schedule","description":"Calculate annual depreciation on a residential rental property over 27.5 years.","category":"other","icon":"calculator","tags":["rental","property","depreciation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"property_value = 300000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":300000,"display":"300,000"},{"text":"land_value = 50000","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":50000,"display":"50,000"},{"text":"recovery_period_years = 27.5","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":27.5,"display":"27.5"},{"text":"building_value = property_value - land_value","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":250000,"display":"250,000"},{"text":"annual_depreciation = building_value / recovery_period_years","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":9090.90909090909,"display":"9,090.91"}]},{"id":"rental-property-macrs-depreciation","title":"Rental Property MACRS Depreciation","description":"Estimate annual tax depreciation for residential rental property.","category":"real-estate","icon":"trending-down","tags":["rental","property","depreciation"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"propertyValueLessLand = 250000 // dollars","label":null,"prefix":null,"suffix":"dollars","section":null,"hidden":false,"hero":false,"slider":null,"value":250000,"display":"250,000"},{"text":"recoveryPeriodYears = 27.5 // years","label":null,"prefix":null,"suffix":"years","section":null,"hidden":false,"hero":false,"slider":null,"value":27.5,"display":"27.5"},{"text":"annualDepreciation = propertyValueLessLand / recoveryPeriodYears // @prefix($) @suffix(/yr) @hero","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":9090.90909090909,"display":"9,090.91"}]},{"id":"rental-yield","title":"Rental Yield","description":"Calculate annual yield and cash flow on a rental property.","category":"real-estate","icon":"building","tags":["rental","property","investment"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"# Property Details","label":null,"prefix":null,"suffix":null,"section":"Property Details","hero":false,"slider":null,"value":null,"display":null},{"text":"$purchase price = 250000 // 50k..2M by 5k","label":null,"prefix":"$","suffix":null,"section":"Property Details","hidden":false,"hero":false,"slider":{"min":50000,"max":2000000,"step":5000},"value":250000,"display":"$250,000.00"},{"text":"$monthly rent = 1800 // 200..10k by 50","label":null,"prefix":"$","suffix":null,"section":"Property Details","hidden":false,"hero":false,"slider":{"min":200,"max":10000,"step":50},"value":1800,"display":"$1,800.00"},{"text":"# Expenses","label":null,"prefix":null,"suffix":null,"section":"Expenses","hero":false,"slider":null,"value":null,"display":null},{"text":"$monthly expenses = 400 // 0..3k by 25 @label(Monthly Expenses (maintenance, insurance, tax))","label":"Monthly Expenses (maintenance, insurance, tax)","prefix":"$","suffix":null,"section":"Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":3000,"step":25},"value":400,"display":"$400.00"},{"text":"vacancy rate = 8 // % 0..30","label":null,"prefix":null,"suffix":"%","section":"Expenses","hidden":false,"hero":false,"slider":{"min":0,"max":30,"step":1},"value":8,"display":"8"},{"text":"# Annual Income","label":null,"prefix":null,"suffix":null,"section":"Annual Income","hero":false,"slider":null,"value":null,"display":null},{"text":"$gross annual rent = monthly rent * 12","label":null,"prefix":"$","suffix":null,"section":"Annual Income","hidden":false,"hero":false,"slider":null,"value":21600,"display":"$21,600.00"},{"text":"$effective rent = gross annual rent * (1 - vacancy rate / 100) // @label(Effective Rent (after vacancy))","label":"Effective Rent (after vacancy)","prefix":"$","suffix":null,"section":"Annual Income","hidden":false,"hero":false,"slider":null,"value":19872,"display":"$19,872.00"},{"text":"$annual expenses = monthly expenses * 12","label":null,"prefix":"$","suffix":null,"section":"Annual Income","hidden":false,"hero":false,"slider":null,"value":4800,"display":"$4,800.00"},{"text":"$net operating income = effective rent - annual expenses","label":null,"prefix":"$","suffix":null,"section":"Annual Income","hidden":false,"hero":false,"slider":null,"value":15072,"display":"$15,072.00"},{"text":"# Returns","label":null,"prefix":null,"suffix":null,"section":"Returns","hero":false,"slider":null,"value":null,"display":null},{"text":"annual yield = round(net operating income / purchase price * 100 * 100) / 100 // @hero @suffix(%)","label":null,"prefix":null,"suffix":null,"section":"Returns","hidden":false,"hero":true,"slider":null,"value":6.03,"display":"6.03"},{"text":"$monthly cash flow = round(net operating income / 12 * 100) / 100","label":null,"prefix":"$","suffix":null,"section":"Returns","hidden":false,"hero":false,"slider":null,"value":1256,"display":"$1,256.00"}]},{"id":"reorder-point","title":"Reorder Point","description":"Determine the inventory level at which a new order should be placed.","category":"business","icon":"alert-circle","tags":["business"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"leadTimeInDays = 10 // days","label":null,"prefix":null,"suffix":"days","section":null,"hidden":false,"hero":false,"slider":null,"value":10,"display":"10"},{"text":"averageDailyUsage = 50 // units","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":false,"slider":null,"value":50,"display":"50"},{"text":"safetyStockLevel = 200 // units","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":false,"slider":null,"value":200,"display":"200"},{"text":"reorderPointValue = (leadTimeInDays * averageDailyUsage) + safetyStockLevel // units @hero","label":null,"prefix":null,"suffix":"units","section":null,"hidden":false,"hero":true,"slider":null,"value":700,"display":"700"}]},{"id":"resilience-quotient","title":"Resilience Quotient","description":"Calculate a resilience score from problem solving, social support, and self-efficacy.","category":"health","icon":"brain","tags":["health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"problem_solving_score = 8","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":8,"display":"8"},{"text":"social_support_score = 7","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":7,"display":"7"},{"text":"self_efficacy_score = 9","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":9,"display":"9"},{"text":"resilience_index = (problem_solving_score + social_support_score + self_efficacy_score) / 3 // 1-10 scale @hero","label":null,"prefix":null,"suffix":"1-10 scale","section":null,"hidden":false,"hero":true,"slider":null,"value":8,"display":"8"}]},{"id":"resonance-frequency-lc","title":"Resonance Frequency Lc","description":"Calculate the resonance frequency of an LC circuit from inductance and capacitance.","category":"science","icon":"flask-conical","tags":["science"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"inductance_henries = 0.001","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.001,"display":"0.001"},{"text":"capacitance_farads = 0.000001","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":false,"slider":null,"value":0.000001,"display":"0.000001"},{"text":"resonance_frequency_hertz = 1 / (2 * 3.14159 * (inductance_henries * capacitance_farads) ** 0.5)","label":null,"prefix":null,"suffix":null,"section":null,"hidden":false,"hero":true,"slider":null,"value":5032.925461578976,"display":"5,032.93"}]},{"id":"respiration","title":"Respiration","description":"Daily, yearly, and lifetime breath counts with awake and sleep rates.","category":"health","icon":"wind","tags":["biology","health"],"featured":false,"provenance":{"status":"draft","updatedAt":"2026-06-04T09:52:53.724Z"},"rows":[{"text":"# Your Day","label":null,"prefix":null,"suffix":null,"section":"Your Day","hero":false,"slider":null,"value":null,"display":null},{"text":"awake hours = 16 // hr 0..24","label":null,"prefix":null,"suffix":"hr","section":"Your Day","hidden":false,"hero":false,"slider":{"min":0,"max":24,"step":1},"value":16,"display":"16"},{"text":"sleep hours = 8 // hr 0..16 by 0.5","label":null,"prefix":null,"suffix":"hr","section":"Your Day","hidden":false,"hero":false,"slider":{"min":0,"max":16,"step":0.5},"value":8,"display":"8"},{"text":"# Breathing Rates","label":null,"prefix":null,"suffix":null,"section":"Breathing Rates","hero":false,"slider":null,"value":null,"display":null},{"text":"awake rate = 17 // breaths/min 6..40","label":null,"prefix":null,"suffix":"breaths/min","section":"Breathing Rates","hidden":false,"hero":false,"slider":{"min":6,"max":40,"step":1},"value":17,"display":"17"},{"text":"sleep rate = 12 // breaths/min 4..30","label":null,"prefix":null,"suffix":"breaths/min","section":"Breathing Rates","hidden":false,"hero":false,"slider":{"min":4,"max":30,"step":1},"value":12,"display":"12"},{"text":"# Daily Breaths","label":null,"prefix":null,"suffix":null,"section":"Daily Breaths","hero":false,"slider":null,"value":null,"display":null},{"text":"awake breaths = awake hours * 60 * awake rate","label":null,"prefix":null,"suffix":null,"section":"Daily Breaths","hidden":false,"hero":false,"slider":null,"value":16320,"display":"16,320"},{"text":"sleep breaths = sleep hours * 60 * sleep rate","label":null,"prefix":null,"suffix":null,"section":"Daily Breaths","hidden":false,"hero":false,"slider":null,"value":5760,"display":"5,760"},{"text":"total daily breaths = awake breaths + sleep breaths // @hero @label(Breaths per day)","label":"Breaths per day","prefix":null,"suffix":null,"section":"Daily Breaths","hidden":false,"hero":true,"slider":null,"value":22080,"display":"22,080"},{"text":"# Longer Spans","label":null,"prefix":null,"suffix":null,"section":"Longer Spans","hero":false,"slider":null,"value":null,"display":null},{"text":"yearly breaths = total daily breaths * 365 // @label(Breaths per year)","label":"Breaths per year","prefix":null,"suffix":null,"section":"Longer Spans","hidden":false,"hero":false,"slider":null,"value":8059200,"display":"8,059,200"},{"text":"lifetime years = 80 // years 1..120","label":null,"prefix":null,"suffix":"years","section":"Longer Spans","hidden":false,"hero":false,"slider":{"min":1,"max":120,"step":1},"value":80,"display":"80"},{"text":"lifetime breaths = total daily breaths * 365 * lifetime years","label":null,"prefix":null,"suffix":null,"section":"Longer Spans","hidden":false,"hero":false,"slider":null,"value":644736000,"display":"644,736,000"},{"text":"# Air Volume","label":null,"prefix":null,"suffix":null,"section":"Air Volume","hero":false,"slider":null,"value":null,"display":null},{"text":"_tidal_volume_ml = 500 // mL","label":null,"prefix":null,"suffix":"mL","section":"Air Volume","hidden":true,"hero":false,"slider":null,"value":500,"display":"500"},{"text":"daily air liters = round(total daily breaths * tidal_volume_ml / 1000) // @label(Air moved per day)","label":"Air moved per day","prefix":null,"suffix":null,"section":"Air Volume","hidden":false,"hero":false,"slider":null,"value":11040,"display":"11,040"}]},{"id":"restricted-stock-unit-rsu-tax","title":"Restricted Sto