Public proof

Public calculation tests

Selected reference cases make calculator behavior inspectable. Each case is machine-verified during the release test suite and shows the model, inputs, expected result, and tolerance.

Reference cases

ToolModelInputsExpectedTolerance
percentage-calcX percent of Y = (X / 100) × Y{"mode":"of","val1":15,"val2":200}{"result":30}±0.000001
percentage-calcPercent change = ((new - old) / old) × 100{"mode":"change","val1":100,"val2":125}{"percent_change":25}±0.000001 percentage points
debt-payoffSingle balance, monthly interest, fixed payment plus extra{"balance":1000,"apr":12,"payment":100,"extra":50}{"payoff_months":7,"base_payoff_months":11,"interest_saved_positive":true}Exact months; currency ±$0.01
debt-payoffSingle balance at zero APR with fixed payment{"balance":1200,"apr":0,"payment":100,"extra":0}{"payoff_months":12,"total_interest":0}Exact months; currency ±$0.01
bmi-calcBMI = kilograms / meters²{"weight":170,"heightFt":5,"heightIn":9}{"bmi":25.1,"category":"Overweight"}±0.1 BMI unit
bmi-calcBMI = kilograms / meters²{"weight":120,"heightFt":5,"heightIn":4}{"bmi":20.6,"category":"Normal"}±0.1 BMI unit
electricity-cost-calculatorkWh = watts / 1000 × hours × days; cost = kWh × tariff{"watts":1000,"hours":2,"days":30,"rate":0.15}{"monthly_kwh":60,"monthly_cost":9}Energy ±0.01 kWh; currency ±$0.01
electricity-cost-calculatorkWh = watts / 1000 × hours × days; cost = kWh × tariff{"watts":60,"hours":5,"days":30,"rate":0.25}{"monthly_kwh":9,"monthly_cost":2.25}Energy ±0.01 kWh; currency ±$0.01
tip-bill-split-calculatorTip on subtotal; equal split{"subtotal":100,"tax":8,"tipPct":20,"people":4,"tipOnTax":false,"roundMode":"none"}{"tip":20,"total":128,"perPerson":32}Currency ±$0.01
tip-bill-split-calculatorEqual split rounded upward per person{"subtotal":50,"tax":0,"tipPct":15,"people":3,"tipOnTax":false,"roundMode":"up-dollar"}{"unroundedTotal":57.5,"total":60,"perPerson":20}Currency ±$0.01
date-calculator-workspaceUTC date-only signed difference with both boundaries counted{"mode":"difference","startDate":"2024-02-28","endDate":"2024-03-01","inclusive":true,"excludeWeekends":true}{"totalDays":3,"weekdayDays":3}Exact calendar days
date-calculator-workspaceAdd one calendar month with month-end preservation{"mode":"add","baseDate":"2024-01-31","direction":"add","years":0,"months":1,"weeks":0,"days":0,"preserveLastDay":true}{"resultDate":"2024-02-29","weekday":"Thursday"}Exact date
discount-percent-off-calculatorSequential percentage discounts, then fixed coupon, then tax{"originalPrice":200,"discount1":20,"discount2":10,"coupon":5,"taxPct":8}{"preTaxFinal":139,"discountAmount":61,"checkoutTotal":150.12}Currency ±$0.01
discount-percent-off-calculatorFixed coupon after percentage discounts with zero floor{"originalPrice":25,"discount1":0,"discount2":0,"coupon":40,"taxPct":10}{"preTaxFinal":0,"discountAmount":25,"checkoutTotal":0}Currency ±$0.01
fuel-trip-cost-calculatorMiles divided by MPG; round trip and repeated trips{"unit":"mpg","distance":120,"roundTrip":true,"efficiency":30,"fuelPrice":3.5,"travelers":4,"trips":2}{"totalDistance":480,"fuelUsed":16,"totalCost":56,"costPerTraveler":14}Distance/fuel ±0.000001; currency ±$0.01
fuel-trip-cost-calculatorKilometers multiplied by L/100 km divided by 100{"unit":"l100km","distance":300,"roundTrip":false,"efficiency":7.5,"fuelPrice":1.7,"travelers":3,"trips":1}{"fuelUsed":22.5,"totalCost":38.25,"costPerTraveler":12.75}Fuel ±0.000001 L; currency ±$0.01
commission-calculatorFlat commission rate on all gross sales{"mode":"flat","sales":50000,"flatRate":5}{"commission":2500,"effectiveRate":5}Currency ±$0.01; rate ±0.000001 percentage points
commission-calculatorProgressive commission brackets{"mode":"tiered","sales":40000,"tier1Limit":10000,"tier1Rate":3,"tier2Limit":25000,"tier2Rate":5,"tier3Rate":7}{"commission":2100,"effectiveRate":5.25}Currency ±$0.01; rate ±0.000001 percentage points
debt-to-income-ratio-calculatorFront-end and back-end required-debt ratios{"grossMonthlyIncome":8000,"housingPayment":1800,"carPayment":400,"studentLoans":100,"creditCards":50,"otherDebt":50,"targetDti":36}{"frontEndDti":22.5,"backEndDti":30,"remainingCapacity":480}Ratios ±0.000001 percentage points; currency ±$0.01
debt-to-income-ratio-calculatorRequired debt above selected planning threshold{"grossMonthlyIncome":5000,"housingPayment":1800,"carPayment":500,"studentLoans":200,"creditCards":100,"otherDebt":0,"targetDti":36}{"backEndDti":52,"remainingCapacity":-800,"withinTarget":false}Ratios ±0.000001 percentage points; currency ±$0.01
down-payment-calculatorPercentage down payment plus percentage closing costs{"homePrice":400000,"mode":"percent","downPercent":20,"downAmount":0,"closingCostPercent":3,"availableCash":100000}{"downPayment":80000,"loanAmount":320000,"ltv":80,"cashToClose":92000,"cashRemaining":8000}Currency ±$0.01; LTV ±0.000001 percentage points
down-payment-calculatorFixed down payment plus percentage closing costs{"homePrice":250000,"mode":"amount","downPercent":0,"downAmount":50000,"closingCostPercent":2,"availableCash":70000}{"downPayment":50000,"loanAmount":200000,"closingCosts":5000,"cashToClose":55000}Currency ±$0.01
401k-employer-match-calculatorSimple employer percentage match up to salary-percentage limit{"annualSalary":80000,"employeePercent":6,"employerMatchPercent":50,"matchLimitPercent":6,"payPeriods":26}{"employeeAnnual":4800,"employerAnnual":2400,"totalAnnual":7200,"unclaimedMatch":0}Currency ±$0.01
401k-employer-match-calculatorEmployee contribution below modeled match limit{"annualSalary":80000,"employeePercent":3,"employerMatchPercent":50,"matchLimitPercent":6,"payPeriods":26}{"employeeAnnual":2400,"employerAnnual":1200,"maximumEmployerMatch":2400,"unclaimedMatch":1200}Currency ±$0.01
rent-vs-buy-calculatorBuyer equity versus renter investment portfolio{"homePrice":400000,"downPercent":20,"mortgageRate":6.5,"mortgageTerm":30,"years":7,"buyClosingPercent":3,"sellCostPercent":6,"propertyTaxPercent":1.2,"annualInsurance":1800,"maintenancePercent":1,"appreciationPercent":3,"monthlyRent":2200,"rentIncreasePercent":3,"annualRenterInsurance":240,"investmentReturnPercent":5}{"buyerEquity":173100.59009255463,"renterPortfolio":187585.86781217443,"wealthAdvantage":-14485.2777196198}Currency ±$0.01
rent-vs-buy-calculatorShort-horizon buyer equity versus renter portfolio{"homePrice":400000,"downPercent":20,"mortgageRate":6.5,"mortgageTerm":30,"years":3,"buyClosingPercent":3,"sellCostPercent":6,"propertyTaxPercent":1.2,"annualInsurance":1800,"maintenancePercent":1,"appreciationPercent":3,"monthlyRent":2200,"rentIncreasePercent":3,"annualRenterInsurance":240,"investmentReturnPercent":5}{"buyerEquity":102330.17790586711,"renterPortfolio":132243.2383420157,"wealthAdvantage":-29913.060436148604}Currency ±$0.01
apr-effective-interest-calculatorFee-adjusted fixed-payment loan APR{"amount":10000,"nominalRate":8,"termMonths":36,"fees":300,"financeFees":false}{"monthlyPayment":313.3636546143113,"estimatedApr":10.081642376496596,"effectiveAnnualRate":10.560785961866582,"totalFinanceCost":1581.0915661152067}Currency ±$0.01; rates ±0.000001 percentage points
apr-effective-interest-calculatorFixed-payment loan with no fees{"amount":10000,"nominalRate":8,"termMonths":36,"fees":0,"financeFees":false}{"estimatedApr":8.000000000000705,"effectiveAnnualRate":8.299950680751845,"totalFinanceCost":1281.0915661152067}Currency ±$0.01; rates ±0.000001 percentage points
inflation-impact-calculatorConstant compound inflation scenario{"amount":1000,"inflationRate":3,"years":10}{"futureCost":1343.916379344122,"purchasingPower":744.0939148967249}Currency ±$0.01
inflation-impact-calculatorZero-inflation identity{"amount":500,"inflationRate":0,"years":20}{"futureCost":500,"purchasingPower":500}Exact
bmr-tdee-calculatorMifflin–St Jeor adult equation{"sex":"male","age":30,"weightKg":80,"heightCm":180,"activity":1.2}{"bmr":1780,"tdee":2136}±0.01 kcal/day
bmr-tdee-calculatorMifflin–St Jeor adult equation{"sex":"female","age":30,"weightKg":60,"heightCm":165,"activity":1.55}{"bmr":1320.25,"tdee":2046.3875}±0.01 kcal/day
break-even-units-calculatorWhole-unit contribution break-even{"fixedCosts":10000,"pricePerUnit":50,"variableCostPerUnit":30,"targetProfit":0}{"contributionMargin":20,"breakEvenUnits":500,"requiredRevenue":25000}Currency ±$0.01; units exact
break-even-units-calculatorWhole units required for target profit{"fixedCosts":10000,"pricePerUnit":50,"variableCostPerUnit":30,"targetProfit":5000}{"contributionMargin":20,"breakEvenUnits":750,"requiredRevenue":37500}Currency ±$0.01; units exact
cash-flow-runway-calculatorConstant monthly cash burn{"startingCash":10000,"monthlyRevenue":2000,"monthlyExpenses":3000,"revenueGrowthPct":0,"expenseGrowthPct":0,"maxMonths":24}{"depletionMonth":10,"endingCash":0}Month exact; currency ±$0.01
cash-flow-runway-calculatorRevenue equals expenses{"startingCash":10000,"monthlyRevenue":3000,"monthlyExpenses":3000,"revenueGrowthPct":0,"expenseGrowthPct":0,"maxMonths":12}{"depletionMonth":null,"breakEvenMonth":1,"endingCash":10000}Exact
price-increase-impact-calculatorContribution after price and volume change{"currentPrice":50,"newPrice":60,"currentUnits":1000,"volumeChangePct":-10,"variableCost":30}{"currentContribution":20000,"newContribution":27000,"contributionDelta":7000}Currency ±$0.01
price-increase-impact-calculatorNo price or volume change{"currentPrice":50,"newPrice":50,"currentUnits":100,"volumeChangePct":0,"variableCost":20}{"contributionDelta":0,"allowableDemandLossPct":0}Exact
macro-planning-calculator4-4-9 macro allocation arithmetic{"adultConfirmed":true,"dailyCalories":2400,"weightKg":80,"proteinPerKg":1.6,"fatPercent":30}{"proteinGrams":128,"fatGrams":80,"carbGrams":292}±0.01 gram
macro-planning-calculator4-4-9 macro allocation arithmetic{"adultConfirmed":true,"dailyCalories":1800,"weightKg":70,"proteinPerKg":1,"fatPercent":30}{"proteinGrams":70,"fatGrams":60,"carbGrams":245}±0.01 gram
customer-lifetime-value-calculatorConstant-churn gross-contribution LTV{"averageOrderValue":50,"purchasesPerYear":4,"grossMarginPct":60,"annualChurnPct":20,"targetLtvCacRatio":3}{"annualGrossContribution":120,"lifetimeValue":600,"maxPlanningCac":200}Currency ±$0.01
customer-lifetime-value-calculatorConstant-churn gross-contribution LTV{"averageOrderValue":100,"purchasesPerYear":1,"grossMarginPct":100,"annualChurnPct":50,"targetLtvCacRatio":2}{"customerLifetimeYears":2,"lifetimeValue":200,"maxPlanningCac":100}±0.01
subscription-churn-impact-calculatorConstant monthly churn model{"startingCustomers":1000,"monthlyChurnPct":5,"newCustomersPerMonth":0,"arpu":20,"months":12}{"endingCustomers":540.3600876626365,"totalChurned":459.6399123373635}±0.01 customer
subscription-churn-impact-calculatorConstant monthly churn and replacement{"startingCustomers":1000,"monthlyChurnPct":5,"newCustomersPerMonth":50,"arpu":20,"months":12}{"endingCustomers":1000,"finalMonthlyRevenue":20000,"requiredNewCustomers":50}±0.01
inventory-reorder-point-calculatorLead-time demand plus safety stock{"averageDailySales":10,"leadTimeDays":7,"safetyStockUnits":20,"currentStockUnits":100}{"leadTimeDemand":70,"reorderPoint":90,"orderNow":false}±0.01 unit
inventory-reorder-point-calculatorLead-time demand plus safety stock{"averageDailySales":5,"leadTimeDays":14,"safetyStockUnits":30,"currentStockUnits":80}{"leadTimeDemand":70,"reorderPoint":100,"orderNow":true}±0.01 unit

Why sequential discounts compound on the shrinking price

Percentage discounts multiply, they do not add. A 20% then 10% discount on $200 is not 30% off: 200 x 0.80 = 160, then 160 x 0.90 = 144, so the effective cut is 28% ($56), not 30% ($60). The calculator mirrors checkout order: percentages first, then the fixed coupon on the discounted price. With the $5 coupon the pre-tax total is 144 - 5 = $139, total discount $61, and 8% tax brings checkout to 139 x 1.08 = $150.12.

The zero floor matters for edge deals: a $25 item with a $40 coupon produces 25 - 40 = -15, clamped to $0 pre-tax and $0 checkout, with discountAmount capped at the original $25. No checkout ever owes you money. Because each step feeds the next, entering percentages in a different order yields the same final price (multiplication commutes) but a different discountAmount breakdown, which matters for receipt reconciliation.

Where these formulas drift from real bills

The electricity model charges every watt at one tariff, so it overstates cost for tiered utility plans. A 1,500 W heater run 0.5 h/day for 30 days uses 22.5 kWh ($5.63 at $0.25/kWh), but on a plan where the first 300 kWh are $0.10 and the rest $0.30, most of that usage sits in the cheap tier and the true cost is closer to $2.25.

The fuel calculator also assumes perfect fill-ups: 120 miles at 30 MPG doubled for a round trip and repeated twice gives 480 miles, 16 gallons, $56 at $3.50, or $14 across 4 travelers. Real driving adds cold starts, idling, and roof drag, typically pushing real consumption 5 to 15% above the sticker figure, so treat the output as a floor. The date tool counts both boundary days in inclusive mode (2024-02-28 to 2024-03-01 inclusive is 3 days), while the DTI tool's remaining capacity of $480 on $8,000 income ignores escrow, insurance, and minimum-card-payment swings that can move back-end DTI several points month to month.