How our calculations work

Our approach

We use standard, published formulas rather than proprietary models, because a calculation you can verify against a textbook is worth more than one you have to trust. Where a method is an approximation - and several are - the tool says so on the page rather than in the small print.

Every formula below is covered by automated unit tests that check it against known values and against the inputs that break calculators: zero, negative, empty, and extreme numbers. A test failure blocks a release.

Loans, mortgages, and amortization

Monthly payments use the standard amortizing-loan formula, where P is the principal, r the monthly rate (annual rate ÷ 12), and n the number of payments:

M = P × [ r(1 + r)ⁿ ] / [ (1 + r)ⁿ − 1 ]

Schedules are built month by month: interest is charged on the outstanding balance, the remainder of the payment reduces principal, and the process repeats. Extra payments are applied entirely to principal in the month they are made. When the rate is zero we fall back to straight-line repayment rather than dividing by zero.

PMI is applied while the loan-to-value ratio exceeds 80%, calculated as an annual percentage of the loan amount. Property tax and insurance are entered as annual figures and divided by twelve.

Auto loans apply sales tax to the price after the trade-in credit, which matches the rule in the majority of US states. A few states tax the full price; check yours if the figure matters precisely.

Home affordability

We apply the 28/36 rule that conventional lenders use: housing costs capped at 28% of gross monthly income, and total debt including housing capped at 36%. The lower of the two limits binds, and the tool tells you which one.

Because property tax scales with the home price, and the home price depends on the loan, we solve for the loan directly rather than iterating - the tool reports which constraint is binding so you know whether to reduce debt or raise income.

Payroll and federal income tax

Our paycheck calculator uses published 2026 figures:

• Federal brackets applied progressively, so only the income within each band is taxed at that band’s rate.
• Standard deduction: $16,100 single, $32,200 married filing jointly, $24,150 head of household.
• Social Security: 6.2% up to a wage base of $184,500.
• Medicare: 1.45% with no cap, plus an additional 0.9% above $200,000 (single) or $250,000 (married filing jointly).
• 401(k): pre-tax contributions capped at the 2026 elective deferral limit of $24,500.

One detail worth stating explicitly, because it is commonly modeled wrong: 401(k) contributions reduce federal taxable wages but not FICA wages. Social Security and Medicare are charged before the deferral.

State tax: an honest caveat

State income tax is modeled as a single effective rate, not full state brackets. States with no wage income tax are exact, and flat-tax states are exact. States with progressive brackets use a representative mid-income effective rate, and the tool labels those results as estimates and lets you override the rate. Local city and county taxes are not modeled at all.

Tax figures are reviewed annually when the IRS and SSA publish new numbers.

Compound interest and retirement

Growth uses A = P × (1 + r/n)^(n×t), with contributions added at each compounding step. Retirement projections compound monthly and add contributions plus any employer match each month.

The drawdown model subtracts the required annual income and applies a real (after-inflation) return to the remainder. The 4% rule figure we display is the widely cited planning heuristic from research on historical 30-year retirements - it is a benchmark, not a guarantee, and it can fail given a poor sequence of early returns.

All projections assume a constant rate of return. Real markets do not behave that way. Run several rates rather than trusting one.

Health calculations

Body mass index

BMI = weight (kg) ÷ height (m)², categorized on the World Health Organization adult thresholds: under 18.5 underweight, 18.5-24.9 healthy, 25-29.9 overweight, 30 and above obesity. These apply to adults only; children are assessed on age and sex percentiles.

Metabolic rate and calories

We use the Mifflin-St Jeor equation, which research has repeatedly found more accurate than the older Harris-Benedict formula:

Men: (10 × kg) + (6.25 × cm) − (5 × age) + 5

Women: (10 × kg) + (6.25 × cm) − (5 × age) − 161

Total daily energy expenditure multiplies this by an activity factor from 1.2 (sedentary) to 1.9 (extremely active). Weight-change targets use the conventional figure of 3,500 calories per pound of body fat. We will not recommend a target below 1,500 calories for men or 1,200 for women, and we say so on the page when that floor is applied.

Mifflin-St Jeor typically lands within 10% of measured resting metabolism, which is a real margin of a few hundred calories. Treat the output as a starting point and adjust from observed results.

Body fat

The US Navy circumference method estimates body fat from height, neck, waist, and (for women) hip measurements. It is convenient rather than precise - typically within 3-4 percentage points of a DEXA scan.

Pregnancy dating

Naegele’s rule: due date = first day of the last menstrual period + 280 days, adjusted when the cycle length differs from 28 days. Dating from conception backs out the assumed 14-day ovulation offset. Ultrasound dating is more accurate and takes clinical precedence.

Dates and calendars

All date arithmetic is performed on UTC-normalized calendar dates, which avoids the off-by-one errors that appear near midnight or across daylight-saving boundaries.

Ages are calculated by advancing whole calendar months from the birth date rather than subtracting date components. Subtraction produces wrong answers when the birth day exceeds the length of the preceding month - 31 January to 1 March is one month and one day, and the naive method cannot produce that. Leap years follow the full rule: divisible by 4, except centuries, unless divisible by 400.

Time zones

Conversions use the IANA time zone database through your browser’s Intl API, so daylight-saving transitions are applied for the specific date you choose rather than from a fixed offset. This matters because the US and EU switch on different dates, so the gap between New York and London is four hours rather than five for about three weeks each March.

Unit conversions

Conversion factors are exact by international definition, not measured approximations. One inch is exactly 2.54 cm, one pound exactly 0.45359237 kg, and one mile exactly 1,609.344 m, all fixed by the international yard and pound agreement of 1959. Temperature uses °F = (°C × 9/5) + 32, which needs an offset as well as a ratio because the two scales have different zero points.

What we do not do

• We do not send your inputs anywhere. Every calculation runs in your browser.
• We do not pad results with false precision. Where a method has a margin of error, the page states it.
• We do not let advertisers influence results. The site is funded by Google-served advertising, and no advertiser has any input into what a calculator says.

Sources

Every figure above comes from a published authority rather than from another calculator. The tax tables are listed with their source, and the year they apply to, on the rates and sources page, which is generated from the same constants the calculators use and therefore cannot disagree with them.

• US federal tax — Internal Revenue Service, Revenue Procedure 2025-32, which sets the inflation-adjusted brackets, standard deduction and contribution limits.
• UK income tax and National Insurance — HMRC rates and thresholds, including the Scottish bands, which differ from the rest of the UK.
• Canada and Australia — the Canada Revenue Agency and the Australian Taxation Office, both linked from the rates page alongside the figures they supplied.
• BMI thresholds — World Health Organization, obesity and overweight. The adult cut-offs are the WHO classification; they are not age- or ethnicity-adjusted, which is part of why we publish the method's limits alongside the number.
• Resting metabolic rate — Mifflin MD, St Jeor ST et al., “A new predictive equation for resting energy expenditure in healthy individuals”, American Journal of Clinical Nutrition, 1990. Chosen over Harris-Benedict because it is more accurate for modern body compositions.
• Unit conversions — the 1959 International Yard and Pound Agreement, which fixes the inch at exactly 25.4 mm and the pound at exactly 0.45359237 kg. Every length and mass factor on this site derives from it, which is why they are exact rather than measured.

If one of these links has rotted, or an authority has published a figure we have not picked up, that is a correction worth sending — see below.

Found an error?

Please tell us. Send the tool, your inputs, the result you got, and the result you expected through the contact page. Corrections are the most valuable messages we receive.