Methodology
How each tool computes its result, and the sources behind the numbers.
Reviewed 2 June 2026
Why this page exists
Every result HandyConvert returns is built on a stated formula and an independently verifiable conversion factor. This page documents both. If you ever want to confirm a number by hand or against another reference, the math you need is here, and the source we used is linked. Nothing is opaque, and nothing depends on the visitor trusting us — the trust is in the citations.
Length, area, volume, mass, temperature
All length, area, volume, and mass conversions use the conversion factors published by the United States National Institute of Standards and Technology (NIST) in Special Publication 811: Guide for the Use of the International System of Units. The two factors used most often are exact by definition: 1 inch = 25.4 millimetres, and 1 pound (avoirdupois) = 0.453 592 37 kilograms. Temperature uses the standard Celsius–Fahrenheit relation: °F = °C × 9 ⁄ 5 + 32, and Kelvin: K = °C + 273.15. Source: NIST SP 811 — https://physics.nist.gov/cuu/pdf/sp811.pdf.
Inch fraction calculator
Inputs are parsed into integer numerator and denominator pairs. Addition and subtraction use the cross-product over a common denominator: a ⁄ b + c ⁄ d = (a · d + b · c) ⁄ (b · d). Multiplication is (a · c) ⁄ (b · d). Division is (a · d) ⁄ (b · c), with a guard for divide-by-zero. The result is simplified by dividing the numerator and denominator by their greatest common divisor, computed with the Euclidean algorithm. Decimal inputs are rounded to the nearest 1 ⁄ 64 inch before being treated as a fraction — 64ths are the smallest practical division on a standard carpentry tape measure. The millimetres readout multiplies the decimal value by 25.4 exactly (NIST SP 811).
Recipe scaler
Each ingredient is multiplied by a single scale factor derived from the target servings divided by the original servings (or from a user-supplied factor). Unicode fractions (½, ⅓, ¾) and mixed numbers (1 1 ⁄ 2) are parsed into rationals; the scaled result is formatted back into the closest readable fraction, rounded to 1 ⁄ 8 or 1 ⁄ 16 depending on whether the ingredient reads more naturally in coarse or fine units (eggs round to whole, flour to 1 ⁄ 8 cup, salt to 1 ⁄ 4 teaspoon). Connector words (of, d’, du, des) are preserved so the line still reads as English or French prose.
Pan substitution calculator
Substitution is by surface area when the recipe is a shallow batter (cakes, brownies), and by volume when the recipe is a deep bake (loaves, casseroles). A round pan of diameter d has surface area π × (d ⁄ 2)². A rectangular pan of L × W has area L × W. When swapping pan shapes the calculator finds the substitute whose surface area matches within a tolerance band, then applies a depth correction so the total batter volume stays the same — important because batter that is too deep takes longer to bake and sinks in the middle. King Arthur Baking’s pan substitution guide is a useful cross-check: https://www.kingarthurbaking.com/learn/guides/pan-substitutions.
Ingredient density converter
Volume-to-weight conversions for 35 common baking and cooking ingredients use a built-in density table whose values are taken from two primary sources: the United States Department of Agriculture FoodData Central (https://fdc.nal.usda.gov), and King Arthur Baking’s ingredient weight chart (https://www.kingarthurbaking.com/learn/ingredient-weight-chart). Where the two sources disagree, we use King Arthur’s figure for flour, sugar, and butter (the baking-relevant ingredients) and USDA for everything else. Volume unit conversions use the US customary definitions: 1 US cup = 236.588 mL, 1 US tablespoon = 14.787 mL, 1 US teaspoon = 4.929 mL. Ounces-to-grams uses 1 oz = 28.3495 g.
Cocktail batch scaler
Each cocktail ingredient is multiplied by the batch factor (target servings divided by single-serve volume). Dilution water is added to mimic the melting ice of a standard serve: 20 % by volume for stirred cocktails, 25 % for shaken cocktails — figures consistent with Dave Arnold’s measured-ice-dilution research published in Liquid Intelligence (2014). Final ABV is computed as the sum of each ingredient’s volume × (proof ⁄ 100), divided by total liquid volume including dilution. Vermouth, liqueurs, and bitters contribute proportionally to their stated proof.
Canadian mortgage calculator
Canadian mortgage interest is compounded semi-annually rather than monthly, as required by section 6 of the federal Interest Act (R.S.C. 1985, c. I-15). The effective monthly rate r_m used in the payment formula is derived from the stated nominal annual rate r by: r_m = (1 + r ⁄ 2)^(1 ⁄ 6) − 1. The monthly payment P for principal A over n monthly payments is then P = A × r_m × (1 + r_m)^n ⁄ ((1 + r_m)^n − 1). High-ratio mortgages (less than 20 % down) are insured by the Canada Mortgage and Housing Corporation (CMHC); insurance premiums are calculated from the CMHC published premiums table for loan-to-value ratios of 65 %, 75 %, 80 %, 85 %, 90 %, and 95 %. Sources: Interest Act of Canada s. 6 — https://laws-lois.justice.gc.ca/eng/acts/i-15/section-6.html; CMHC — https://www.cmhc-schl.gc.ca/professionals/mortgage-loan-insurance/calculating-mortgage-loan-insurance-premium.
US mortgage calculator
United States mortgages use monthly compounding, not the Canadian semi-annual convention. The effective monthly rate is r_m = r ⁄ 12, and the payment formula is the same as above with that monthly rate. Private mortgage insurance (PMI) is required for conventional loans with less than 20 % down, and is approximated at 0.5 % to 1.5 % of the loan amount annually depending on credit profile and loan-to-value. FHA loans use a different premium structure documented in the HUD Mortgagee Letter series — https://www.hud.gov/program_offices/housing/sfh/lender/origination/mortgagee_letters. Reference: Consumer Financial Protection Bureau (CFPB) — https://www.consumerfinance.gov/owning-a-home.
Mortgage comparison
Three scenarios are computed using the formulas above. The comparison reports monthly payment, total interest paid over the amortization period, total cost (principal + interest + insurance), and equity at the end of every year. Equity at month m is the principal A minus the outstanding balance B_m, where B_m is computed by applying m months of the standard mortgage amortization recurrence: B_m = A × (1 + r_m)^m − P × ((1 + r_m)^m − 1) ⁄ r_m. All three scenarios use the same compounding convention you selected (Canadian semi-annual or US monthly), so the comparison is apples-to-apples.
Live unit converter (homepage)
The multi-sector converter on the homepage uses the same NIST SP 811 conversion factors as the individual tools. Temperature, fuel economy (L ⁄ 100 km ↔ mpg ↔ km ⁄ L), and oven gas marks each use their own dedicated handler: temperature is linear in Kelvin space, fuel economy is inverse for the mpg ↔ L ⁄ 100 km conversion (mpg = 235.214 583 ⁄ L per 100 km for US gallons; 282.480 936 ⁄ L per 100 km for Imperial gallons), and gas marks are interpolated linearly across the standard table (Gas 1 = 140 °C, Gas 2 = 150 °C, … Gas 9 = 240 °C). Beaufort wind scale uses v = 0.836 × B^(3 ⁄ 2) m ⁄ s, the WMO empirical fit.
Authoritative sources cited
National Institute of Standards and Technology (NIST) — Special Publication 811. Interest Act of Canada, R.S.C. 1985, c. I-15. Canada Mortgage and Housing Corporation (CMHC). Financial Consumer Agency of Canada (FCAC). Bank of Canada — daily rate releases. Consumer Financial Protection Bureau (CFPB). US Department of Agriculture (USDA) FoodData Central. King Arthur Baking ingredient weight chart. World Meteorological Organization (WMO) — Beaufort scale. Dave Arnold, Liquid Intelligence (W. W. Norton, 2014). HUD Mortgagee Letters. These are the references whose definitions we adopt verbatim — if a HandyConvert number disagrees with any of these sources, the source wins and we will update the tool.
Review cycle
Every formula on this page is reviewed annually, or sooner whenever an underlying standard is revised (a NIST SP 811 republication, a CMHC premium update, a change to the Interest Act, a new edition of King Arthur’s weight chart). The “Reviewed” date above this page reflects the most recent review. A public corrections log will be added at /changelog as part of the next site update so any change to a formula is publicly dated.