Methodology: formulas, methods and examples

Every calculator on this site shows its own formula, a worked example and its assumptions. This page brings those methods together in one place, with plain explanations and examples, so you can see how the numbers are produced.

How the calculators work in general

Financial calculators

Loan and mortgage payment (fixed rate)

A fixed-rate loan is repaid in equal payments. The payment covers interest on the remaining balance and gradually pays down the amount borrowed.

Formula. Let P be the loan amount, r the monthly interest rate (annual rate ÷ 12, as a decimal), and n the number of monthly payments (years × 12). The monthly payment M is:

M = P × r × (1 + r)n ÷ ((1 + r)n − 1). If the rate is 0, M = P ÷ n. Total interest = M × n − P.

Worked example (mortgage). Home price $350,000 with $70,000 down means borrowing P = $280,000. At 6.5% for 30 years, r = 0.065 ÷ 12 and n = 360. The principal-and-interest payment is about $1,769.91 per month, total paid about $637,167, and total interest about $357,167. This does not include property taxes, homeowners insurance, mortgage insurance or fees.

Compound interest

Compound interest means you earn (or owe) interest on both the original amount and the interest added before it.

Formula. For a lump sum, A = P × (1 + r/n)n×t, where P is the principal, r the annual rate (decimal), n the compounding periods per year, and t the time in years. Interest earned = A − P (before any separate contributions).

Worked example. $1,000 at 5% compounded monthly for 10 years: A = 1000 × (1 + 0.05/12)120 ≈ $1,647.01, so about $647.01 in interest.

Simple interest, tip and discount

Simple interest: I = P × r × t and A = P + I. Example: $2,000 at 4% for 3 years gives interest $240 and total $2,240.

Tip: tip = bill × (tip% ÷ 100), total = bill + tip. Example: $80 with a 18% tip is $14.40 tip, $94.40 total (before splitting).

Discount: saving = price × (discount% ÷ 100), sale price = price − saving. Example: $120 at 25% off saves $30, so you pay $90.

Fitness and health calculators

Body Mass Index (BMI)

BMI is a screening measure based on height and weight. It does not directly measure body fat.

Formula. Metric: BMI = weight(kg) ÷ height(m)2. US units: BMI = 703 × weight(lb) ÷ height(in)2.

Worked example. 65 kg and 1.70 m: BMI = 65 ÷ 1.70² ≈ 22.5, which falls in the adult “healthy weight” range (18.5–24.9). For children and teens, BMI is interpreted using age- and sex-specific percentiles (CDC reference data) rather than the adult cut-offs.

Basal Metabolic Rate (BMR) and daily calories

BMR estimates the energy your body uses at rest. Daily calorie needs are often estimated by multiplying BMR by an activity factor.

Standard resting-calorie formula. Men: BMR = 10×weight(kg) + 6.25×height(cm) − 5×age + 5. Women: BMR = 10×weight(kg) + 6.25×height(cm) − 5×age − 161.

Worked example. A 30-year-old woman, 165 cm, 68 kg: BMR = 10×68 + 6.25×165 − 5×30 − 161 = 680 + 1031.25 − 150 − 161 ≈ 1,400 kcal/day at rest. With moderate activity (factor ~1.55) that is about 2,170 kcal/day to maintain weight. These are estimates; individual needs vary.

Body fat, pace and other measures

Body fat (circumference method) estimates body fat percentage from circumference measurements (and height). It is an estimate, not a clinical measurement. Pace relates distance, time and speed: pace = time ÷ distance, speed = distance ÷ time. Example: 5 km in 25:00 is 5:00 per km (12.0 km/h).

Math calculators

Percentage. “X% of Y” is Y × (X ÷ 100). Percentage change is ((new − old) ÷ old) × 100%. Example: 15% of 200 is 30; a change from 80 to 100 is +25%.

Area. Rectangle: length × width. Circle: π × r². Triangle: ½ × base × height. Example: a circle with radius 3 m has area π×9 ≈ 28.27 m².

Quadratic equation. For ax² + bx + c = 0, the discriminant is D = b² − 4ac and the roots are (−b ± √D) ÷ (2a) when D ≥ 0. Example: x² − 3x − 10 = 0 gives D = 49, so roots (3 ± 7)/2 = 5 and −2.

Average. Mean = sum of values ÷ count. Median is the middle value when sorted; mode is the most frequent value. Example: 2, 4, 4, 9 has mean 4.75, median 4, mode 4.

Weather and environment calculators

These tools use standard public formulas to estimate “feels like” conditions from measured temperature and humidity or wind. They are estimates for general awareness, not a substitute for official weather warnings.

Wind chill (air at or below 50°F / 10°C and wind above about 3 mph) uses the U.S./Canadian formula: Wind chill (°F) = 35.74 + 0.6215T − 35.75V0.16 + 0.4275T·V0.16, with T in °F and V in mph. Example: 20°F with 15 mph wind feels like about 6°F.

Heat index combines air temperature and relative humidity (Rothfusz regression used by U.S. agencies) to estimate perceived heat. Dew point is derived from temperature and relative humidity (commonly via the Magnus formula) and indicates how much moisture is in the air.

Chemistry and science calculators

Molarity. M = moles of solute ÷ litres of solution (mol/L). If you start from mass, moles = mass ÷ molar mass. Example: 58.44 g NaCl (molar mass 58.44 g/mol) in 1.0 L gives 1.0 mol/L.

Dilution. M₁V₁ = M₂V₂ (amount of solute stays the same). Example: to make 500 mL of 1 M from a 5 M stock, V₁ = (1×500) ÷ 5 = 100 mL of stock, topped up to 500 mL.

Density. density = mass ÷ volume. Example: 200 g occupying 250 cm³ has density 0.8 g/cm³.

Half-life. Remaining amount after time t is N = N₀ × (1/2)t / t½. Example: 80 g with a 2-day half-life leaves 10 g after 6 days (three half-lives).

Construction and home calculators

These estimate materials from dimensions you enter. Always allow for waste, cutting, compaction and product-specific coverage, and confirm with your supplier or a professional for real projects.

Volume. Rectangular area/slab: volume = length × width × depth (in consistent units). Example: a slab 4 m × 3 m × 0.1 m is 1.2 m³ of concrete (before waste/ordering allowances).

Mulch, gravel, concrete. Calculated as volume over an area at a given depth, then converted to cubic yards/feet/metres and, where relevant, to bag counts or weight estimates.

Paint and tile. Paint estimates wall area minus openings and divides by coverage per coat. Tile counts tiles to cover an area and adds a waste allowance for cuts and breakage.

Other and everyday tools

Date and age. Based on calendar arithmetic (accounting for month lengths and leap years). Unit conversion multiplies by defined conversion factors (for example 1 inch = 2.54 cm exactly). GPA is a credit-weighted average of grade points. Password generator creates random characters locally in your browser. Base64 encodes/decodes text locally without sending it anywhere.

Love calculator. A fun, entertainment-only tool: it keeps the letters from the two names, combines them in a consistent order, and applies a simple, repeatable number formula to produce a playful score from 0% to 100% with a light-hearted message. It is based only on the letters entered (not on real compatibility, feelings or personal information) and runs entirely in your browser.

Where to find more detail

Open any individual calculator to see the exact formula it uses, a worked example tailored to that tool, and its specific assumptions and limits. If you believe a formula or example is wrong, the Contact page explains what to include when reporting it.

Last updated: 10 November 2026.