How Our Calculators Work
Every calculator on this site runs on standard, published mathematics — and we believe you shouldn't have to take that on trust. This page documents the exact formula each tool uses, the rounding rules we apply, the assumptions we make, and test cases you can verify yourself against authoritative examples. If you find any discrepancy, report it and we will investigate and correct it publicly.
Last reviewed: June 2026 · See also our editorial policy
General Principles
- Everything runs in your browser. Calculations execute locally in JavaScript; your inputs are never transmitted to or stored on our servers. The only exception is the currency converter, which fetches exchange rates (but not your amounts) from our server.
- Precision and rounding. We calculate at full 64-bit floating-point precision and round only for display — money to 2 decimal places, percentages to 2 decimal places unless noted. Intermediate steps are never rounded, which is why our results can differ by a cent from tools that round early.
- Estimates, not advice. Financial results are mathematical estimates. Lenders and providers add fees, use day-count conventions, or round differently. Always confirm with the provider before making a decision. Nothing on this site is financial, medical, or legal advice.
- Corrections. Verified errors are fixed promptly and noted on the affected page. The "Last reviewed" date on each calculator reflects the most recent accuracy check.
Loan Calculator
Formula
Monthly payment uses the standard amortization (annuity) formula with monthly compounding:
M = P × [ r(1+r)ⁿ ] ÷ [ (1+r)ⁿ − 1 ]
where r = annual rate ÷ 12 ÷ 100, n = total monthly payments
where r = annual rate ÷ 12 ÷ 100, n = total monthly payments
Assumptions
- Fixed interest rate for the whole term; payments made monthly in arrears.
- Interest compounds monthly (annual rate ÷ 12). Some lenders use daily interest accrual, which produces slightly different figures.
- No arrangement fees, insurance, or early-repayment charges are included.
- The amortization schedule allocates each payment to interest first (balance × r), remainder to principal.
Verified test cases
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$250,000 at 6.5% over 30 years → $1,580.17/month — total paid $568,861.22, total interest $318,861.22. Matches the standard textbook annuity result.✓
$20,000 at 5% over 5 years → $377.42/month — total paid $22,645.48, total interest $2,645.48.Savings Calculator
Formula
Lump sum: FV = P × (1 + r/m)^(m×t)
Regular deposits: FV = d × [ ((1 + r/m)^(m×t) − 1) ÷ (r/m) ]
Regular deposits: FV = d × [ ((1 + r/m)^(m×t) − 1) ÷ (r/m) ]
where r = annual rate as a decimal, m = compounding periods per year, t = years, d = deposit per period (made at the end of each period).
Assumptions
- A constant interest rate for the whole horizon — real savings rates change.
- Deposits at the end of each period (ordinary annuity). Depositing at the start ("annuity due") yields slightly more.
- No tax or withdrawal effects are modelled.
Verified test cases
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$1,000 lump sum at 5%, compounded monthly, 10 years → $1,647.01✓
$100/month at 5%, 10 years → $15,528.23 ($12,000 deposited + $3,528.23 interest)Percentage Calculator
Formulas
X% of Y = Y × X ÷ 100
Increase by X% = Y × (1 + X/100)
Decrease by X% = Y × (1 − X/100)
X as % of Y = (X ÷ Y) × 100
% change = ((new − old) ÷ old) × 100
Increase by X% = Y × (1 + X/100)
Decrease by X% = Y × (1 − X/100)
X as % of Y = (X ÷ Y) × 100
% change = ((new − old) ÷ old) × 100
Notes
- Percentage change uses the original value as the base — the standard convention. A change from 100 to 120 is +20%; from 120 back to 100 is −16.67%, not −20%.
- Results display to 2 decimal places; computation is unrounded.
Verified test cases
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15% of 80 = 12 · change 200 → 230 = +15% · 43 of 60 = 71.67%VAT Calculator
Formulas
Add VAT: gross = net × (1 + rate/100)
Remove VAT: net = gross ÷ (1 + rate/100)
Remove VAT: net = gross ÷ (1 + rate/100)
Notes
- Removing VAT divides by the multiplier — it does not subtract the percentage. £120 including 20% VAT is £100 net, not £96. This matches HMRC guidance on VAT arithmetic.
- Real invoices may round per line or per total; jurisdictions differ. We display to 2 decimal places without intermediate rounding.
Verified test cases
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£100 net + 20% VAT = £120 gross · £120 gross at 20% → £100 net, £20 VATBMI Calculator
Formula
BMI = weight(kg) ÷ height(m)² (imperial: 703 × lb ÷ in²)
Notes & limitations
- Categories follow the WHO classification: under 18.5 underweight, 18.5–24.9 healthy, 25–29.9 overweight, 30+ obese.
- BMI does not distinguish muscle from fat and can misclassify athletes, older adults, and some ethnic groups (the NHS notes lower thresholds may apply for people of South Asian, Chinese, and Black African origin). It is a screening number, not a diagnosis — see a healthcare professional for assessment.
Verified test case
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70 kg at 1.75 m → BMI 22.86 (healthy range) — matches the WHO/NHS worked example convention.Discount Calculator
Sale price = original × (1 − discount/100)
Stacked: price = original × (1 − d₁/100) × (1 − d₂/100)
Stacked: price = original × (1 − d₁/100) × (1 − d₂/100)
- Stacked discounts multiply — 20% then 10% is 28% off in total, not 30%. Each discount applies to the already-reduced price.
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$100 with 20% then 10% off → $72 (28% total)Tip Calculator
Tip = bill × rate/100 · Per person = (bill + tip) ÷ people
- Tip is calculated on the amount entered. Whether to tip on pre-tax or post-tax totals is a custom that varies by country; our country guide on the tip calculator page covers the differences.
Currency Converter
Data source
- Mid-market exchange rates from exchangerate.host, with automatic fallback to Frankfurter (which publishes European Central Bank reference rates). Rates are cached for 5 minutes.
- Mid-market rates are not what you get at a bank or kiosk. Providers add a spread (typically 1–5%) and fees. Use our result as the fair-value baseline to compare offers against.
- The rate's publication date is shown alongside results.
Unit Converter
- Conversion factors follow the International System of Units (SI) and the exact legal definitions: 1 inch = 25.4 mm exactly, 1 lb = 0.45359237 kg exactly, 1 mile = 1,609.344 m exactly.
- Temperature: °F = °C × 9/5 + 32; Kelvin = °C + 273.15 (exact by definition).
- Results display to a precision appropriate to the unit; computation is unrounded.
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10 miles = 16.09344 km (exact) · 100°C = 212°F (exact)Age Calculator
- Age is computed in calendar years, months, and days using the proleptic Gregorian calendar via the browser's native
Datehandling, which accounts for leap years automatically. - A birthday on 29 February is treated as completed on 1 March in non-leap years — the convention used in most legal systems.
Found an error?
We treat accuracy reports as the highest-priority feedback we receive. If any calculator produces a result you believe is wrong, tell us with the inputs you used. We will reproduce it, fix it if confirmed, and note the correction on the affected page.