Percentage Calculator

A percentage is a ratio written as a fraction of 100 — “per cent” literally means “per hundred.” Every mode in this calculator is built from that one idea, so the arithmetic is exact and there are no lookup tables or approximations. Here is the formula behind each of the six modes:

1. What is X% of Y? — the part is the whole scaled by the fraction: result = Y × (X ÷ 100).
2. X is what % of Y? — divide the part by the whole, then scale to 100: result = (X ÷ Y) × 100. The whole (Y) cannot be zero.
3. X is Y% of what? — the reverse of mode 1, recovering the whole from a part: whole = (X × 100) ÷ Y. The percentage (Y) cannot be zero.
4. % change from A to B — the change relative to the original value: change% = ((B − A) ÷ A) × 100. A positive result is an increase, negative is a decrease, and A cannot be zero.
5. Increase / decrease A by B% — add or take off a percentage of the number: result = A × (1 ± B ÷ 100). This is the mode for VAT, markups, tips and discounts.
6. % difference between A and B — the gap relative to the average of the two values: diff% = |A − B| ÷ ((A + B) ÷ 2) × 100. Because it uses the mean, the order of A and B does not matter.

The distinction between mode 4 and mode 6 is the one people most often get wrong. Percentage changeis directional and anchored to a reference point — the original value — which is why it is the right tool for “prices rose 20%.” Percentage difference is symmetric and anchored to the average of the two numbers, which is why scientists use it to compare two measurements where neither is the “before.” The same pair, 80 and 100, gives a 25% change but a 22.22% difference. The calculator keeps them as separate modes so you never mix them up.

Rounding is applied only when the answer is displayed, at the decimal precision you choose (0–4 places). The plain-English sentence and the step-by-step working use the same rounded figures, so what you read and what you copy always agree. Division by zero and non-numeric input are caught before any calculation runs, so you get a clear message instead of NaN or a blank box.

• Encyclopædia Britannica — “percentage” (definition: a ratio expressed as a fraction of 100)
• NIST / standard arithmetic — percentage change vs. percentage difference conventions
• Inland Revenue Department of Sri Lanka — standard VAT rate 18% (used only for the add-VAT example)

The formulas on this page are standard arithmetic and were last reviewed on 2026-07-08. The Sri Lanka VAT figure is used purely to make the add-VAT example concrete — no tax rate is built into the tool itself, so it stays correct for any country or unit.