How to Calculate Percentage Change (Increase and Decrease)

Percentage change answers one question: how big was the move, relative to where it started? That last part — relative to the start — is where every common mistake lives.

The formula

(New − Old) ÷ Old × 100. The result is positive for an increase, negative for a decrease. Going from 50 to 65: (65 − 50) ÷ 50 × 100 = +30%. Going from 65 back to 50: (50 − 65) ÷ 65 × 100 = −23.1% — not −30%, because the base changed.

The asymmetry trap

A 50% fall followed by a 50% rise does not return you to the start: 100 → 50 → 75. Each change applies to its own base, and the second base is smaller. This is why an investment that drops 50% needs a +100% gain just to break even — a fact worth internalizing before reading any market headline.

Reversing a change: finding the original

If a price is £66 after a 10% increase, the original was 66 ÷ 1.10 = £60 — not 66 minus 10%. Divide by (1 + rate) to undo an increase, by (1 − rate) to undo a decrease. This is the calculation VAT-inclusive prices need, and the one most people get wrong by subtracting.

Doing it fast

Anchor on 10% (move the decimal), then scale: a change of 6 on a base of 120 — 10% would be 12, so 6 is 5%. For anything that doesn’t divide neatly, the percentage change calculator gives the signed result and absolute difference live, and the general percentage formulas guide covers the other two percentage questions.