How to calculate percentages (with the formulas you actually need)

Almost every everyday percentage question is one of four calculations. Here they are with the formula and a worked example — and the Percentage calculator does them for you.

1. What is X% of Y?

Formula: Y × X ÷ 100

What is 15% of 64? → 64 × 15 ÷ 100 = 9.60.

2. X is what percent of Y?

Formula: X ÷ Y × 100

42 correct answers out of 60? → 42 ÷ 60 × 100 = 70%.

3. By what percentage did it change?

Formula: (new − old) ÷ old × 100

Rent went from 750 to 800? → (800 − 750) ÷ 750 × 100 = +6.67%.

A negative result is a decrease. The Percentage increase and Percentage decrease calculators handle both directions.

4. What was the price before the percentage?

Formula: final ÷ (1 + p ÷ 100)

A price is 96 after a 20% increase — what was it before? → 96 ÷ 1.20 = 80. Not 96 − 20% = 76.80! The percentage was applied to the original, not the final value. The same logic removes VAT from a price.

Trap 1: percentages don't add up

A 30% discount followed by an extra 10% is not 40% off. The second discount applies to the reduced price: 0.70 × 0.90 = 0.63, so 37% off. The Discount calculator handles stacked discounts.

Trap 2: up and down are not symmetrical

A share price falls 50% (100 → 50) and then rises 50% (50 → 75). You're still 25% down. To get back to 100 you need a 100% rise.

Trap 3: percent vs percentage points

An interest rate going from 2% to 3% rises by 1 percentage point, which is a 50% increase. News reports often mix the two.

Comparing two numbers fairly

When neither number is “the original” — two quotes, two measurements — use the Percentage difference, which divides by their average.