Percentage Calculator

Guide: Percentage Calculator

How percentages work

A percent is a fraction of 100. "15%" means 15 per hundred, or 0.15. Almost every percentage problem is one of three questions about a part, a whole and a rate, and this calculator solves each one live as you type.

The formulas

• X% of Y: result = (X ÷ 100) × Y
• X is what percent of Y: percent = (X ÷ Y) × 100
• X is Y% of what number: whole = X ÷ (Y ÷ 100)
• Percent change: (new − old) ÷ |old| × 100
• Increase or decrease by a percent: new = old × (1 ± percent ÷ 100)

Worked examples

A jacket costs 80 and is marked down to 60. The change is (60 − 80) ÷ 80 × 100 = −25%, a 25% discount. A 15% tip on 48 is 0.15 × 48 = 7.20. If 18 students are 60% of a class, the class has 18 ÷ 0.60 = 30 students.

Common mistakes

Percent change always uses the old value as its base, so the same gap looks bigger or smaller depending on direction. Percentages of different bases cannot simply be added or averaged, and a change in percentage points is not a percent change. Type numbers with a dot or a comma as the decimal separator; every result is formatted for your language settings and can be copied with one click.

FAQ

How do I calculate X% of a number?

Divide the percentage by 100 and multiply by the number. For example, 15% of 200 is 0.15 × 200 = 30.

How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100. 30 is (30 ÷ 200) × 100 = 15% of 200.

How is percent change calculated?

Subtract the old value from the new value, divide by the old value and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%.

Why is a 20% drop not undone by a 20% rise?

The second percentage applies to a different base. 100 minus 20% is 80, and 80 plus 20% is only 96. You need a 25% rise to get back to 100.

Is percent change the same as percentage points?

No. Going from 10% to 12% is a 2 percentage-point change but a 20% relative increase.