How to calculate a percentage
A percentage is a number out of 100: 15% means 15 per 100, or 0.15. Every calculator on this page is built on that idea. Choose the question that matches what you want to know, type your two numbers, and the answer appears straight away with the working underneath, so you can check it or copy the method.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 200 = 30 |
| X is what percent of Y? | X ÷ Y × 100 | 30 is 15% of 200 |
| Percentage change from A to B | (B − A) ÷ A × 100 | 80 to 100 = 25% increase |
| Increase Y by X% | Y × (1 + X ÷ 100) | 200 + 15% = 230 |
| Decrease Y by X% | Y × (1 − X ÷ 100) | 200 − 15% = 170 |
| X is Y% of what? | X ÷ (Y ÷ 100) | 45 is 30% of 150 |
| Percentage difference | |A − B| ÷ ((A + B) ÷ 2) × 100 | 90 and 110 = 20% |
Percentage increase and decrease
To find how much something has grown or shrunk, subtract the old value from the new one, divide by the old value and multiply by 100. A price that rises from 80 to 100 has gone up by 20 ÷ 80 = 25%. If the answer is negative, it's a decrease: a fall from 100 to 80 is a 20% decrease, not 25%, because the starting value is different. The percentage change calculator labels the result as an increase or a decrease for you.
A rise and a fall of the same percentage don't cancel out. Increase 100 by 50% and you get 150; decrease 150 by 50% and you get 75, not 100. Each percentage is worked out from the value at that moment.
Percentage change, percentage difference and percentage points
Percentage change compares a new value with an old one, so the order matters. Percentage difference compares two values with no "before" and "after", such as two shop prices or two measurements, so it divides by their average and the order doesn't matter. Percentage points describe the gap between two percentages: an interest rate going from 4% to 5% has risen by 1 percentage point, which is a 25% increase in the rate.
Discounts, tips and quick mental maths
For a discount, the percent off calculator shows the sale price and how much you save: 25% off 80 saves 20, so you pay 60. Two tricks help without a calculator. To find 10%, move the decimal point one place left: 10% of 64 is 6.4. Then build other percentages from it: 5% is half of 10%, 20% is double, and 15% is 10% plus 5%. Percentages are also reversible: 8% of 50 is the same as 50% of 8, which is 4.
Using percentages in spreadsheets
In Excel or Google Sheets, type a percentage as =A1*15% or =A1*0.15. For percentage change use =(B1-A1)/A1 and format the cell as a percentage. Because the formulas on this page are the standard ones, you can check a spreadsheet's results here.
Frequently asked questions
How do I calculate a percentage 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 calculate a percentage increase?
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 = a 25% increase.
How do I work out what percent one number is of another?
Divide the first number by the second and multiply by 100. For example, 30 out of 200 is 30 ÷ 200 × 100 = 15%.
What is the difference between percentage change and percentage difference?
Percentage change measures a change from an old value to a new one, so it divides by the old value. Percentage difference compares two values on equal terms, so it divides by their average.
How do I calculate 20% off a price?
Multiply the price by 0.8, or find 20% and subtract it. 20% off 50 is 50 × 0.8 = 40, a saving of 10.
Why don't a 50% increase and a 50% decrease cancel out?
Each percentage is taken from a different starting value. 100 increased by 50% is 150, and 150 decreased by 50% is 75.
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