What is a percentage?
“Per cent” means “per hundred”. A percentage expresses a number as a fraction of 100, so 15% means 15 out of every 100, or 0.15 as a decimal. Percentages make it easy to compare amounts of different sizes: a 15% tip, a 15% exam deduction and a 15% sales increase all mean the same proportion, whatever the underlying numbers are.
Almost every everyday percentage question is one of three types, and this page has a calculator for each. They all come from one relationship: part = percentage × whole ÷ 100. Whichever two values you know, you can find the third.
How to use the percentage calculator
- Pick the card that matches your question: X% of Y, X is what percent of Y, or X is Y% of what.
- Type your two numbers. Decimals, negatives and thousands separators are all fine.
- Read the answer and the full sentence underneath, then copy it with one click.
Formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 240 = 36 |
| X is what % of Y? | X ÷ Y × 100 | 36 is 15% of 240 |
| X is Y% of what? | X ÷ (Y ÷ 100) | 36 is 15% of 240 |
To find a percentage increase or decrease between two numbers, use the percentage change calculator instead.
Everyday examples
- Exam score: 42 marks out of 60 is 42 ÷ 60 × 100 = 70%.
- Tax: 8% of a 125 purchase is 0.08 × 125 = 10.
- Finding the original: if 18 people are 12% of a group, the group has 18 ÷ 0.12 = 150 people.
- Mental shortcut: X% of Y always equals Y% of X, so 4% of 75 is the same as 75% of 4, which is 3.
More worked examples
Test score: 18 correct answers out of 24 is 18 ÷ 24 × 100 = 75%.
VAT: 20% UK VAT on a £45 item is 0.20 × 45 = £9, so the price including VAT is £54.
Common mistakes to avoid
- Swapping the part and the whole. “X is what percent of Y” divides X by Y, not Y by X.
- Removing a percentage by subtracting it. A price including 20% tax divided by 1.2 gives the pre-tax price; subtracting 20% does not.
- Using this for changes over time. For increases and decreases, use the percentage change calculator.
Sources and methodology
The calculations on this page follow these published standards and references. The code is covered by automated tests against known values.
- Standard percentage arithmetic