Percentage calculator
Work out a percentage of a number, what percent one number is of another, and percentage change.
How it works
Three different questions get called "percentage" and they need different arithmetic, which is why they are separated here rather than crammed into one box.
What is X% of Y multiplies: 15% of 240 is 0.15 × 240 = 36. X is what percent of Y divides: 36 out of 240 is 36 ÷ 240 = 0.15, or 15%. Percentage change compares an old value to a new one: from 240 to 300 is (300 − 240) ÷ 240 = 25% up.
The one that catches people is that a percentage rise and the equivalent fall are not the same size. A price that goes up 50% and then falls 50% does not return to where it started — it ends 25% below, because the second percentage is taken from the larger number. This is also why a 50% discount followed by a further 20% off is 60% off in total, not 70%.
Worked examples
| Question | Arithmetic | Answer |
|---|---|---|
| What is 15% of 240? | 0.15 × 240 | 36 |
| 36 is what percent of 240? | 36 ÷ 240 × 100 | 15% |
| 240 to 300 is what change? | (300 − 240) ÷ 240 × 100 | +25% |
| 300 to 240 is what change? | (240 − 300) ÷ 300 × 100 | −20% |
This tool runs entirely in your browser. Nothing you enter is sent to a server, logged or stored, and the page keeps working with the network disconnected.
Common questions
- How do you calculate a percentage of a number?
- Divide the percentage by 100 and multiply. For 15% of 240: 15 ÷ 100 = 0.15, then 0.15 × 240 = 36.
- Why is a 50% rise then a 50% fall not back to the start?
- Because each percentage is taken from a different base. 100 rises by 50 to 150; 50% of 150 is 75, so it falls to 75 — a quarter below where it began.
- How do you add two discounts together?
- You multiply what remains rather than adding the discounts. 50% off then 20% off leaves 0.5 × 0.8 = 0.4 of the price, which is 60% off in total, not 70%.
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