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How to calculate a percentage
A percentage is a number out of 100. To find a percentage of a number, multiply the number by the percentage and divide by 100.
X is what % of Y = X ÷ Y × 100
Example: 15% of 250 is 15 ÷ 100 × 250 = 37.5.
Percentage increase and decrease
Percentage change shows how much a value went up or down compared with where it started. Subtract the old value from the new value, divide by the old value, then multiply by 100.
Example: a price that goes from 80 to 100 rose by (100 − 80) ÷ 80 × 100 = 25%. Going back from 100 to 80 is a 20% decrease, not 25%, because the starting value is different.
Adding or subtracting a percentage
To add X% to a number, multiply it by (1 + X ÷ 100). To take X% off, multiply by (1 − X ÷ 100). This is how discounts, markups and tips work.
| Task | Formula | Example |
|---|---|---|
| 10% discount | price × 0.90 | 200 → 180 |
| 15% tip | bill × 1.15 | 60 → 69 |
| 25% markup | cost × 1.25 | 40 → 50 |
Percentage points vs percent
When a rate moves from 4% to 5%, it has risen by one percentage point, but by 25 percent, because 1 is a quarter of 4. News reports about interest rates, election results and unemployment often mix these up. Use the "Percentage change" box above to see the relative change, and simple subtraction for the change in points.
Tips for everyday percentages
- 10% is easy: move the decimal point one place to the left. 10% of 340 is 34, so 5% is half of that, 17.
- Percentages are reversible: 8% of 50 is the same as 50% of 8, which is 4.
- Stacked discounts multiply: 20% off and then another 10% off is 0.8 × 0.9 = 0.72, a 28% discount, not 30%.
- Check the base: before comparing two percentages, make sure they are taken from the same starting number.
Frequently asked questions
How do I calculate 20% of a number?
Multiply the number by 20 and divide by 100, or simply multiply by 0.2. For example, 20% of 150 is 30.
How do I work out a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. Going from 50 to 65 is a 30% increase.
Why is a 50% drop not undone by a 50% rise?
Each percentage is taken from a different starting value. 100 minus 50% is 50, but 50 plus 50% is only 75. To get back to 100 you need a 100% rise.
How do I remove a percentage that was already added?
Divide the total by (1 + rate ÷ 100). A price of 115 that includes 15% is 115 ÷ 1.15 = 100 before the increase.