Three common percentage sums in one place: what is X% of a number, what percentage one number is of another, and the percentage change between two numbers. Results update as you type.
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The formulas
- X% of Y = X ÷ 100 × Y. So 15% of 240 = 36.
- X as a percentage of Y = X ÷ Y × 100. So 36 out of 240 = 15%.
- Percentage change = (new − old) ÷ old × 100. From 80 to 100 is +25%.
Everyday examples
| Question | Sum | Answer |
|---|---|---|
| A 12.5% tip on a £64 bill | 12.5 ÷ 100 × 64 | £8 |
| Rent went from £950 to £1,045 | (1,045 − 950) ÷ 950 × 100 | +10% |
| Scored 42 out of 60 | 42 ÷ 60 × 100 | 70% |
| A £79 jacket, 30% off | 79 × (1 − 0.30) | £55.30 |
Percentages that trip people up
- Up then down isn’t back to the start. A price rising 20% then falling 20% ends 4% lower: 100 → 120 → 96.
- Percentage points vs percent. An interest rate moving from 4% to 5% is a rise of 1 percentage point, but 25%.
- Reverse percentages. To find the price before a 20% rise, divide by 1.2, don’t subtract 20%. The VAT calculator uses this.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 240 is 0.15 × 240 = 36.
How do I calculate percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100.
What is the difference between percent and percentage points?
Percentage points are the simple difference between two percentages; percent change is relative. 4% to 5% is +1 point but +25%.
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