Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 80 = 12 |
| X is what % of Y? | X ÷ Y × 100 | 45 of 60 = 75% |
| Percentage change | (new − old) ÷ old × 100 | 80 → 92 = +15% |
| Increase by X% | Y × (1 + X ÷ 100) | 250 + 20% = 300 |
| Decrease by X% | Y × (1 − X ÷ 100) | 250 − 20% = 200 |
| Reverse a percentage increase | Y ÷ (1 + X ÷ 100) | 300 before a 20% rise = 250 |
Three percentage mistakes to avoid
Percentage change always uses the old value as the base.
Reversing a percentage. If a price is 300 after a 20% rise, the original is 300 ÷ 1.20 = 250, not 300 − 20% = 240. This is the same mistake people make when removing VAT.
Adding successive changes. A 10% rise followed by a 10% fall leaves you 1% lower (1.10 × 0.90 = 0.99), not back where you started.
Percent vs percentage points. A rate that moves from 4% to 5% has risen by 1 percentage point, which is a 25% increase in the rate.
Pro-tip: to find a percentage in your head, find 10% (move the decimal point one place left) and scale it. 15% of 80 is 10% (8) plus half of that (4), so 12.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12.
How do I work out percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 92 is (92 − 80) ÷ 80 × 100 = 15%.
How do I find the original number before a percentage was added?
Divide by 1 plus the percentage as a decimal. If 300 includes a 20% increase, the original is 300 ÷ 1.20 = 250.
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages. Moving from 4% to 5% is a rise of 1 percentage point, which is a 25% increase in the rate itself.