Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 20% of 150 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 30 of 120 = 25% |
| % change from X to Y | (Y − X) ÷ |X| × 100 | 80 → 100 = +25% |
| Increase Y by X% | Y × (1 + X ÷ 100) | 200 + 15% = 230 |
| Decrease Y by X% | Y × (1 − X ÷ 100) | 200 − 15% = 170 |
Everyday examples
- Tips: an 18% tip on a $64 bill is 0.18 × 64 = $11.52.
- Discounts: 25% off $80 is 80 × 0.75 = $60.
- Test scores: 42 right out of 50 is 42 ÷ 50 × 100 = 84%. See the test score calculator.
- Pay rises: going from $20 to $22 an hour is a (22 − 20) ÷ 20 = 10% raise.
A common mistake
Percentage increases and decreases aren't symmetrical. If a price rises 50% and then falls 50%, you don't end up where you started: $100 → $150 → $75. That's because the second percentage is taken from a bigger number.