The five formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 240 = 36 |
| X is what % of Y? | X ÷ Y × 100 | 36 of 240 = 15% |
| Change from X to Y | (Y − X) ÷ X × 100 | 80 to 100 = +25% |
| Y increased by X% | Y × (1 + X ÷ 100) | 240 + 15% = 276 |
| Y is X% of what? | Y ÷ X × 100 | 36 is 15% of 240 |
Two classic traps
Up and down are not symmetric. A price that falls 20% and then rises 20% ends 4% lower, because the rise is 20% of a smaller number: 100 → 80 → 96. To get back to 100 after a 20% fall you need a 25% rise.
Percent versus percentage points. If a mortgage rate goes from 6% to 7%, it rose by 1 percentage point, but by 16.7 percent. News reports mix the two up often; lenders and central banks talk in points.
Percentages in money
Sales tax, tips, discounts, raises, interest and inflation are all percentages. Two stacked discounts of 20% and 10% give 28% off, not 30%. A raise of 3% when inflation is 3.4% is a real pay cut. For the money versions of these calculations see the tip, salary and inflation calculators.