How to calculate percentages
A percentage is just a number out of 100 — the word literally means "per hundred." Most everyday percentage questions come down to three relationships between a part, a whole, and a percent, plus comparing two values to measure change.
Worked example
Suppose a $80 jacket is marked up by 25%. To find the new price, first find 25% of 80: that is 80 × 25 ÷ 100 = 20. Add it back to the original: 80 + 20 = 100. Equivalently, multiply directly: 80 × (1 + 25 ÷ 100) = 80 × 1.25 = 100. If instead the jacket were discounted 25%, you would compute 80 × 0.75 = 60.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 20% of 80 = 16 |
| X is what % of Y? | X ÷ Y × 100 | 24 of 60 = 40% |
| Percentage change | (new − old) ÷ old × 100 | 80→100 = +25% |
| Increase Y by X% | Y × (1 + X ÷ 100) | 80 +25% = 100 |
| Decrease Y by X% | Y × (1 − X ÷ 100) | 80 −25% = 60 |
Frequently asked questions
- How do I calculate a percentage?
- A percentage is a fraction of 100. To turn a fraction into a percentage, divide the part by the whole and multiply by 100. For example, 30 out of 50 is 30 ÷ 50 × 100 = 60%.
- What is X% of Y?
- Multiply Y by X and divide by 100, or multiply Y by X ÷ 100. For example, 20% of 80 is 0.20 × 80 = 16.
- How do I find what percent one number is of another?
- Divide the first number by the second and multiply by 100. For example, 24 is what percent of 60? 24 ÷ 60 × 100 = 40%.
- What is the percentage change formula?
- Percentage change = (new value − old value) ÷ old value × 100. A positive result is an increase, a negative result is a decrease. For example, from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase.
- How do I add or subtract a percentage from a number?
- To add X% to a number Y, compute Y × (1 + X ÷ 100). To subtract, use Y × (1 − X ÷ 100). For example, 80 increased by 25% is 80 × 1.25 = 100; 80 decreased by 25% is 80 × 0.75 = 60.
- How do I calculate a percentage increase?
- Subtract the old value from the new value, divide by the old value, and multiply by 100. For example, going from 40 to 50 is (50 − 40) ÷ 40 × 100 = 25% increase.