Percentage Calculator
Find a percent of a value, what percent one number is of another, or a percent change.
To find a percent change, use (new − old) ÷ old × 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%, a 25% increase. For a percent of a value, multiply: 20% of 80 is 0.20 × 80 = 16.
Three percentage questions, one idea
Every percentage problem is really a fraction out of 100. “X% of Y” scales a value down to a part. “X is what % of Y” turns a part-and-whole into a proportion. Percent change compares a new value to an old one. The same arithmetic — divide, then multiply by 100 — sits underneath all three.
a negative result is a decrease; “% of” is (percent ÷ 100) × value
Worked example
A price rises from 80 to 100. What is the percent change?
- 1 Find the difference. new − old = 100 − 80 = 20.
- 2 Divide by the original value. 20 ÷ 80 = 0.25.
- 3 Multiply by 100. 0.25 × 100 = 25% — a 25% increase. Note the reverse drop from 100 back to 80 is −20%, not −25%.
Common percentages as fractions and decimals
Handy mental anchors — a percent is just a fraction out of 100.
| Percent | Fraction | Decimal |
|---|---|---|
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 25% | 1/4 | 0.25 |
| 33.3% | 1/3 | 0.333… |
| 50% | 1/2 | 0.5 |
| 75% | 3/4 | 0.75 |
Percent change vs. percentage points
This is the classic trap. Going from 20% to 25% is a 5 percentage-point rise, but a 25% relative increase (5 ÷ 20 × 100). News headlines mix these up constantly. This tool always reports the relative change.
Increases and decreases do not cancel. A 50% rise followed by a 50% fall does not return you to the start: 100 → 150 → 75. To fully undo a 50% increase you need a 33.3% decrease.
The base matters. “20% off” means 20% of the original price, so 20% of 80 is 16, leaving 64. Always check which number the percent is taken of. To see a percent as a fraction or decimal, every percent is just that value over 100.