What is a percentage?
A percentage is a number expressed as a share of 100. So 20% means 20 out of every 100, which is the same as the fraction 20/100 or the decimal 0.2.
Percentage formulas
Percent of a number: result = (percent ÷ 100) × number
What percent: percent = (part ÷ whole) × 100
Percent change: change = (new − old) ÷ |old| × 100
How to use this calculator
- Choose what to find. Pick percent of a number, what percent, or percent change.
- Enter your two numbers. Negative numbers and decimals are fine.
- Read your result. The answer and a plain-English explanation update instantly.
Worked examples
Percent of a number: 20% of 150 is 0.2 × 150 = 30. A 20% tip on a $150 bill is $30.
What percent: 30 is what percent of 150? 30 ÷ 150 × 100 = 20%.
Percent change: going from 80 to 100 is a change of 20. 20 ÷ 80 × 100 = 25% increase.
Common percentages as fractions
| Percent | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.1 | 1/10 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1 | 1/1 |
Percent change isn’t reversible
A rise followed by the same percentage fall doesn’t bring you back to where you started. If 100 goes up 25% it becomes 125, but 125 has to fall 20% to get back to 100, because the second percentage is taken from a bigger number.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. For example, 20% of 150 is 0.2 × 150 = 30.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100. Going from 80 to 100 is 20 ÷ 80 × 100 = a 25% increase.
Why can’t I calculate percent change from zero?
Percent change divides by the starting value, and you can’t divide by zero. The change from zero has no defined percentage.
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