How to Calculate a Percentage
A percentage is simply a number out of 100 — the word comes from the Latin per centum, meaning per hundred. 20% means 20 out of every 100. Once you know the four formulas below, you can work out any percentage by hand, and the free calculators on the home page will check your answer in seconds.
How to calculate a percentage — step by step
Find X% of a number
Multiply the number by the percentage and divide by 100. Formula: (percentage / 100) x number. Example: 20% of 150 = (20 / 100) x 150 = 0.20 x 150 = 30.
Find what percent one number is of another
Divide the first number by the second and multiply by 100. Formula: (part / whole) x 100. Example: 45 is what percent of 150? (45 / 150) x 100 = 0.30 x 100 = 30%.
Find a percentage increase or decrease
Subtract the old number from the new number, divide by the old number and multiply by 100. Formula: ((new - old) / old) x 100. Example: a price rises from 150 to 180: (180 - 150) / 150 x 100 = 30 / 150 x 100 = +20%. If the result is negative, it is a decrease.
Increase or decrease a number by a percentage
To increase: new = old x (1 + percentage / 100). Example: increase 150 by 20% = 150 x 1.20 = 180. To decrease: new = old x (1 - percentage / 100). Example: decrease 150 by 20% = 150 x 0.80 = 120.
Find the whole from a part (reverse percentage)
Divide the part by the percentage and multiply by 100. Formula: (part / percentage) x 100. Example: 30 is 20% of what number? (30 / 20) x 100 = 150.
Tell percent and percentage points apart
A percentage point is the simple difference between two percentages. If a rate rises from 20% to 25%, that is a rise of 5 percentage points — but a relative increase of 25% (5 / 20 x 100). The two numbers answer different questions, so do not mix them up.
Percentage formulas at a glance
| What you want | Formula | Example |
|---|---|---|
| X% of a number | (X / 100) x number | 20% of 150 = 30 |
| What % is X of Y? | (X / Y) x 100 | 45 is 30% of 150 |
| Percentage change | ((new - old) / old) x 100 | 150 to 180 = +20% |
| Increase by X% | old x (1 + X / 100) | 150 + 20% = 180 |
| Decrease by X% | old x (1 - X / 100) | 150 - 20% = 120 |
| Reverse percentage | (part / X) x 100 | 30 is 20% of 150 |
Five tips for working with percentages
- Turn the percent into a decimal first: 20% is 0.20, 5% is 0.05, 150% is 1.50. Multiply by the decimal instead of dividing by 100 — it is the same maths, one step shorter.
- Use 10% as a shortcut: 10% of any number is the number divided by 10. 20% is twice that, 5% is half of it, 15% is 10% plus 5%. So 20% of 150 is 15 + 15 = 30.
- Check a discount backwards: If a shop says 120 after a 20% discount, the original price was 120 / 0.80 = 150. That is a reverse percentage — the calculators above do it for you.
- Watch the base number: A 20% rise followed by a 20% fall does not bring you back to the start: 150 + 20% = 180, then 180 - 20% = 144, not 150 — because the second 20% is taken from 180, not 150.
- Round only at the end: Keep full decimals while you work and round only the final answer. Rounding in the middle can move the answer by a whole unit on large numbers.
Frequently asked questions
What is the formula for percentage?
The basic formula is (part / whole) x 100. To find X% of a number, use (X / 100) x number. To find a percentage change, use ((new - old) / old) x 100.
How do I calculate 20% of 150?
Multiply 150 by 20 and divide by 100: 150 x 20 / 100 = 30. Or use the shortcut: 10% of 150 is 15, so 20% is 15 + 15 = 30.
How do I calculate a percentage increase?
Subtract the old number from the new number, divide by the old number and multiply by 100. For 150 to 180: (180 - 150) / 150 x 100 = +20%.
What is the difference between percent and percentage points?
A percentage point is the simple difference between two percentages: 20% to 25% is 5 percentage points. The relative increase is 5 / 20 x 100 = 25%.
How do I find the original number before a percentage was taken?
Use a reverse percentage: divide the part by the percentage and multiply by 100. If 30 is 20% of a number, the number is (30 / 20) x 100 = 150.