Percentage formulas
| Question |
Formula |
Example |
| What is X% of Y? |
Y × X ÷ 100 |
20% of 150 = 30 |
| X is what percent of Y? |
X ÷ Y × 100 |
30 of 150 = 20% |
| Percent change from X to Y |
(Y − X) ÷ |X| × 100 |
80 to 100 = +25% |
| Increase X by Y% |
X × (1 + Y ÷ 100) |
200 + 15% = 230 |
| Decrease X by Y% |
X × (1 − Y ÷ 100) |
200 − 15% = 170 |
Percent versus percentage points
If an interest rate rises from 4% to 5%, it has gone up by one percentage point, but by 25 percent. Mixing the two up is a common mistake.
A useful trick
X% of Y always equals Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 80 is 80 × 15 ÷ 100 = 12.
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value and multiply by 100.
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100. For example, 45 is 45 ÷ 60 × 100 = 75% of 60.
How do I reverse a percentage increase?
Divide by 1 plus the percentage as a decimal. A price of 120 after a 20% rise was 120 ÷ 1.2 = 100.
