What is X% of Y?
12
80 × 15 ÷ 100 = 12
X is what percent of Y?
25%
30 ÷ 120 × 100 = 25
Percentage change from X to Y
Increase of 25%
(100 − 80) ÷ 80 × 100 = 25
Increase or decrease a number by a percentage
300
250 × 1.2 = 300
Original value before a percentage change (reverse percentage)
100
120 ÷ 1.2 = 100
How to calculate a percentage of a number
Per cent means per hundred, so 15% of a number is 15 hundredths of it: multiply by 15 and divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12. The same thing written as a decimal is 80 × 0.15.
In your head, start from 10%, which only moves the decimal point: 10% of 80 is 8, 5% is half of that, 4, so 15% is 12. Our guide to percentages in your head has more shortcuts like this one.
How to work out what percent one number is of another
Divide the part by the whole, then multiply by 100. 30 out of 120 is 30 ÷ 120 = 0.25, so 25%. A test score of 42 out of 60 is 42 ÷ 60 × 100 = 70%.
How to calculate a percentage increase or decrease
Take the difference between the new value and the old one, divide by the old value and multiply by 100. A price going from 80 to 100 rose by 20, and 20 ÷ 80 = 0.25, so 25%. From 100 to 80 it fell by 20, and 20 ÷ 100 = 0.2, so 20%: the starting value changes, so the percentage changes too.
To apply a change, multiply by a single number: a 20% increase is × 1.2, a 20% decrease is × 0.8, a 7.5% increase is × 1.075.
| Change | Multiply by | 100 becomes | 250 becomes |
|---|---|---|---|
| +10% | 1.1 | 110 | 275 |
| +20% | 1.2 | 120 | 300 |
| +25% | 1.25 | 125 | 312.5 |
| −10% | 0.9 | 90 | 225 |
| −20% | 0.8 | 80 | 200 |
| −50% | 0.5 | 50 | 125 |
Reverse percentages: finding the original value
If a price after a 20% increase is 120, the original is not 120 minus 20%. The increase was 20% of the original, so 120 is 1.2 times the original: 120 ÷ 1.2 = 100. After a 20% decrease, divide by 0.8 instead: a sale price of 64 was 64 ÷ 0.8 = 80 before the discount. The same logic removes VAT from a price, as our VAT calculator shows.
Common percentages as fractions and decimals
| Percentage | Fraction | Decimal | Quick way |
|---|---|---|---|
| 50% | 1/2 | 0.5 | halve |
| 25% | 1/4 | 0.25 | halve twice |
| 20% | 1/5 | 0.2 | divide by 5 |
| 10% | 1/10 | 0.1 | move the point |
| 5% | 1/20 | 0.05 | half of 10% |
| 1% | 1/100 | 0.01 | move the point twice |
Our guide to fractions, decimals and percentages explains how to move between the three forms.
Do it in your head next time
Kalc trains times tables, fractions, percentages and algebra in about ten minutes a day.
Frequently asked questions
How do you calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12.
How do you work out what percentage one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 120 is 30 ÷ 120 × 100 = 25%.
How do you calculate a percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 100 is a 25% increase.
How do you find the original price before a percentage increase?
Divide the final price by 1 plus the percentage as a decimal. 120 after a 20% increase was 120 ÷ 1.2 = 100.
Why is a 20% increase followed by a 20% decrease not back to the start?
Because the second percentage applies to a bigger number. 100 plus 20% is 120, and 120 minus 20% is 96.