The formulas
- Percentage of a number: number × percentage ÷ 100. 20% of 150 = 150 × 20 ÷ 100 = 30.
- What percent A is of B: A ÷ B × 100. 30 out of 200 = 30 ÷ 200 × 100 = 15%.
- Percentage change: (final − initial) ÷ initial × 100. From 80 to 100 = (100 − 80) ÷ 80 × 100 = +25%. From 100 to 80 it is −20%: the base is always the starting value, which is why rises and falls are not symmetrical.
- Increase or decrease by a percentage: number × (1 + percentage ÷ 100). 1,200 increased by 15% = 1,200 × 1.15 = 1,380; decreased by 15% = 1,200 × 0.85 = 1,020.
Mental-maths shortcuts
10% is the number with the decimal point moved one place (10% of 240 = 24); 5% is half of 10%; 1% is one hundredth. For 15% add 10% and 5%: 15% of 240 = 24 + 12 = 36. And remember that a% of b equals b% of a: 8% of 50 is the same as 50% of 8, i.e. 4.
Mind the percentage points
If a rate goes from 2% to 3% it has risen by one percentage point, but in relative terms it has grown by 50%. The two are often confused in news and advertising.
Frequently asked questions
How do I calculate the percentage between two numbers?
Divide the first number by the second and multiply by 100: 45 out of 60 = 45 ÷ 60 × 100 = 75%.
How do I work out a discount percentage?
Use the change formula: (sale price − full price) ÷ full price × 100. For prices there is also our dedicated discount calculator.
Can I use a comma for decimals?
Yes, the calculator accepts both a comma and a point.