Percentage calculator
Percentages of a number, what share one figure is of another, how much something has gone up or down and the result of applying an increase or a discount. With an explanation of each calculation.
How to calculate percentages
Choose what you want to know: what a percentage of a number is, what percentage one figure is of another, how much something changed in percentage terms or what a number becomes after increasing or decreasing it. The calculator gives you the result and the working, so you can repeat it yourself.
Example: 15% of 200 is 30. Going from 80 to 100 is a 25% increase, but going back from 100 to 80 is a 20% decrease. And if you increase 100 by 20% (120) and then decrease it by 20%, you end up at 96, not 100.
How it is calculated
- Percentage of a number = percentage ÷ 100 × number.
- What percentage A is of B = A ÷ B × 100.
- Percentage change = (final value − initial value) ÷ initial value × 100. Increasing or decreasing by p % = number × (1 + p ÷ 100).
Assumptions
- A percentage change is always measured on the initial value: that is why rising and falling by the same percentage does not bring you back to the start.
Frequently asked questions
How do you calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 15% of 200 is 200 × 15 ÷ 100 = 30.
How do I work out what percentage one number is of another?
Divide the part by the total and multiply by 100. 30 out of 200 is 30 ÷ 200 × 100 = 15%.
How do you calculate percentage change?
(Final value − initial value) ÷ initial value × 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%.
Why doesn't a 20% increase followed by a 20% decrease give the same number?
Because each percentage is calculated on a different base. 100 + 20% = 120, but 20% of 120 is 24, so you drop to 96. To get back to 100 from 120 you need a 16.67% decrease.
What is the difference between percentage points and percent?
If an interest rate goes from 2% to 3%, it rises by 1 percentage point, but in percentage terms it rises by 50%, because 1 is half of 2. Keep them apart when comparing rates, margins or returns.
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