How to Work Out Percentage
Every percentage calculation you’ll ever need, in one place. Get an instant answer and see the exact formula used, so you can work it out by hand next time too.
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Pick the type of percentage question you have below, enter your numbers, and get an instant answer along with the formula used to reach it.
Percentage Calculator
Four common percentage calculations in one tool
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The Four Formulas Explained
Almost every percentage question you’ll come across fits into one of four patterns. Here’s how to work out each one by hand.
Working Out Percentages by Hand
The core method behind each calculation type
Finding X% of a Number
Divide the percentage by 100, then multiply by the number: (% ÷ 100) × number. For example, 20% of 150 is (20 ÷ 100) × 150 = 30.
Finding What Percent One Number Is of Another
Divide the part by the whole, then multiply by 100: (part ÷ whole) × 100. For example, 30 out of 150 is (30 ÷ 150) × 100 = 20%.
Percentage Increase or Decrease
Subtract the original from the new value, divide by the original, then multiply by 100: ((new − old) ÷ old) × 100. A negative result means a decrease.
Finding the Original Number
Divide the new value by 1 plus the percentage as a decimal for an increase, or 1 minus the percentage for a decrease: new ÷ (1 ± %). For example, £120 after a 20% increase means the original was 120 ÷ 1.20 = £100.
Percentage Checklist
Confirm these before trusting your answer
Common Percentage Shortcuts
Handy mental-maths shortcuts for percentages you’ll use often.
| Percentage | Quick Method | Example (of 240) |
|---|---|---|
| 50% | Divide by 2 | 120 |
| 25% | Divide by 4 | 60 |
| 10% | Move decimal point one place left | 24 |
| 5% | Half of 10% | 12 |
| 1% | Move decimal point two places left | 2.4 |
| 20% | Divide by 5 | 48 |
Percentage FAQ
Answers to the most frequently asked questions about working out percentages.
The basic formula is: part divided by whole, multiplied by 100. This tells you what percentage the part represents of the whole. To find a percentage of a number, rearrange this to: (percentage divided by 100) multiplied by the number.
Subtract the original number from the new number, divide the result by the original number, then multiply by 100. For example, going from 50 to 65 is an increase of 15, and 15 divided by 50 multiplied by 100 equals a 30% increase.
If a value has increased by a known percentage, divide the new value by (1 plus the percentage as a decimal). If it has decreased, divide the new value by (1 minus the percentage as a decimal). For example, if £120 is the price after a 20% increase, the original price is 120 divided by 1.20, which equals £100.
A percentage point is the simple arithmetic difference between two percentages, while percent describes a relative change. For example, moving from 20% to 25% is a rise of 5 percentage points, but it is a 25% relative increase in the underlying value.