How to work out percentages
"Per cent" means "out of 100", so 20% is 20 out of every 100, or 0.2 as a decimal. Every percentage sum comes back to that idea. This page has five calculators covering the questions people ask most often, and each one shows its working so you can check it or do it yourself next time.
1. How to find a percentage of a number
Divide the percentage by 100 and multiply by the number.
X% of Y = X ÷ 100 × Y
Example: 20% of 150 = 20 ÷ 100 × 150 = 30. A quick mental trick: 10% is just the number divided by 10, so 10% of 150 is 15, and 20% is double that.
2. How to work out what percentage one number is of another
X as a % of Y = X ÷ Y × 100
Example: you scored 30 out of 120 in a test. 30 ÷ 120 × 100 = 25%.
3. How to calculate percentage increase or decrease
Find the difference, divide by the starting value and multiply by 100. A positive answer is an increase and a negative one is a decrease.
% change = (new − old) ÷ old × 100
Example: your rent rises from £800 to £1,000 a month. (1,000 − 800) ÷ 800 × 100 = 25% increase. If a share price falls from 250p to 200p, that's (200 − 250) ÷ 250 × 100 = 20% decrease.
Always divide by the starting number. That's why a 25% rise followed by a 20% fall takes you back to where you began: 80 up 25% is 100, and 100 down 20% is 80.
4. How to add or take off a percentage
add X%: number × (1 + X ÷ 100)
take off X%: number × (1 − X ÷ 100)
Example: a £200 bill plus a 15% tip is 200 × 1.15 = £230. A £80 jacket with 12.5% off is 80 × 0.875 = £70.
5. Reverse percentages: finding the original amount
If you know a price after a percentage was added, divide by (1 + the percentage ÷ 100). Don't just take the percentage off the new price, as that gives the wrong answer.
original = new amount ÷ (1 + X ÷ 100)
Example: something costs £120 including 20% VAT. The price before VAT was 120 ÷ 1.2 = £100, not £96. For a discount, use a minus percentage: if a sale price of £54 is 10% off, the original was 54 ÷ 0.9 = £60. Our VAT calculator does this for you at the 20% standard rate.
Percentage examples at a glance
| Question | Sum | Answer |
|---|---|---|
| What is 15% of £60? | 0.15 × 60 | £9 |
| What is 5% of 2,500? | 0.05 × 2,500 | 125 |
| 45 out of 60 as a percentage | 45 ÷ 60 × 100 | 75% |
| £25,000 to £26,500 pay rise | 1,500 ÷ 25,000 × 100 | 6% increase |
| £40 with 30% off | 40 × 0.7 | £28 |
| £90 after a 50% markup: original? | 90 ÷ 1.5 | £60 |
Percentage points vs percent
When an interest rate goes from 4% to 5%, it has risen by one percentage point, but by 25% in relative terms (1 ÷ 4 × 100). News reports and banks often mix these up, so check which one is meant. For savings and loans, the compound interest calculator shows how small percentage differences add up over time, and the savings calculator projects a regular deposit.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 80 is 15 ÷ 100 × 80 = 12.
How do I work out a percentage increase?
Take the new number away from the old one, divide by the old number and multiply by 100. Going from 50 to 65 is (65 − 50) ÷ 50 × 100 = a 30% increase.
How do I take 20% off a price?
Multiply the price by 0.8. A £45 item with 20% off costs £36. To take off any percentage, multiply by (100 minus the percentage) ÷ 100.
How do I find the original price before a percentage increase?
Divide the new price by 1 plus the percentage as a decimal. If a price of £138 includes a 15% increase, the original was £138 ÷ 1.15 = £120.
What percentage is 30 out of 40?
30 ÷ 40 × 100 = 75%.
Last reviewed October 2026 using 2026/27 figures. This calculator gives an estimate for guidance only.