Percentages turn up everywhere — sale discounts, exam marks, pay rises, interest rates, tax, tips, statistics in the news. They are also famously easy to get wrong, especially when you need to reverse a change or compare two numbers. This calculator handles the four jobs people actually need: finding a percentage of a number, working out what percentage one number is of another, calculating percentage increase or decrease, and applying a percentage change to a price.
Percentage Calculator
Three everyday percentage questions, one tool. Pick the tab that matches what you’re trying to work out.
Result
30
20% of 150 is 30.
How it works: A percentage is simply a fraction of 100. To find X% of Y, multiply Y by X ÷ 100. To find what percentage X is of Y, divide X by Y and multiply by 100. For change between two values, subtract the old value from the new one, divide by the old value, and multiply by 100 — a positive answer is an increase, a negative one is a decrease.
How it works
Pick the type of calculation and enter your two numbers. To find a percentage of something — 15% of £240, say — enter the percentage and the amount. To find what percentage one figure is of another — 45 marks out of 60 — enter both figures. For a change, enter the start and end values and the calculator tells you the percentage increase or decrease, and how big the difference is in plain numbers too.
No formulas to memorise and no sign errors: the calculator labels an increase as an increase and a decrease as a decrease, which is where mental maths most often lets people down.
How the calculation works
Three formulas cover almost everything:
- Percentage of a number: (percentage ÷ 100) × number. So 15% of £240 is 0.15 × 240 = £36.
- One number as a percentage of another: (part ÷ whole) × 100. So 45 out of 60 is (45 ÷ 60) × 100 = 75%.
- Percentage change: ((new value − old value) ÷ old value) × 100. Always divide by the original value — this is the single most common percentage mistake.
That last point explains why changes do not cancel out. If a £100 item rises 20% to £120, then falls 20%, the fall is 20% of £120 (£24), landing at £96 — not back at £100. Similarly, undoing a 20% increase requires a fall of about 16.7%, not 20%.
Worked example
A jacket is priced at £45 with 20% off in a sale. What do you pay?
- Discount amount: 20% of £45 = 0.20 × £45 = £9
- Sale price: £45 − £9 = £36
Or in one step: 100% − 20% = 80%, and 80% of £45 = 0.80 × £45 = £36. You pay £36 and save £9.
A second everyday check — percentage change: if your energy bill rises from £120 to £138, the increase is (138 − 120) ÷ 120 × 100 = 15%. Dividing by the new figure (138) instead would wrongly give 13%, which is why news reports and bills sometimes seem to disagree with your own maths.
Tips
- Build from 10%. For quick mental estimates: 10% is the number divided by 10, 5% is half of that, and 1% is the number divided by 100. Combine them — 15% of £240 is 10% (£24) + 5% (£12) = £36.
- Apply stacked discounts one at a time, in order. “30% off, then an extra 10% off” is not 40% off: it is £100 → £70 → £63, a total saving of 37%. Each discount applies to the already-reduced price.
- Be careful with “percentage points”. If an interest rate rises from 4% to 5%, that is a 1 percentage point rise but a 25% relative increase. Politicians and advertisers pick whichever sounds better; now you can spot it.
- Reverse a percentage by dividing, not subtracting. To find the price before a 20% increase, divide the current price by 1.20. To find the price before VAT at 20%, divide by 1.20 as well — the same trick.
- Check your exam or test scores properly. Marks as a percentage need the maximum possible marks, not the number of questions, when questions carry different weights.
FAQ
How do I work out a percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. 25% of 80 = 0.25 × 80 = 20. A shortcut: 25% is a quarter, 50% is a half, 10% is a tenth.
How do I calculate percentage increase?
Subtract the old value from the new value, divide the difference by the old value, and multiply by 100. A rise from £50,000 to £54,000 is (4,000 ÷ 50,000) × 100 = an 8% increase.
What is 20% off £45?
The discount is £9, so you pay £36. You can also multiply directly: 80% of £45 = £36.
Why don’t a 20% rise and a 20% fall cancel out?
Because each percentage is calculated on a different base. The rise is calculated on the starting price; the fall is calculated on the new, higher price, so the fall is a larger cash amount. Percentages only cancel when the base stays the same.
How do I find the original price after a discount?
Divide the sale price by what remains after the discount as a decimal. If you paid £36 after 20% off, the original was £36 ÷ 0.80 = £45. Subtracting the discount percentage from the sale price would give the wrong answer.
What percentage is 30 of 150?
(30 ÷ 150) × 100 = 20%. The first number is always divided by the total or whole amount.