How to use the percentage calculator
Every common percentage question has its own calculator on this page, written as a sentence with gaps for your numbers. Replace the example values and the answer appears immediately, with the working underneath. There's no Calculate button to press and nothing to reset between sums; each card is independent, so you can keep several calculations on screen at once. Press Enter to jump to the next box.
You can type numbers the way they appear in real life: £1,249.99, 12.5%, −3 or even 2,5 with a decimal comma. Symbols and grouping commas are ignored. Use the Decimals control to fix the number of decimal places — two for money, none for whole-number answers — or leave it on Auto, which shows up to four and trims trailing zeros. The copy button on each card copies the answer as a complete sentence, such as “80 to 92 is a 15% increase”.
When a question has no sensible answer — a percentage change from zero, a whole of zero, or a 100% discount you want to reverse — the calculator tells you why rather than showing NaN or infinity.
Percentage formulas, with worked examples
“Per cent” means “per hundred”, so every percentage is just a fraction with 100 on the bottom: 15% is 15/100, or 0.15. Every calculator on this page is one of these rearrangements of part = percentage ÷ 100 × whole.
| Question | Formula | Worked example |
|---|---|---|
| What is P% of W? | P ÷ 100 × W | 15% of 240 = 0.15 × 240 = 36 |
| X is what % of W? | X ÷ W × 100 | 45 of 60 = 45 ÷ 60 × 100 = 75% |
| X is P% of what? | X ÷ (P ÷ 100) | 30 is 15% of 30 ÷ 0.15 = 200 |
| % change from A to B | (B − A) ÷ A × 100 | 80 → 92: 12 ÷ 80 × 100 = 15% increase |
| Increase A by P% | A × (1 + P ÷ 100) | 250 + 20% = 250 × 1.2 = 300 |
| Decrease A by P% | A × (1 − P ÷ 100) | 250 − 20% = 250 × 0.8 = 200 |
| Original before +P% | F ÷ (1 + P ÷ 100) | £120 inc. VAT ÷ 1.2 = £100 |
| % difference | |A − B| ÷ mean(A, B) × 100 | 40 and 50: 10 ÷ 45 × 100 = 22.2% |
A handy mental trick: P% of W equals W% of P. So 8% of 50 is the same as 50% of 8, which is 4.
VAT, discounts and the reverse-percentage trap
The standard rate of VAT in the UK is 20%, with a reduced rate of 5% on things like domestic energy and children's car seats. Adding VAT is simple: multiply the net price by 1.2. Removing it is where most people go wrong. Taking 20% off a VAT-inclusive price does not give you the price before VAT, because the 20% was calculated on the smaller, net amount.
Take a £120 price including VAT. 20% of £120 is £24, and £120 − £24 = £96 — but £96 plus 20% is only £115.20. The correct net price is £120 ÷ 1.2 = £100, and the VAT is £20, which is one-sixth of the gross price, not one-fifth. The Reverse percentage calculator does this properly and shows the wrong answer alongside so you can see the difference; the Remove VAT 20% button sets it up in one click.
Discounts work the same way in reverse. If a jacket costs £56 in a 30% off sale, the original price was £56 ÷ 0.7 = £80, not £56 + 30% = £72.80. And successive changes don't cancel: a 10% rise followed by a 10% cut leaves you 1% below where you started, because the cut is taken from the larger figure.
Percentage change, difference and percentage points
- Percentage change has a direction. It compares a new value with an old one and divides by the old value, so going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease. Use it for prices, salaries, sales and anything over time.
- Percentage difference has no direction. It compares two values of equal standing — two quotes, two measurements — and divides by their average, so the answer is the same whichever you put first. 80 and 100 differ by 22.2%.
- Percentage points describe the gap between two percentages. If an interest rate rises from 4% to 5%, it has risen by one percentage point, but by 25% in relative terms. News reports mix these up constantly.
A change from a negative starting value is divided by the size of the starting value, so a loss of −£50 improving to a profit of £25 shows as a 150% increase rather than a misleading negative. A change from exactly zero is undefined, because there is nothing to divide by, and the calculator says so.
For business pricing, margin is profit as a percentage of the selling price and markup is profit as a percentage of cost. A product bought for £60 and sold for £80 has a 25% margin but a 33.3% markup — and a 50% markup is only a 33.3% margin. Other everyday maths lives nearby: the unit converter for measurements and the random number generator for draws and dice.
Frequently asked questions
How do I work out a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 15% of 240, that is 0.15 × 240 = 36. On a phone calculator you can type 240 × 15 %. Mentally, find 10% by moving the decimal point one place left (24), then 5% is half of that (12), so 15% is 24 + 12 = 36.
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 80 to 92: 92 − 80 = 12, 12 ÷ 80 = 0.15, × 100 = 15%. If the answer is negative, it is a decrease. Always divide by the starting value, not the new one — that is why a rise and fall of the same amount give different percentages.
How do I remove 20% VAT from a price?
Divide the VAT-inclusive price by 1.2. £120 ÷ 1.2 = £100, so the VAT was £20. Do not subtract 20% of the gross price — that gives £96, which is wrong because VAT is charged on the net price. For the 5% reduced rate, divide by 1.05. The Reverse percentage calculator has buttons for both rates.
What is the difference between percentage change and percentage difference?
Percentage change measures movement from an old value to a new one and divides by the old value, so direction matters. Percentage difference compares two values with no before and after, dividing by their average, so order does not matter. Going from 40 to 50 is a 25% increase, while the percentage difference between 40 and 50 is 22.2%.
How do I convert a fraction to a percentage?
Divide the top number by the bottom number and multiply by 100. 3/8 is 3 ÷ 8 = 0.375, which is 37.5%. To go the other way, put the percentage over 100 and simplify: 37.5% = 37.5/100 = 375/1000 = 3/8. For recurring decimals such as 33.33%, the calculator also shows the closest simple fraction, 1/3.
Why does a 10% rise then a 10% fall not get me back to where I started?
Because the second percentage is taken from a different base. £100 plus 10% is £110; 10% of £110 is £11, so the fall takes you to £99. In multiplier terms, 1.1 × 0.9 = 0.99, a 1% net loss. The same asymmetry means a 50% loss needs a 100% gain to recover.