How to use the percentage calculator
- Pick the question you are asking from the four tabs. The labels on the two boxes change to match.
- Type the two numbers. Decimals and thousands separators are fine (12.5, 2,450).
- Read the answer and the line under it, which shows the sum with your numbers filled in so you can check it or copy it into your own working.
Use Swap numbers when you typed them the wrong way round, which matters most for percentage change: going from 80 to 100 is a 25% rise, but going from 100 to 80 is a 20% fall.
The four formulas
Every percentage question is one of these four, written here with the numbers called X and Y:
The third formula divides by the starting value, which is why the order of the numbers matters. The fourth handles both increases and decreases: enter a negative percentage to take a percentage off.
Worked examples
| Question | Working | Answer |
|---|---|---|
| A 18% tip on a 2,450 bill | 18 ÷ 100 × 2,450 | 441 |
| 45 marks out of 60, as a percentage | 45 ÷ 60 × 100 | 75% |
| Rent went from 1,200 to 1,500 | (1,500 − 1,200) ÷ 1,200 × 100 | +25% |
| Rent went back from 1,500 to 1,200 | (1,200 − 1,500) ÷ 1,500 × 100 | −20% |
| A price of 1,250 plus 20% | 1,250 × 1.20 | 1,500 |
| Price after a 20% rise is 1,500. What was it before? | 1,500 ÷ 1.20 | 1,250 |
Rows three and four show why a rise and an equal fall don't cancel: the same difference of 300 is 25% of the smaller number and 20% of the larger one.
Reverse percentages: finding the original price
A common mistake is to work backwards by subtracting the same percentage. If a jacket costs 1,500 after a 20% price rise, taking 20% off 1,500 gives 1,200, which is wrong. The 20% was added to the old price, so you divide instead: 1,500 ÷ 1.20 = 1,250. The Add / remove % tab prints this undo step for you.
The same rule finds a price before tax. With a 17% sales tax, a total of 2,340 came from 2,340 ÷ 1.17 = 2,000 before tax, and the tax itself was 340.
Percent or percentage points?
When a rate moves from 4% to 5%, it has gone up by one percentage point, but by 25 percent of its old value, because 1 is a quarter of 4. News reports about interest rates, inflation and exam pass rates often mix the two. If you are quoting a change in something that is already a percentage, say "points" for the plain difference and use the % change tab only for the relative change.
Accuracy and limits
Results are calculated with standard double-precision numbers and shown to four decimal places, which is far more than everyday use needs. Very large or very small results switch to scientific notation (for example 1.2e+18). For money, round to the smallest coin your currency uses only at the final step, not in the middle of a calculation.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 15% of 80: 15 ÷ 100 × 80 = 12. Use the first tab of the calculator to do it automatically.
How do I work out percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30% increase.
Why isn't a 50% rise followed by a 50% fall back to the start?
The fall is taken from the bigger number. 100 rises 50% to 150, then 50% of 150 is 75, which leaves 75: an overall drop of 25%.
How do I remove VAT or sales tax from a price?
Divide the total by 1 plus the tax rate as a decimal. With 18% tax, 1,180 ÷ 1.18 = 1,000 before tax.
Can the result be more than 100%?
Yes. If X is bigger than Y, X is more than 100% of Y. For example 150 is 300% of 50, and a price that triples has risen by 200%.