Percentage Calculator
Work out X% of Y, what percentage one number is of another, and percentage increase or decrease between two values.
A percentage calculator handles the four questions that actually come up: what is X% of Y, X is what percent of Y, the percentage change between two numbers, and removing a percentage from a total. Each has a different formula and mixing them up is the usual source of error.
Runs entirely in your browser · no signup · nothing is uploaded · updated 2026-08-29
How to use it
- 1.Choose which of the three questions you are asking.
- 2.Enter the two numbers.
- 3.Read the answer and the sentence that spells out what it means.
The four percentage formulas
Nearly every percentage error is using one of these formulas where another was needed.
| Question | Formula | Worked example |
|---|---|---|
| What is X% of Y? | Y x (X / 100) | 15% of 240 = 240 x 0.15 = 36 |
| X is what percent of Y? | (X / Y) x 100 | 36 of 240 = (36 / 240) x 100 = 15% |
| Percentage increase | (new - old) / old x 100 | 240 to 300 = 60 / 240 = 25% |
| Percentage decrease | (old - new) / old x 100 | 300 to 240 = 60 / 300 = 20% |
| Add a percentage | Y x (1 + rate) | 100 plus 20% VAT = 100 x 1.2 = 120 |
| Remove a percentage | Y / (1 + rate) | 120 minus 20% VAT = 120 / 1.2 = 100 |
| Reverse a discount | price / (1 - rate) | 56 after 30% off = 56 / 0.7 = 80 |
| Compound change | Y x (1 + rate)^n | 5% monthly for 12 months = 1.05^12 = +79.6% |
Frequently asked questions
How do I calculate a percentage increase?
Subtract the old value from the new, divide by the old value, multiply by 100. Going from 40 to 50 is a 25% increase, because 10 divided by 40 is 0.25.
Why is a 50% rise then a 50% fall not back to the start?
Because the second percentage applies to a larger base. 100 up 50% is 150; 150 down 50% is 75. Percentage changes do not cancel out.
What is the difference between percent and percentage points?
Moving from 10% to 12% is a rise of 2 percentage points but a 20% increase. Confusing the two is the most common error in reporting statistics.
How do I remove a percentage from a total?
Divide, do not subtract. To remove 20% VAT from 120, divide by 1.2 to get 100 - subtracting 20% gives 96, which is wrong.
How do I calculate a discount?
Multiply by one minus the discount. 30% off 80 is 80 x 0.7 = 56. To find the original price from a discounted one, divide: 56 / 0.7 = 80.
How do I work out VAT or sales tax?
To add 20%, multiply by 1.2. To remove it from a gross figure, divide by 1.2. Subtracting 20% from the gross gives the wrong answer.
What is the formula for percentage change?
(new - old) / old x 100. Use the old value as the denominator; using the new one gives a different and usually wrong number.
How do I calculate a percentage of a percentage?
Multiply the decimals. 20% of 50% is 0.2 x 0.5 = 0.1, which is 10% of the original.
The guide behind this tool
3 min readMetric and imperial: which conversions are exact
Which unit conversions are defined exactly, where US and imperial measures diverge, and the volume and temperature traps that produce wrong answers.
3 min readPercentage calculations: the four formulas
Percentage of, percentage change, reverse percentages and percentage points - the four calculations people mix up, and the arithmetic behind each.
3 min readRoman numerals: the rules and the 3999 limit
How subtractive notation works, which pairs are legal, why 3999 is the ceiling, and what to do about numbers the system cannot express.
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