How to use the percentage calculator
- Pick the calculator that matches your question: What is X% of Y?, X is what percent of Y?, Percentage change from X to Y, Percentage difference between X and Y or Increase or decrease Y by X%.
- Type your numbers into its two boxes (a decimal point or comma both work).
- Read the answer in the result box. Underneath it you see the formula and the working with your numbers filled in.
- Change Decimal places if you need a fixed number of decimals, and use the copy button to copy a result.
The five percentage formulas
A percentage is a number expressed as a fraction of 100: 15% means 15 per hundred, or 0.15. Every calculation on this page is a variation of that idea.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 80 = 12 |
| X is what percent of Y? | X ÷ Y × 100 | 30 is 25% of 120 |
| Percentage change from X to Y | (Y − X) ÷ |X| × 100 | 80 → 100 is +25% |
| Percentage difference | |X − Y| ÷ ((X + Y) ÷ 2) × 100 | 80 and 100 differ by 22.22% |
| Increase or decrease Y by X% | Y × (1 ± X ÷ 100) | 80 + 15% = 92 |
Percentage change vs percentage difference
Percentage change has a direction: it compares a new value with an old one and divides by the old value. Going from 80 to 100 is a 25% increase, but going back from 100 to 80 is a 20% decrease, because the starting point changed. The sign tells you which way it went. If the old value is negative, the calculator divides by its absolute value so that a rise still shows as a positive change. A change from 0 cannot be expressed as a percentage, because it would mean dividing by zero.
Percentage difference has no direction. It compares two values on an equal footing by dividing the gap between them by their average, so swapping X and Y gives the same answer: 80 and 100 differ by 20 ÷ 90 × 100 = 22.22%. Use it when neither number is the "before" value, such as prices in two shops.
Why a 20% rise and a 20% fall do not cancel out
Each percentage is taken of a different starting number. Increase 100 by 20% and you get 120; decrease 120 by 20% and you get 96, not 100. The same is true of discounts stacked on discounts: 20% off and then a further 10% off is 28% off in total (0.8 × 0.9 = 0.72), not 30%.
Everyday examples
- Discounts: a 25% discount on 60 is 15 off, so you pay 45 (use calculator 5 with Decrease).
- Tips and tax: 18% of a 42.50 bill is 7.65 (calculator 1).
- Test scores: 43 correct answers out of 50 is 86% (calculator 2).
- Price rises and salaries: a rent going from 950 to 1,020 is a 7.37% increase (calculator 3).
- Comparing measurements: two readings of 4.8 and 5.2 differ by 8% (calculator 4).
Privacy: every calculation runs in your browser and nothing you type is sent to a server. Your last numbers and your decimal setting are kept only in this browser's local storage so they are still there next time.
Related tools: work out an exact age or the time between two dates with the age calculator, draw numbers for a raffle with the random number generator, or see all everyday tools.
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 = 0.15, and 0.15 × 80 = 12.
How do I work out what percentage one number is of another?
Divide the part by the whole and multiply by 100. If you scored 43 out of 50, that is 43 ÷ 50 × 100 = 86%. The whole cannot be zero.
How do I calculate a percentage increase or decrease?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. A negative result is a decrease: from 100 to 80 is −20%.
What is the difference between percentage change and percentage difference?
Percentage change measures how much a value moved from a starting point, so it depends on which number came first. Percentage difference compares two values without a starting point, by dividing their gap by their average, so the order does not matter.
How do I add a percentage to a number?
Multiply the number by 1 plus the percentage as a decimal. Adding 15% to 80 is 80 × 1.15 = 92. To take 15% off, multiply by 1 minus the decimal: 80 × 0.85 = 68.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount as a decimal. If an item costs 45 after 25% off, the original price was 45 ÷ 0.75 = 60. Taking 25% off the sale price would not give you the original.
Updated