How to use the percentage calculator
- Pick the question you want to answer from the list.
- Enter the numbers. The labels match the question, so X and Y are always the numbers in the sentence you picked.
- The answer updates as you type, with the working underneath.
The five percentage questions
| Question | Formula | Example |
|---|---|---|
| What is P% of Y? | P ÷ 100 × Y | 20% of 150 = 30 |
| X is what percent of Y? | X ÷ Y × 100 | 30 is 20% of 150 |
| X is P% of what? | X ÷ (P ÷ 100) | 30 is 20% of 150 |
| Change from X to Y | (Y − X) ÷ X × 100 | 50 to 65 is +30% |
| Difference between X and Y | |X − Y| ÷ average × 100 | 50 and 65 differ by 26.09% |
"Per cent" means "per hundred", so every percentage question comes down to converting between a percentage and a fraction of 100.
Worked example
The calculator starts with 20% of 150:
- 20% as a decimal: 20 ÷ 100 = 0.2
- 0.2 × 150 = 30
The same numbers answer the reverse questions: 30 is 30 ÷ 150 × 100 = 20% of 150, and if 30 is 20% of a number, that number is 30 ÷ 0.2 = 150.
Percentage change vs. percentage difference
Percentage change has a direction: it measures from a starting value to an ending value. A price rising from 50 to 65 is a change of (65 − 50) ÷ 50 × 100 = +30%, and falling back from 65 to 50 is a change of −23.08%, because the starting value is different.
Percentage difference compares two values with no "before" and "after", such as two shop prices. It divides the gap by the average of the two: |50 − 65| ÷ 57.5 × 100 = 26.09%, and it gives the same answer whichever order you enter them in.
Percentage points
When a percentage itself changes, say an interest rate going from 4% to 5%, the change is 1 percentage point but 25% in relative terms (1 ÷ 4 × 100). News reports and loan offers mix these up often, so it's worth checking which one is meant.
Frequently asked questions
How do I calculate a percentage of a number in my head?
Find 10% by moving the decimal point one place left, then scale it. For 15% of 80: 10% is 8, 5% is half of that (4), so 15% is 12. For 20%, double the 10% figure.
How do I add a percentage to a number?
Multiply by 1 plus the percentage as a decimal. Adding 20% to 150 is 150 × 1.2 = 180. To take 20% off, multiply by 0.8 instead: 150 × 0.8 = 120.
Why is a 50% drop not undone by a 50% rise?
Because the second percentage is taken from a smaller number. 100 falling 50% is 50, and 50 rising 50% is only 75. To get back to 100 you need a 100% rise.
Can a percentage be more than 100%?
Yes. 300 is 200% of 150, and a price that triples has risen by 200%. A share of a whole, such as the share of a pizza you ate, can't be more than 100%.
Related calculators
- Percent Error Calculator — How far a measured value is from the accepted value, as a percent error with the sign and the working shown.
- Discount Calculator — Final price after a percent or dollar discount, with an optional second stacked discount and sales tax.
- Ratio Calculator — Simplify ratios, solve A : B = C : D for a missing value, scale a ratio or split a total, with fractions and percentages.
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