How to calculate a percentage
A percentage is a number out of 100. To find a percentage of a number, divide the percentage by 100 and multiply: 15% of 80 is 0.15 × 80 = 12. This calculator handles the three questions people ask most often: X% of Y, what percent X is of Y, and the percent change from X to Y.
The three modes
Pick a mode from the Calculation menu, then enter X and Y. What X and Y mean depends on the mode.
| Mode | X is | Y is | Formula |
|---|---|---|---|
| X% of Y | the percentage | the base number | X ÷ 100 × Y |
| X is what % of Y | the part | the whole | X ÷ Y × 100 |
| % change from X to Y | the original value | the new value | (Y − X) ÷ |X| × 100 |
Results are shown with up to four decimal places, with trailing zeros removed, so 1 out of 3 shows as 33.3333% and 15% of 80 shows as 12.
Worked examples
X% of Y: what is 15% of 80?
- Choose X% of Y.
- Enter 15 as X and 80 as Y.
- 15 ÷ 100 × 80 = 12.
X is what % of Y: 12 is what percent of 80?
- Choose X is what % of Y.
- Enter 12 as X and 80 as Y.
- 12 ÷ 80 × 100 = 15%.
Percent change: from 80 to 100
- Choose % change from X to Y.
- Enter 80 as X (the original) and 100 as Y (the new value).
- (100 − 80) ÷ 80 × 100 = 25%.
Swap them, from 100 down to 80, and the result is −20%. The difference is 20 either way, but it's measured against a different starting point.
Common percentage questions
| Question | Mode | X | Y | Answer |
|---|---|---|---|---|
| What is 20% of 45.50? | X% of Y | 20 | 45.5 | 9.1 |
| What is 150% of 40? | X% of Y | 150 | 40 | 60 |
| I scored 1 out of 3. What percent is that? | X is what % of Y | 1 | 3 | 33.3333% |
| Rent went from 50 to 150. By what percent? | % change | 50 | 150 | 200% |
| A rate went from 4% to 5%. By what percent? | % change | 4 | 5 | 25% |
Percentages above 100 work in every mode. 150% of a number is one and a half times it, and a value that triples has risen by 200%, not 300%.
Questions the modes don't answer directly
Adding or taking off a percentage. To increase 80 by 15%, find 15% of 80 (12) and add it: 92. To decrease by 15%, subtract: 68. You can also multiply by 1.15 or 0.85 in one step. For prices, the discount calculator does the subtraction for you.
Reverse percentages. If 60 is the price after a 25% cut, the original isn't 60 + 25% of 60. Divide by what's left: 60 ÷ 0.75 = 80. The same idea is how tax is extracted from a tax-inclusive price.
Percentage points. When the values you're comparing are already percentages, say whether you mean the difference in points (4% to 5% is 1 point) or the relative change (25%). News reports about interest rates and polls often mix the two.
Things to watch
- X can't be zero in percent change, and Y can't be zero in "what % of", because both would mean dividing by zero. The calculator shows an error.
- Negative starting values. Percent change divides by the size of the original value (ignoring its sign), so the sign of the answer always matches the direction of the change. Going from −50 to −25 is an increase and shows 50%; going from −50 to −75 shows −50%.
- Order matters in percent change and "what % of". Make sure the original or whole value goes in the right box.
Related calculators
- Discount calculator: the sale price and savings for a percentage off.
- Profit margin calculator: profit as a percentage of price and of cost.
- Ratio calculator: compare two quantities as a ratio instead of a percentage.
- Fraction calculator: work with fractions, which percentages are a special case of.
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