Percentage Calculator
Work out percentages, percentage change and what percent one number is of another.
Written by Rahman · Last reviewed
Quick answer
A percentage is a fraction of 100: X% of Y is (X ÷ 100) × Y. To find what percentage X is of Y, divide X by Y and multiply by 100. For percentage change use (new − old) ÷ old × 100, and note that a 50% fall followed by a 50% rise does not return you to the start, because each is applied to a different base.
Results are estimates for general guidance only. Double-check any figure you rely on for an important decision.
About the Percentage Calculator
Percentages express a number as a fraction of 100, making them a quick way to compare values, describe change and split totals. They appear everywhere: discounts, taxes, interest, statistics and exam scores.
This calculator handles the three most common percentage questions: finding a percentage of a number, finding what percentage one number is of another, and measuring the percentage change between two values.
Percentage points are not percent
When the thing being measured is itself a percentage, there are two different ways to describe a change and they give different numbers. Moving from 5% to 6% is a rise of one percentage point, and also a rise of 20%, because one is a fifth of five.
Both statements are correct and they are not interchangeable. Reporting on interest rates, unemployment, tax rates, poll shares and conversion rates all runs into this, and the ambiguity is exploited often enough that it is worth reading carefully. "Rates rose by 20%" and "rates rose 20 percentage points" describe wildly different events.
- Use percentage points for the arithmetic difference between two percentages, and percent for the relative change between them.
- The relative figure is always larger when the starting percentage is below 100, and the smaller the base the more dramatic it looks.
- Basis points remove the ambiguity entirely in finance: one basis point is a hundredth of a percentage point, so a rise from 5% to 6% is 100 basis points.
Percentage changes are not symmetric
A fall and a rise of the same percentage do not cancel, because each is calculated from a different base. The fall is measured against the original value; the recovery has to be measured against the reduced one.
An investment that falls 50% needs a 100% gain to return to where it started. A 20% fall needs 25% to recover, and a 90% fall needs 900%. This is the arithmetic behind why large drawdowns are so damaging, and why an average of percentage gains and losses overstates what actually happened.
- A 10% rise followed by a 10% fall leaves you at 99% of the original, not 100%.
- The order does not matter (multiplication commutes), so applying the fall first gives the same result.
- To reverse a percentage change, divide by (1 + change) rather than subtracting the same percentage.
Frequently Asked Questions
How do I find a percentage of a number?
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Divide the percentage by 100 and multiply by the number. For example, 25% of 200 is 0.25 × 200 = 50.
How do I work out percentage change?
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Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive result is an increase; a negative result is a decrease.
What does "X is what percent of Y" mean?
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It tells you the share X represents of Y: divide X by Y and multiply by 100.
Can a percentage be more than 100?
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Yes. A value larger than the reference number gives a percentage above 100%; for example, 250 is 125% of 200.