How it works
A percentage is a number out of 100. So 15% means 15 for every 100, which is the same as 0.15. Every calculation on this page is one of four simple rearrangements of that idea.
To find a percentage of a number, multiply the number by the percentage and divide by 100. To find what percent one number is of another, divide the part by the whole and multiply by 100.
Percentage change compares a new value with a starting value. The difference is divided by the starting value, which is why a change from 80 to 92 (+15%) is not the same size as a change from 92 back to 80 (about -13%).
X% of Y = Y × X ÷ 100 X as a % of Y = X ÷ Y × 100 % change = (New − Start) ÷ |Start| × 100 Y increased by X% = Y × (1 + X ÷ 100) Y decreased by X% = Y × (1 − X ÷ 100)
Worked example: a price rise
A monthly bus pass goes from 80 to 92. The difference is 12. Divide 12 by the starting price of 80 and you get 0.15, so the price rose by 15%.
If the price later drops back from 92 to 80, the difference is still 12, but now you divide by 92. That gives about 13.04%, so the fall is smaller in percentage terms than the rise was.
Good to know
- Adding 10% and then taking 10% off does not bring you back to where you started. 100 plus 10% is 110, and 110 minus 10% is 99.
- A percentage change from zero cannot be calculated, because any increase from nothing is infinitely large in percentage terms.
- Percentage points are different from percentages. An interest rate moving from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate itself.
Questions people ask
How do I calculate a percentage of a number in my head?
Find 10% by moving the decimal point one place to the left, then scale it. For 15% of 240, 10% is 24, 5% is half of that (12), so 15% is 36.
What is the difference between percentage change and percentage difference?
Percentage change has a direction: it measures how much a value moved from a starting point. Percentage difference compares two values with no starting point, using their average as the base. This page calculates percentage change.
How do I remove a percentage that was already added, like tax?
Divide by 1 plus the rate instead of subtracting the percentage. A price of 115 that includes 15% tax had a base price of 115 ÷ 1.15 = 100. Subtracting 15% of 115 would give 97.75, which is wrong.
Are my numbers sent anywhere?
No. Every calculation runs in your browser. Nothing you type leaves your device.