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How to use the percentage calculator
Choose what you need to find, then enter the two numbers. The labels change to match the mode.
- X% of Y finds a part of a number, such as a 20% discount on a $50 item.
- X is what % of Y shows X as a share of Y, such as 30 out of 200.
- % change from X to Y shows how much a value went up or down.
The formulas
Percent of a number: part = percent ÷ 100 × number
Share: share = part ÷ whole × 100
Change: change = (new − old) ÷ |old| × 100
Example: a price rises from $80 to $100. The change is (100 − 80) ÷ 80 × 100 = +25%. A 25% increase on $80 is $20, which matches the difference.
Percent and percentage points
If an interest rate goes from 10% to 15%, it has risen by 5 percentage points. In relative terms it rose by 50%, because 5 is half of 10. News stories and adverts often mix these two ideas, so check which one is meant.
Shortcuts for mental maths
- 10% of any number: move the decimal point one place to the left.
- 20% off: multiply by 0.8. 30% off: multiply by 0.7.
- Adding 21% tax: multiply by 1.21.
Questions about percentages
How do I work out a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. Choose “% change” above to do this automatically.
Why doesn’t a 50% fall followed by a 50% rise get back to the start?
Each percentage applies to a different base. $100 falls 50% to $50, then rises 50% of $50 to $75, not $100. Two equal percentage changes in opposite directions do not cancel out.
Why can’t the old value be zero?
Percent change divides by the old value, and dividing by zero is undefined. If you start from zero, look at the difference in absolute terms instead.