Percentage calculator
Pick the question you are trying to answer, enter two numbers, and see the steps.
Percent of a number
To find X% of Y, divide X by 100 and multiply by Y. So 15% of 200 is 0.15 × 200 = 30. To go the other way, divide the part by the whole and multiply by 100.
Percent change
Percent change is (new − old) ÷ old × 100. A positive result is an increase and a negative result is a decrease. Note that going up 50% and then down 50% does not return you to the start, because the second percentage is taken from a bigger number.
Increase and decrease
To raise a value by Y%, multiply it by 1 + Y/100. To lower it, multiply by 1 − Y/100. This is how sales prices, tips, and tax are worked out.
Percentage points
If a rate moves from 20% to 25%, it rose by 5 percentage points, which is a 25% relative increase. Teachers and textbooks use these two ideas differently, so check which one a question wants.
Worked examples
Percent of a number: 15% of 80 = 0.15 × 80 = 12. Percent change: going from 50 to 65 is (65 − 50) ÷ 50 × 100 = +30%. Increase: 200 increased by 15% is 200 × 1.15 = 230.
Working backward: a jacket costs $48 after a 20% discount. The sale price is 80% of the original, so the original price = 48 ÷ 0.80 = $60, not 48 × 1.20 = $57.60.
Frequently asked questions
Why can’t I undo a percent change by reversing it?
The base changes. A 50% increase from 100 gives 150, but a 50% decrease from 150 gives 75. To undo an increase of p%, divide by (1 + p/100) instead.
What is the difference between percent and percentage points?
If a rate goes from 10% to 15%, it rose by 5 percentage points, but by 50% in relative terms. News reports often mix these up.
How do I convert a fraction to a percent?
Divide and multiply by 100: 3/8 = 0.375 = 37.5%.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100: 18 out of 24 is 18 ÷ 24 × 100 = 75%.