Percentage Calculator
Calculate X% of Y, percentage change between two values, and percentage difference.
Percent change is measured against the starting value, so it depends on direction. Percent difference compares two values against their average, so it does not.
Three questions that look like one
Almost every percentage problem is one of three. What is X% of Y? — multiply: 15% of 80 is 0.15 × 80 = 12. X is what percent of Y? — divide and multiply by 100: 12 out of 80 is 15%. X is Y% of what? — divide: 12 is 15% of 12 ÷ 0.15 = 80. Identifying which of the three you have is most of the difficulty.
Percentage change is a separate operation and the source of most errors. The change from 40 to 50 is (50 − 40) / 40 = 25%, but going back from 50 to 40 is a 20% decrease — the base changed. Percentage changes are not symmetric, which is why a 50% loss requires a 100% gain to recover, and why successive discounts never simply add up.
Two things worth keeping straight. A percentage point is not a percent: moving a rate from 4% to 5% is one percentage point but a 25% increase. And percentages commute — 8% of 50equals 50% of 8, which is 4 and far easier. Reversing an awkward percentage often turns it into one you can do in your head.
Frequently Asked Questions
How do you calculate what is X% of Y?
Multiply Y by X, then divide by 100. For example, 20% of 150 = (20 × 150) / 100 = 30.
What is percentage change?
Percentage change measures relative change over time: ((New Value - Old Value) / |Old Value|) × 100.
What is percentage difference?
Percentage difference compares two numbers when neither is a baseline: (|V1 - V2| / ((V1 + V2)/2)) × 100.
How do I calculate a percentage change?
(new - old) / old x 100. A rise from 40 to 50 is a 25% increase; a fall from 50 to 40 is a 20% decrease. The asymmetry is real and catches people out: the two changes are not equal because they divide by different bases.