Percentage calculator
Solve any percentage calculation in seconds: X% of an amount, what percentage one number is of another, increases and decreases, and the percentage change between two values.
The three questions a percentage answers
Almost everything we need percentages for falls into one of three questions, and it pays to tell them apart because each is worked out differently. First: what is 21% of 350? Multiply, 350 × 21 ÷ 100 = 73.5. Second: what percentage is 73.5 of 350? Divide and multiply by a hundred, 73.5 ÷ 350 × 100 = 21%. And the third, the one people get stuck on: if 73.5 is 21%, what's the total? Work backwards, 73.5 ÷ 21 × 100 = 350. This tool covers all three, but knowing which one you're doing prevents most mistakes.
Increases and decreases: percentage change
To see how much a price, an audience or any figure has changed, subtract the old value from the new one, divide by the old value and multiply by a hundred. If a rent goes from £700 to £770, the rise is (770 − 700) ÷ 700 × 100 = 10%. The sign tells you the direction: a negative result means it fell.
The mistake that costs money: a fall and a rise of the same percentage don't cancel out
It feels obvious that if something falls 50% and then rises 50%, you're back where you started. You're not. £100 that falls 50% becomes £50; that same £50 rising 50% only reaches £75, not £100. The reason is that the second percentage is applied to a smaller base. The same happens with shares or salaries: to recover from a 50% fall you don't need a 50% rise, but a 100% one.
Percentage points are not the same as percent
If a rate goes from 4% to 6%, it has risen by 2 percentage points, but it has increased by 50% in relative terms (because 2 is half of 4). Both figures are correct and measure different things; mixing them up is a classic source of misleading headlines. Whenever you read a figure about unemployment, interest or taxes, check whether it's talking about points or percent, because they don't mean the same thing.
Where it turns up every day
Working out a tip, seeing how much you save in a sale, splitting a shared bill, finding a weighted average grade or understanding the interest on a loan: it's all percentages. Being clear about the difference between "the percentage of" and "the percentage that something represents" makes these sums far less daunting. Everything is calculated in your browser, with nothing sent anywhere.