How to Calculate Percentages: Formulas and Everyday Examples

Discounts, pay rises, tax or test scores: the four basic percentage formulas and the most common mistakes, with worked examples.

A percentage is just a number divided by a hundred. It sounds trivial, yet when one turns up on a receipt, in a pay rise or in a loan offer, most of us hesitate for a second. The trick is to recognise which of four patterns you are dealing with. Once you know the question, the maths takes seconds.

1. What is X percent of a number?

Formula: number × percent ÷ 100. Fifteen percent of a 240 jacket is 240 × 15 ÷ 100 = 36. To do it in your head, find 10 percent first (24), then add half of that (12). You get 36 again.

2. What percent of one number is another?

Formula: part ÷ whole × 100. If you answered 62 of 80 questions correctly, your score is 62 ÷ 80 × 100 = 77.5 percent. The usual mistake is swapping the numbers. Asking "which number is the whole?" settles it.

3. By what percent did it go up or down?

Formula: (new − old) ÷ old × 100. If your rent rose from 1,500 to 1,875, the increase is (1,875 − 1,500) ÷ 1,500 × 100 = 25 percent. A negative result means a fall. If the old value is zero, percentage change is undefined, because you cannot divide by zero.

4. Working back from a price that already includes a percentage

This is the one that trips people up. If you paid 120 including 20 percent tax, the price before tax is not 120 − 24 = 96. It is 120 ÷ 1.20 = 100, because the 20 percent was added to 100, not to 120. Discounts work the same way: an item reduced by 25 percent to 75 used to cost 75 ÷ 0.75 = 100.

Successive percentages do not add up

A 20 percent discount followed by another 10 percent is not 30 percent off. It is 28 percent: 100 drops to 80, then to 72. Rises behave the same way, so two 10 percent increases make 21 percent in total. With successive rates, always work from the new amount each time.

Percent and percentage points are different

When an interest rate moves from 4 percent to 5 percent, it did not rise "by 1 percent". It rose by one percentage point, which is a 25 percent increase in relative terms. News reports about inflation and interest rates mix these up all the time.

A quick checklist

Decide which of the four patterns the question is.
Put the number that represents the whole in the denominator.
When working back from an amount that includes a percentage, divide rather than subtract.
Apply successive discounts or rises one at a time.
Sanity-check the result: a discounted price that ends up higher than the original means something went wrong.

If you would rather not do it by hand, enter the number and the rate in the percentage calculator. For an increase or decrease, use the percentage change calculator.