How to Calculate a Percentage

A percentage says how big a part is compared with the whole, using 100 as the reference. Divide the part by the whole and multiply by 100.

$a$ is the part, $b$ is the whole and $p$ is the share in per cent. On its own $\dfrac{a}{b}$ is a decimal between 0 and 1; multiplying by 100 puts it on the familiar scale.

Example

With a part of 30 and a whole of 120, $p = \dfrac{30}{120} \times 100 = 25$. The part is 25% of the whole.

Notes

Be clear about which number is the whole. For "30 out of 120 people" the whole is 120 and the part is 30. Swapping them gives 400%, an entirely different claim.

A part larger than the whole gives more than 100%. That is not an error: figures compared with last year pass 100% all the time.

If the whole is 0 there is nothing to divide by and no percentage exists.

To go back the other way, multiply: the part is $b \times \dfrac{p}{100}$. Taking 25% of 120 gives $120 \times 0.25 = 30$, the part we started from.