Formula

Percent of a number

Also written: percentage of an amount · part whole percent formula

\text{part} = \frac{\text{percent}}{100} \times \text{whole}

To find a percent of a number, turn the percent into a decimal and multiply. The word "of" in a percent problem always means multiply.

What each part means

$\text{part}$: the amount you are looking for
$\text{percent}$: the rate, before dividing by 100
$\text{whole}$: the amount being taken a part of

When to use it

You know the whole and the percent and want the part. Rearranged, the same relationship answers the other two percent questions as well.

One relationship, three questions

The formula ties together three quantities. A problem gives you two and asks for the third, so the same relationship answers all three percent questions.

Missing	Rearranged as	Example
the part	$\text{part} = 0.30 \times 80$	$30\%$ of $80$ is $24$
the percent	$\tfrac{\text{part}}{\text{whole}}$	$24$ out of $80$ is $30\%$
the whole	$\tfrac{\text{part}}{\text{decimal}}$	$24$ is $30\%$ of $80$

Naming which one is missing is most of the work; the arithmetic is one step.

Why "of" means multiply

A percent is a fraction with denominator $100$ , and taking a fraction of an amount has meant multiplication since multiplying fractions:

30\% \text{ of } 80 = \frac{30}{100} \times 80 = \frac{2400}{100} = 24

Nothing new is introduced by the percent sign. It fixes the denominator and changes nothing else.

The size check

Below $100\%$ the answer must be smaller than the whole; above $100\%$ it must be larger. That single check catches almost every misplaced decimal point, which is the dominant error on this formula.

Benchmarks for mental arithmetic

$10\%$ is one decimal-point move and $1\%$ is two. Everything else is built from those.

Percent	How	On $240$
$10\%$	point one place left	$24$
$1\%$	point two places left	$2.4$
$5\%$	half of $10\%$	$12$
$15\%$	$10\% + 5\%$	$36$
$18\%$	$20\% - 2\%$	$43.2$

Swapping is allowed

$8\%$ of $50$ is awkward; $50\%$ of $8$ is $4$ on sight. They are the same product, because multiplication does not care about order:

0.08 \times 50 = 50 \times 0.08 = 4

When one arrangement is unpleasant, turn it around. See percent of a number.

Lessons that teach this

How to Find a Percent of a Number
Three ways to find a percent of a number: convert to a decimal and multiply, use a fraction, or build it from 10% and 1% in your head.
What Percent Is One Number of Another?
How to find what percent one number is of another: divide the part by the whole and multiply by 100, and how to tell which number is the whole.
Percent Word Problems: Which of the Three Questions Is It?
Every percent word problem is one of three questions. How to tell which you have been asked, and how to solve each one, with worked examples.