The factorial of a number, written with an exclamation mark, is the product of every whole number from 1 up to it. So 5 factorial is 5 times 4 times 3 times 2 times 1, which is 120. Factorials count the ways things can be arranged.

What is zero factorial?

Zero factorial is defined as 1. There is exactly one way to arrange nothing, so the convention keeps the maths of combinations and permutations consistent.

Why do factorials get so large?

Each step multiplies by a larger number, so factorials grow extremely fast. By 20 factorial the result is already over two quintillion, which is why very large factorials are shown in scientific notation.

Factorial Calculator

Work out the factorial of a whole number. Enter a number from 0 to 170 and the calculator multiplies every whole number up to it. Factorials count the number of ways a set of things can be arranged, and they appear throughout probability and combinatorics.

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Number (0 to 170)

120

5! = 5 x 4 x 3 x 2 x 1

How it works

The factorial multiplies the number by every smaller whole number down to one. Because the result grows so fast, numbers above about 21 are shown in scientific notation, and the calculator caps at 170, beyond which the value is too large to display as an ordinary number.

Worked example

5 factorial is 5 times 4 times 3 times 2 times 1, which is 120. That is also the number of ways to arrange five different items in a row.

Related calculators

Exponent Calculator: powers of a number.
Probability Calculator: probabilities.
Scientific Calculator: advanced functions.
Binomial Distribution Calculator: uses factorials.

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