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

This calculator works out the factorial of any whole number from 0 to 170, the value you get from multiplying that number by every smaller whole number down to 1. Factorials matter because they sit behind counting problems throughout maths: they tell you how many different ways a set of items can be arranged in order, and they are the building blocks for permutations, combinations and probability calculations used in statistics, games and computer science. You simply enter a whole number into the field, and the calculator instantly returns two things: the factorial itself, shown as a full number, and the expansion underneath it, spelling out the actual multiplication such as 5! = 5 x 4 x 3 x 2 x 1, so you can see exactly how the answer is built rather than just taking the total on faith. Factorials grow extremely quickly. By the time you reach 20 factorial the result is already past two quintillion, so once the answer gets large the calculator switches to scientific notation to keep it readable, and it caps out at 170 because beyond that the number becomes too big to represent as an ordinary figure at all. Use it to check homework, explore how quickly factorials explode, or work through the maths behind permutations and combinations for a statistics course or a probability problem.

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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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