Factorial Calculator

What is a factorial?

A factorial, written with an exclamation mark like 5!, means you multiply together every whole number from 1 up to that number. So 5! is 5 × 4 × 3 × 2 × 1, which comes to 120. Factorials answer the question "how many ways can I arrange these items in order," which is why they sit at the heart of permutations, combinations, and probability.

One quirk worth remembering: 0! is defined as 1, not 0. That is a convention, but a useful one, because it keeps the combination and permutation formulas working correctly.

How to use this calculator

1. Enter a non-negative whole number, such as 5 or 10.
2. Click calculate to get the factorial value.
3. Read the result, which shows \(n!\).
4. If needed, compare the step-by-step multiplication to check your work.

The formula explained

The formula \(n! = n \times (n-1) \times \cdots \times 2 \times 1\) computes the product of all positive integers from \(n\) down to 1. By definition, \(0! = 1\).

• n = a non-negative integer input
• n! = the factorial of n, the product of all positive integers from n down to 1

Step by step method

1. Start with the number you want, for example 5.
2. Multiply it by the next smaller whole number until you reach 1.
3. Write the final product as the factorial value.

Worked example

Problem. Find \(6!\).

1. Write out the product: \(6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1\).
2. Multiply in order: \(6 \times 5 = 30\), \(30 \times 4 = 120\), \(120 \times 3 = 360\), \(360 \times 2 = 720\), \(720 \times 1 = 720\).
3. So \(6! = 720\).

Tips and common mistakes

• Factorial only works for non-negative integers, so \(3.5!\) is not defined in this calculator.
• Remember that \(0! = 1\), not 0.

Frequently asked questions