dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day! You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Tool for computing factorials. Factorial n! is the product of all integers numbers (not zero) inferior or equal to n.

Answers to Questions

How to calculate a factorial?

Factorial of a number \( n \) is calculated with a simple multiplication: it is the product of the positive integers numbers (not null) less or equal to \( n \).

The usual notation to indicate a factorial is the exclamation mark positioned after the number. The factorial of \( n \) is noted \( n! \).

Note that the factorial of zero is equal to one : \( 0! = 1 \)

Example: Here are the values of the first factorials $$ 0! = 1 \\ 1! = 1 \\ 2! = 2 \\ 3! = 6 \\ 4! = 24 \\ 5! = 120 \\ 6! = 720 \\ 7! = 5040 \\ 8! = 40320 \\ 9! = 362880 \\ 10! = 3628800 $$

What is the Gamma Function?

Euler-Gamma is an extension of the factorial function over the Complex numbers. dCode offers calculation over the Reals. $$ \forall\,n \in \mathbb{N}, \; \Gamma(n+1)=n! $$

How to calculate a negative factorial?

Use the Gamma function.

How to quickly compute a factorial value?

For large numbers, it is possible to estimate the value of \( n! \) with a good precision using the Stirling formula. $$ n!\sim\sqrt{2\pi n}\left(\frac{n}{e}\right)^n $$

Ask a new question

Source code

dCode retains ownership of the source code of the script Factorial online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. So if you need to download the online Factorial script for offline use, check contact page !