# Stirling Approximation Calculator

Instructions: Use this Stirling Approximation Calculator, to find an approximation for the factorial of a number $$n!$$. Please type a number (up to 30) to compute this approximation.

Type $$n$$ (A number, decimal, fraction, up to 30) =

## Stirling Approximation Calculator

Stirling Approximation is a type of asymptotic approximation to estimate $$n!$$. What is the point of this you might ask? After all $$n!$$ can be computed easily (indeed, examples like $$2!$$, $$3!$$, those are direct).

Well, you are sort of right. The problem is when $$n$$ is large and mainly, the problem occurs when $$n$$ is NOT an integer, in that case, computing the factorial is really depending on using the Gamma function $$\Gamma$$, which is very computing intensive to domesticate.

That is where Stirling's approximation excels. The approximation is

$n! \approx \displaystyle\sqrt{2\pi n}\left(\frac{n}{e}\right)^n$

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