Stirling's formula
Stirling showed that with the constant $k = e$ the sequence $(x_{n})$ with $x_{n} = n! \Large\frac{k^{n}}{n^{n+\frac 1 2}}$ converges to $\sqrt{2\pi}$.
This means that for large $n$ we have the approximation $n! \approx \sqrt {2\pi n} \Large (\frac{n}{e})\large ^{n}$.
This means that for large $n$ we have the approximation $n! \approx \sqrt {2\pi n} \Large (\frac{n}{e})\large ^{n}$.
n  n!  Stirling's approximation

10  3.629 × 106  3.604 × 106

100  9.333 × 10157  9.425 × 10157

1000  4.024 × 102576  4.464 × 102576 