Stirling showed that with the constant *k* = *e* the sequence (*x*_{n}) with *x*_{n} = ^{n!kn}/_{}*n*^{n+½} converges to √(2π).

This means that for large *n* we have the approximation *n*! ≈ √(2π*n*) (^{n}/_{e})^{n}.

n | n! | Stirling's approximation |
---|---|---|

10 | 3.629 × 10^{6} | 3.604 × 10^{6} |

100 | 9.333 × 10^{157} | 9.425 × 10^{157} |

1000 | 4.024 × 10^{2576} | 4.464 × 10^{2576} |