# Stirling's approximation

(definition)

**Definition:**
For large values of n, *n!* ≈ (n/e)^{n} √(2nπ).

**See also**
*factorial*, *gamma function*.

*Note:
This approximation is taken directly from **Stirling's formula*.

Author: PEB

## More information

Peter Luschny lists and evaluates many approximation formulas for n!. See Eric W. Weisstein, Stirling's Approximation for a derivation and other approximations. A slightly different approximation and relative errors from Bart j. Van Zeghbroeck's book.

Go to the
Dictionary of Algorithms and Data
Structures home page.

If you have suggestions, corrections, or comments, please get in touch
with Paul Black.

Entry modified 4 May 2009.

HTML page formatted Mon Feb 2 13:10:40 2015.

Cite this as:

Paul E. Black, "Stirling's approximation", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 4 May 2009. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/stirlingsApproximation.html