# Stirling's formula

(definition)

**Definition:**
For large values of n, (n/e)^{n} √(2nπ) < *n!* < (n/e)^{n}(1 + 1/(12n-1)) √(2nπ).

**See also**
*Stirling's approximation*, *factorial*, *gamma function*.

*Note:
After CRC Standard Mathematical Tables, Fourteenth Edition, Samuel M. Selby, ed., page 433, 1965.*

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.

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Entry modified 10 November 2008.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Paul E. Black, "Stirling's formula", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 10 November 2008. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/stirlingsFormula.html