NIST

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.


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 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