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Stirling’s formula
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Quick Facts
Also called:
Stirling’s approximation
Key People:
Abraham de Moivre
James Stirling
Related Topics:
factorial
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Stirling’s formula

mathematics
Also known as: Stirling’s approximation
Written by
William L. Hosch
William L. Hosch was an editor at EncyclopĂŚdia Britannica.
William L. Hosch
Fact-checked by
Britannica Editors
Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree....
Britannica Editors
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•History

Stirling’s formula, in analysis, a method for approximating the value of large factorials (written n!; e.g., 4! = 1 × 2 × 3 × 4 = 24) that uses the mathematical constants e (the base of the natural logarithm) and π. The formula is given by Stirling's Formula

The Scottish mathematician James Stirling published his formula in Methodus Differentialis sive Tractatus de Summatione et Interpolatione Serierum Infinitarum (1730; “Differential Method with a Tract on Summation and Interpolation of Infinite Series”), a treatise on infinite series, summation, interpolation, and quadrature.

For practical computations, Stirling’s approximation, which can be obtained from his formula, is more useful: lnn! ≅ nlnn − n, where ln is the natural logarithm. Using existing logarithm tables, this form greatly facilitated the solution of otherwise tedious computations in astronomy and navigation.

William L. Hosch