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A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. In this work, the term "constant" is generally reserved for real nonintegral numbers of interest, while "number" is used to refer to interesting integers (e.g., Brun's constant, but beast number). However, in contexts such as linear combination, the term "constant" is generally used to mean "scalar" or "real number," and need not exclude integer values.

A constant function assumes the same value at every point of its domain.

Certain constants are known to many decimal digits and recur throughout many diverse areas of mathematics, often in unexpected and surprising places (e.g., pi, e, and to some extent, the Euler-Mascheroni constant ). Other constants are more specialized and may be known to only a few digits. S. Plouffe maintains a site about the computation and identification of numerical constants. Plouffe's site also contains a page giving the largest number of digits computed for the most common constants. S. Finch maintains a delightful, more expository site containing detailed essays and references on constants both common and obscure.

The mathematician Glaisher remarked, "No doubt the desire to obtain the values of these quantities to a great many figures is also partly due to the fact that most of them are interesting in themselves; for , , , , and many other numerical quantities occupy a curious, and some of them almost a mysterious, place in mathematics, so that there is a natural tendency to do all that can be done towards their precise determination" (Glaisher 1915, p. 79).

The following table lists some common constants, their symbols, and approximate values.

Gourdon and Sebah and Lyster maintain web pages comparing the fastest known algorithms for computing digits of common constants.

See also

Coefficient, Constant Function, Constant of Integration, Constant Polynomial, Number, Piecewise Constant Function, Real Number, Scalar

Related Wolfram sites

https://functions.wolfram.com/Constants/

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References

Bailey, D. H. and Crandall, R. E. "On the Random Character of Fundamental Constant Expansions." Exper. Math. 10, 175-190, 2001. https://doi.org/10.1080/10586458.2001.10504441.Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, p. 145, 2003.Borwein, J. and Borwein, P. A Dictionary of Real Numbers. London, England: Chapman & Hall, 1990.Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, 2003.Finch, S. R. Mathematical Constants II. Cambridge, England: Cambridge University Press, 2019.Finch, S. R. "Errata and Addenda to Mathematical Constants." 27 May 2024. https://arxiv.org/abs/2001.00578.Glaisher, J. W. L. "Logarithms and Computation." In Napier Tercentenary Memorial Volume (Ed. C. G. Knott). London, England: Longmans, Green and Company, pp. 63-80, 1915. https://archive.org/details/napiertercentena00knotuoft/page/79/mode/1up.Gourdon, X. and Sebah, P. "Numbers, Constants and Computation." http://numbers.computation.free.fr/Constants/constants.html.Gourdon, X. and Sebah, P. "User Constants (Compute log(2), zeta(3), Catalan Constant, Pi with Arctan Formulas ... with pifast." http://numbers.computation.free.fr/Constants/PiProgram/userconstants.html.Gourdon, X. and Sebah, P. "Constants and Records of Computation." http://numbers.computation.free.fr/Constants/Miscellaneous/Records.html.Jasinski, A. "The On-Line Encyclopedia of the Mathematical Constants." https://oemc.pl/.Kondo, S. "PI WORLD OF JA0HXV." http://ja0hxv.calico.jp/pai/estart.html.Le Lionnais, F. Les nombres remarquables. Paris, France: Hermann, 1983.Lyster, S. "Stu's Pi Page: The Fastest Pi Programs on the Planet." https://web.archive.org/web/20080825030820/http://home.istar.ca/~lyster/otherconstants.html.Michon, G. P. "Final Answers: Numerical Constants." https://www.numericana.com/answer/constants.htm.Munafo, R. "Notable Properties of Specific Numbers." http://home.earthlink.net/~mrob/pub/math/numbers.html.Niklasch, G. "Some Number-Theoretical Constants Arising as Products of Rational Functions of over the Primes." https://guests.mpim-bonn.mpg.de/moree/Moree.en.html. Pegg, E. Jr. Mathematical Games. Episode 36: "Mathematical Constants." Dec. 18, 2025. https://www.youtube.com/watch?v=4cyETT3Xgwk. https://community.wolfram.com/t/26244.Plouffe, S. "Plouffe's Inverter." https://web.archive.org/web/20050812010306/http://pi.lacim.uqam.ca/eng/.Plouffe, S. "Plouffe's Inverter: Table of Current Records for the Computation of Constants." https://www.plouffe.fr/simon/articles/TableofRecords.pdf.Plouffe, S. "Miscellaneous Mathematical Constants." https://web.archive.org/web/20071201153419/http://www.worldwideschool.org:80/library/books/sci/math/MiscellaneousMathematicalConstants/toc.html.Robinson, H. P. and Potter, E. Mathematical Constants. Report UCRL-20418. Berkeley, CA: University of California, 1971.Sloane, N. J. A. Sequences A000796, A001113, A001620, A001622, A002117, A002162, A002193, A002210, A002580, A006752, A070769, and A074962 in "The On-Line Encyclopedia of Integer Sequences."Trott, M. "Mathematical Constants." §2.2.4 in The Mathematica GuideBook for Programming. New York: Springer-Verlag, pp. 171-180, 2004. https://www.mathematicaguidebooks.org/.Wells, D. W. The Penguin Dictionary of Curious and Interesting Numbers. Harmondsworth, England: Penguin Books, 1986.

Referenced on Wolfram|Alpha

Constant

Cite this as:

Weisstein, Eric W. "Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Constant.html

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