Floor Function

Pronunciation: /flɔr ˈfʌŋk ʃən/ Explain

A graph showing the floor function.
Figure 1: Floor function.

The floor function is a function that returns the largest integer less than or equal to the argument. The floor function is denoted ⌊x⌋. A floor function is a type of step function.

-4⌊-4⌋ = -4
-3.5⌊-3.5⌋ = -4
-0.5⌊-0.5⌋ = -1
0⌊0⌋ = 0
0.5⌊0.5⌋ = 0
1.375⌊1.375⌋ = 1
22.2⌊22.2⌋ = 22
1394.75⌊1394.75⌋ = 1394
Table 1


  1. Richard Crandall, Carl Pomerance . Prime Numbers: A Computational Perspective. 2nd edition. Ch. 3.1. Springer. August 4, 2005. Buy the book
  2. Refaat El Attar. Special Functions and Orthogonal Polynomials. 2nd edition. pg 102. Lulu.com. February 2, 2006. Buy the book
  3. Mike Faust. SQL Built-In Functions and Stored Procedures: The i5/iSeries Programmer's Guide. pg 27. Mc Press. June 15, 2005. Buy the book

More Information

  • McAdams, David E.. Ceiling Function. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 10/25/2009. http://www.allmathwords.org/en/c/ceilingfunction.html.

Cite this article as:

McAdams, David E. Floor Function. 7/11/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/floorfunction.html.

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Revision History

7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/4/2010: Added "References". (McAdams, David E.)
1/13/2009: Initial version. (McAdams, David E.)

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