The ceiling of a real number is the smallest integer greater than or equal to the number. The ceiling of x is usually denoted by x.

Some examples: 6.2=7, 0.4=1, 7=7, -5.1=-5, π=4, -4=-4.

Note that this function is not the integer part ([x]), since 3.5=4 and [3.5]=3.

The notation for floor and ceiling was introduced by Iverson in 1962[1].


  • 1 N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.
Title ceiling
Canonical name Ceiling
Date of creation 2013-03-22 11:48:21
Last modified on 2013-03-22 11:48:21
Owner yark (2760)
Last modified by yark (2760)
Numerical id 17
Author yark (2760)
Entry type Definition
Classification msc 26A09
Classification msc 11-00
Synonym ceiling function
Synonym smallest integer function
Synonym smallest integer greater than or equal to
Related topic BeattysTheorem
Related topic Floor