gives the smallest integer greater than or equal to x.

gives the smallest multiple of a greater than or equal to x.


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Ceiling[x] can be entered in StandardForm and InputForm as x, EsclcEsc EscrcEsc or
  • Ceiling[x] returns an integer when is any numeric quantity, whether or not it is an explicit number.
  • For exact numeric quantities, Ceiling internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
  • Ceiling applies separately to real and imaginary parts of complex numbers.
  • Ceiling automatically threads over lists.
Introduced in 1988
| Updated in 2007