gives the greatest integer less than or equal to x.

gives the greatest multiple of a less than or equal to x.


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