Ceiling

Ceiling[x]

gives the smallest integer greater than or equal to x.

Ceiling[x,a]

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

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Ceiling[x] can be entered in StandardForm and InputForm as ⌈x⌉, lc rc or
    ∖[LeftCeiling]x∖[RightCeiling].
  • 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.

Examples

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Basic Examples  (2)

Round up to the nearest integer:

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Round up to the nearest multiple of 10:

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Scope  (17)

Generalizations & Extensions  (5)

Applications  (4)

Properties & Relations  (9)

Possible Issues  (1)

Neat Examples  (1)

Introduced in 1988
(1.0)
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Updated in 2007
(6.0)