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Ceiling

Ceiling[x]
gives the smallest integer greater than or equal to x.
Ceiling
gives the smallest multiple of a greater than or equal to x.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • 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.
Round up to the nearest integer:
Round up to the nearest multiple of 10:
Round up to the nearest integer:
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Round up to the nearest multiple of 10:
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Use exact numeric quantities:
Ceiling threads element-wise over lists:
Round up to the nearest multiple of :
Manipulate Ceiling symbolically:
Evaluate an integral:
TraditionalForm formatting:
Evaluate for complex numbers:
Ceiling can deal with real-valued intervals:
Infinite arguments give symbolic results:
Series expansion:
Use Esc lc Esc and Esc rc Esc to enter a short notation for Ceiling:
Self-counting sequence:
Minimal number of elements in a box according to the pigeonhole principle:
Negative numbers round up to the nearest integer above:
Convert Ceiling to Piecewise:
De-nest Ceiling functions:
Reduce equations containing Ceiling:
Ceiling function in the complex plane:
Ceiling does not automatically resolve the value:
Convergence of the Fourier series of Ceiling:
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