Ceiling function

The ceiling function, also known as the "least integer function," gives the least integer greater than or equal to its argument. The ceiling of $x$ is usually denoted by $\lceil x \rceil$. The action of the function is also described by the phrase "rounding up." On the negative real numbers, this corresponds to the action "dropping everything after the decimal point".


  • $\lceil 3.14 \rceil = 4$
  • $\lceil 5 \rceil = 5$
  • $\lceil -3.2\rceil = -3$
  • $\lceil 100.2 \rceil = 101$

Relation to the Floor Function

For an integer, the ceiling function is equal to the floor function. For any other number, the ceiling function is the floor function plus one.

See Also