Ceiling

The ceiling of a real number \(x,\) denoted \(\lceil x \rceil\) or sometimes \(\operatorname{ceil}(x),\) is the first integer \(n \ge x.\) For example, \(\lceil 3.72 \rceil = 4, \lceil 4 \rceil = 4,\) and \(\lceil -3.72 \rceil = -3.\) In other words, the ceiling function rounds its input up to the nearest integer.

For the function that rounds its input down to the nearest integer, see floor. Ceiling and floor are not to be confused with fix and ceilfix, which round towards and away from zero (respectively).

Formally, ceiling is a function of type \(\mathbb R \to \mathbb Z.\) The ceiling function can also be defined on complex numbers.