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# Ceiling

(Redirected from Ceiling function)
Ceiling is a function that gives the smallest integer above a given real number ${\displaystyle x}$. It is generally notated ${\displaystyle \lceil x\rceil }$, or in computer programming languages, ceil(x). For example, ${\displaystyle \lceil {\sqrt {48}}\rceil =7}$. For ${\displaystyle x\leq 0}$, ${\displaystyle \lceil x\rceil }$ is the same as the integer part of ${\displaystyle x}$; but if ${\displaystyle x>0}$, then ${\displaystyle \lceil x\rceil }$ is one more than the integer part. For example, ${\displaystyle \lceil \pi ^{2}\rceil =10}$, but for ${\displaystyle \lceil (\pi i)^{2}\rceil =-9}$.