Ceiling in LaTeX (\lceil x \rceil)

Where it is used

Rounds x up to the smallest integer greater than or equal to it: the ceiling function.

Ceilings show up in algorithm analysis (\lceil \log_2 n \rceil comparisons, \lceil n/2 \rceil in merge sort), in number theory, and in counting problems like the pigeonhole principle, where some box holds at least \lceil n/k \rceil items. For negative inputs remember that \lceil -2.5 \rceil = -2. When the argument is a fraction or a tall expression, use \left\lceil ... \right\rceil so the brackets grow. Do not substitute square brackets [x]: older texts used [x] for the floor, which makes it ambiguous.

Also listed under: Number Theory, Computer Science

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Ceiling: $\lceil x \rceil$

\[ \left\lceil \frac{n}{k} \right\rceil \ge \frac{n}{k} \]
\end{document}

Related symbols

• Floor Left\lfloor
• Ceiling Right\rceil
• Floor Right\rfloor
• Ceiling Left\lceil
• Floor\lfloor x \rfloor
• Angle Brackets\langle x \rangle

Frequently asked questions

How do I write Ceiling in LaTeX?

Type \lceil x \rceil in math mode, for example $\left\lceil \frac{n}{k} \right\rceil \ge \frac{n}{k}$. It works in plain LaTeX without loading any package.

Which package do I need for \lceil x \rceil?

None. \lceil x \rceil is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \lceil x \rceil in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\lceil x \rceil$ in running text.