Ceiling Left in LaTeX (\lceil)

Where it is used

Left ceiling bracket, the opening half of the ceiling function that rounds up to an integer.

\lceil opens the ceiling notation \lceil x \rceil, the least integer at least x. It is a delimiter, so it works with \left\lceil ... \right\rceil for tall content like \frac{n}{2}, and with \big-style sizing. The ceiling bracket has its horizontal stroke on top, while the floor bracket \lfloor has it on the bottom, an easy pair to mix up when proofreading. Some authors also use \lceil and \rceil as corner quotes for Godel numbering, where \ulcorner is an alternative.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Ceiling Left: $\lceil$

\[ \lceil \log_2 n \rceil = k \iff 2^{k-1} < n \le 2^{k} \]
\end{document}

Related symbols

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

Frequently asked questions

How do I write Ceiling Left in LaTeX?

Type \lceil in math mode, for example $\lceil \log_2 n \rceil = k \iff 2^{k-1} < n \le 2^{k}$. It works in plain LaTeX without loading any package.

Which package do I need for \lceil?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\lceil$ in running text. If you only need the glyph in text, paste the Unicode character ⌈ instead (with XeLaTeX or LuaLaTeX and a font that has it).