Brackets and delimiters in LaTeX
Delimiters are the brackets that surround an expression; in LaTeX \left and \right automatically size any delimiter to its contents, and commands like \lfloor and \langle give special brackets.
LaTeX command
\left( \frac{a}{b} \right)Not the symbol you meant? Draw it to find the command →
The pair \left( ... \right) grows the parentheses to match whatever they enclose, so a tall fraction or a stacked sum gets full-height brackets. The delimiter after \left and \right can be any bracket: ( ) [ ] \{ \} | and more. They must always come in matching pairs, even if one side is invisible.
To leave one side open, use a full stop as the invisible delimiter: \left. ... \right| is the classic evaluation bar. Beyond the usual brackets, \lfloor and \rfloor give the floor function, \lceil and \rceil the ceiling, and \langle and \rangle the angle brackets used for inner products and sequences.
When \left and \right size a delimiter too aggressively, size it by hand with \big, \Big, \bigg and \Bigg. These are useful for nested brackets where you want the outer pair visibly larger. All of these delimiter commands are core LaTeX and render in KaTeX.
Other forms
\lfloor x \rfloorfloor\lceil x \rceilceiling\langle x, y \rangleangle bracketsExamples
$\left( \sum_{i=1}^n x_i \right)^2$parentheses auto-sized around a sum
$\lfloor 3.7 \rfloor = 3$the floor function
$\langle u, v \rangle$angle brackets for an inner product
$\left. \frac{dy}{dx} \right|_{x=0}$an evaluation bar with an invisible left delimiter
$\Bigg( \bigg( \Big( \big( x \big) \Big) \bigg) \Bigg)$manual bracket sizes from \big to \Bigg
Tips and common mistakes
\leftand\rightmust be balanced; every\leftneeds a matching\rightor compilation fails.- Use
\left.or\right.(with a full stop) to make one side invisible, as in an evaluation bar. - When auto-sizing looks wrong, set the size by hand with
\big,\Big,\biggand\Bigg. - For literal curly braces write \{ and \}; bare { and } are grouping characters and print nothing.
- Use
\langleand\ranglefor inner products, not the less-than and greater-than signs < and >.
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How do I auto-size brackets in LaTeX?
Wrap the content in \left( ... \right). The parentheses grow to match the height of what they enclose. This works for any delimiter, including [ ], \{ \} and |.
How do I write curly braces?
Escape them: \{ and \}. Unescaped { and } are grouping characters that produce no visible output, so you must escape them to print a literal brace.
How do I write floor and ceiling brackets?
Use \lfloor x \rfloor for the floor and \lceil x \rceil for the ceiling. Pair them with \left and \right if the content is tall.
How do I make an evaluation bar?
Use an invisible left delimiter: \left. \frac{dy}{dx} \right|_{x=0}. The \left. produces nothing, and \right| draws the bar with the subscript limit.