> For the complete documentation index, see [llms.txt](https://overleaf-pro.ayaka.space/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://overleaf-pro.ayaka.space/latex/mathematics/03-brackets-and-parentheses.md). # Brackets and Parentheses ## Introduction Parentheses and brackets are very common in mathematical formulas. You can easily control the size and style of brackets in LaTeX; this article explains how. Here's an table of listing some common math braces and parentheses used in LaTeX: | Type | LaTeX markup | Renders as | | --------------------------- | --------------------- | -------------------------- | | Parentheses; round brackets | `(x+y)` | $$(x+y)$$ | | Brackets; square brackets | `[x+y]` | $$\[x+y]$$ | | Braces; curly brackets | `\{ x+y \}` | $${ x+y }$$ | | Angle brackets | `\langle x+y \rangle` | $$\langle x+y\rangle$$ | | Pipes; vertical bars | `\|x+y\|` | $$\displaystyle\| x+y \|$$ | | Double pipes | \`\\ | x+y\\ | ## Some examples The size of brackets and parentheses can be manually set, or they can be resized dynamically in your document, as shown in the next example: ```latex \[ F = G \left( \frac{m_1 m_2}{r^2} \right) \] ``` [Open this LaTeX fragment in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+1\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cbegin%7Bdocument%7D%0A%5C%5B+%0AF+%3D+G+%5Cleft%28+%5Cfrac%7Bm_1+m_2%7D%7Br%5E2%7D+%5Cright%29%0A%5C%5D%0A%5Cend%7Bdocument%7D) The above example produces the following output: $$F = G \left( \frac{m\_1 m\_2}{r^2} \right)$$ Notice that to insert the parentheses or brackets, the `\left` and `\right` commands are used. Even if you are using only one bracket, *both* commands are mandatory. `\left` and `\right` can dynamically adjust the size, as shown by the next example: ```latex \[ \left[ \frac{ N } { \left( \frac{L}{p} \right) - (m+n) } \right] \] ``` [Open this LaTeX fragment in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+2\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cbegin%7Bdocument%7D%0A%5C%5B+%0A+%5Cleft%5B++%5Cfrac%7B+N+%7D+%7B+%5Cleft%28+%5Cfrac%7BL%7D%7Bp%7D+%5Cright%29++-+%28m%2Bn%29+%7D++%5Cright%5D%0A%5C%5D%0A%5Cend%7Bdocument%7D) The above example produces the following output: $$\left\[ \frac{ N } { \left( \frac{L}{p} \right) - (m+n) } \right]$$ When writing multi-line equations with the `align`, `align*` or `aligned` environments, the `\left` and `\right` commands must be balanced *on each line and on the same side of `&`*. Therefore the following code snippet will fail with errors: ```latex \begin{align*} y = 1 + & \left( \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \ldots \\ & \quad + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right) \end{align*} ``` [Open this LaTeX fragment in Overleaf (with errors)](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+with+errors\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Balign%2A%7D%0Ay++%3D+1+%2B+%26+%5Cleft%28++%5Cfrac%7B1%7D%7Bx%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E2%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E3%7D+%2B+%5Cldots++%5C%5C%0A++%26+%5Cquad++%2B+%5Cfrac%7B1%7D%7Bx%5E%7Bn-1%7D%7D+%2B+%5Cfrac%7B1%7D%7Bx%5En%7D+%5Cright%29%0A%5Cend%7Balign%2A%7D%0A%5Cend%7Bdocument%7D) The solution is to use "invisible" brackets to balance things out, i.e. adding a `\right.` at the end of the first line, and a `\left.` at the start of the second line after `&`: ```latex \begin{align*} y = 1 + & \left( \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \ldots \right. \\ &\left. \quad + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right) \end{align*} ``` [Open this LaTeX fragment in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+4\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Balign%2A%7D%0Ay++%3D+1+%2B+%26+%5Cleft%28++%5Cfrac%7B1%7D%7Bx%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E2%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E3%7D+%2B+%5Cldots+%5Cright.+%5C%5C%0A++%26%5Cleft.+%5Cquad+%2B+%5Cfrac%7B1%7D%7Bx%5E%7Bn-1%7D%7D+%2B+%5Cfrac%7B1%7D%7Bx%5En%7D+%5Cright%29%0A%5Cend%7Balign%2A%7D%0A%5Cend%7Bdocument%7D) The above example produces the following output: ![Paren-ex03.png](/files/fRdt4C0hTqZJ3HGwM775) ## Controlling types and sizes The size of the brackets can be controlled explicitly, as shown in this LaTeX code fragment: ```latex \[ \Biggl \langle 3x+7 \biggr \rangle \] ``` [Open this LaTeX fragment in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+5\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cbegin%7Bdocument%7D%0A%5C%5B%0A+%5CBiggl+%5Clangle+3x%2B7+%5Cbiggr+%5Crangle%0A%5C%5D%0A%5Cend%7Bdocument%7D) The above example produces the following output: $$\Biggl \langle 3x+7 \biggr \rangle$$ The commands `\Biggl` and `\biggr` establish the size of the delimiters `<` and `>` respectively, with the `l` or `r` indicating whether it's the left or the right parenthesis. For a complete list of parentheses and sizes see the [reference guide](#reference-guide). ## Reference guide | LaTeX markup | Renders as | | ----------------------------------------------------------- | --------------------------------------------------------- | | `\bigl( \Bigl( \biggl( \Biggl(` | $$\big( \Big( \bigg( \Bigg($$ | | `\bigr] \Bigr] \biggr] \Biggr]` | $$\big] \Big] \bigg] \Bigg]$$ | | `\bigl\{ \Bigl\{ \biggl\{ \Biggl\{` | $$\big{ \Big{ \bigg{ \Bigg{$$ | | `\bigl \langle \Bigl \langle \biggl \langle \Biggl \langle` | $$\big \langle \Big \langle \bigg \langle \Bigg \langle$$ | | `\bigr \rangle \Bigr \rangle \biggr \rangle \Biggr \rangle` | $$\big \rangle \Big \rangle \bigg \rangle \Bigg \rangle$$ | | `\big\| \Big\| \bigg\| \Bigg\|` | $$\big\| ; \Big\| ; \bigg\| ; \Bigg\|$$ | | \`\big\\ | \Big\\ | | `\bigl \lceil \Bigl \lceil \biggl \lceil \Biggl \lceil` | $$\big \lceil \Big \lceil \bigg \lceil \Bigg \lceil$$ | | `\bigr \rceil \Bigr \rceil \biggr \rceil \Biggr \rceil` | $$\big \rceil \Big \rceil \bigg \rceil \Bigg \rceil$$ | | `\bigl \lfloor \Bigl \lfloor \biggl \lfloor \Biggl \lfloor` | $$\big \lfloor \Big \lfloor \bigg \lfloor \Bigg \lfloor$$ | | `\bigr \rfloor \Bigr \rfloor \biggr \rfloor \Biggr \rfloor` | $$\big \rfloor \Big \rfloor \bigg \rfloor \Bigg \rfloor$$ | ## Further reading * [Mathematical expressions](/latex/mathematics/01-mathematical-expressions.md) * [Subscripts and superscripts](/latex/mathematics/02-subscripts-and-superscripts.md) * [Aligning equations with amsmath](/latex/mathematics/06-aligning-equations-with-amsmath.md) * [Display style in math mode](/latex/mathematics/10-display-style-in-math-mode.md) * [Operators](/latex/mathematics/07-operators.md) * [The not so short introduction to LaTeX2ε](http://www.ctan.org/tex-archive/info/lshort/) --- # Agent Instructions This documentation is published with GitBook. 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