Missing \right inserted

This error happens when typesetting math if the \left command is used but the corresponding \right is missing. This article talks about common causes of this error and how to fix them.

Brief introduction to the \left and \right commands

The \left and \right commands typeset dynamically-sized delimiters and must be used together, within mathematical material, in the form

\[\verb'\left'\thinspace\textit{delim}_{\thinspace\text{L}}\quad\textit{math expression}\quad \verb'\right'\thinspace\textit{delim}_{\thinspace\text{R}}\]

where \(\textit{delim}_{\thinspace\text{L}}\) and \(\textit{delim}_{\thinspace\text{R}}\) are delimiters used to enclose your \(\textit{math expression}\). Typically, \(\textit{delim}_{\thinspace\text{L}}\) and \(\textit{delim}_{\thinspace\text{R}}\) are one of the characters () [] | \| \{ \} or the dot ‘.’, which is used as a “blank delimiter”.

Example

Here is an example using \left and \right to typeset parentheses which fully enclose a fraction:

\[ 
  \left(\frac{x}{y} \right)
\]

This code produces \[\left(\frac{x}{y}\right)\]

If you don’t use the \left and \right commands when placing delimiters, including parentheses, those delimiters will not fully enclose the mathematical expression; for example, writing

\[
  (\frac{x}{y})
\]

produces this

\[(\frac{x}{y})\]

Causes of this error and some solutions

Forgetting to include a \right command

Writing a \left command without its corresponding \right is a frequent cause of this error. This oversight, as illustrated in the example below, can lead to a cascade of errors, including Missing \right. inserted.

\[ 
\pi = 
\left( \int_{-\infty}^{+\infty} e^{-x^2} dx )
\]

 Open this error-generating example in Overleaf

To fix those errors, add the missing \right command:

\[ 
\pi = 
\left( \int_{-\infty}^{+\infty} e^{-x^2} dx \right)
\]

 Open this corrected example in Overleaf

This code produces the following output

\[ \pi = \left( \int_{-\infty}^{+\infty} e^{-x^2} dx \right) \]

Forgetting a blank delimiter

A common cause of this error occurs when trying to write functions such as the one shown below:

\[f(x)= \left\{\begin{array}{lr} 0 & x\leq 0 \\ 1 & x > 0 \end{array}\right.\]

If you attempt to typeset this function by writing

\[ 
f(x)= \left\{
  \begin{array}{lr} 
      0 & x\leq 0 \\
      1 & x > 0 
      \end{array}
\]

 Open this error-generating example in Overleaf

then you will generate errors because the \right delimiter is missing.

To typeset a \left delimiter only, use a dot character (‘.’) as the \right delimiter by writing \right. which, as shown below, typesets a blank, i.e. “null”, delimiter.

\[ 
f(x)= \left\{
  \begin{array}{lr} 
      0 & x\leq 0 \\
      1 & x > 0 
      \end{array}
\right.
\]

 Open this corrected example in Overleaf

This corrected example produces the desired result:

\[f(x)= \left\{\begin{array}{lr} 0 & x\leq 0 \\ 1 & x > 0 \end{array}\right.\]

Another option: use the cases environment

You can avoid direct use of \left and \right commands via the cases environment provided by the amsmath package. Our function can be typeset as shown below:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ 
f(x)= \begin{cases} 
      0 & x\leq 0 \\
      1 & x > 0 
      \end{cases}
\]
\end{document}

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Using line breaks inside \left and \right commands

When writing multi-line equations using the amsmath package environments align, align* or aligned, the \left and \right commands must be balanced on each line and on the same side of &. LaTeX will generate a series of errors if you try to include line breaks between pairs of \left and \right commands.

The following code snippet uses a line break (\\) between \left and \right commands, causing it to fail with errors:

\begin{align*}
y  = 1 + & \left(  \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \cdots  \\
  & \quad  + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right)
\end{align*}

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How to fix these errors: two solutions

Solution 1: Use blank delimiters

This solution uses blank delimiters by adding a \right. at the end of the first line, and a \left. at the start of the second line, after the &:

\begin{align*}
y  = 1 + & \left(  \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \cdots \right. \\
  &\left. \quad + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right)
\end{align*}

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This example produces the following output:

\[\begin{align*} y = 1 + & \left( \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \cdots \right. \\ &\left. \quad + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right)\end{align*}\]

Solution 2: Manually select the delimiter sizes

We can use \biggl( and \biggr) because they will work across the line break:

\begin{align*}
y  = 1 + & \biggl(  \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \cdots  \\
  & \quad + \frac{1}{x^{n-1}} + \frac{1}{x^n} \biggr)
\end{align*}

 Open this corrected LaTeX fragment in Overleaf

This solution produces the same result:

\[\begin{align*}y = 1 + & \left( \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \cdots \right. \\ &\left. \quad + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right)\end{align*}\]

Some notes on manually selecting delimiter sizes

LaTeX provides a number of commands to manually set the delimiter size. Delimiters selected by those commands are a fixed size—they are not sized dynamically to suit the math expression they enclose. They have the advantage of not needing to be paired in the same way as \left and \right commands.

The size of delimiter, in order of increasing size, is \big, \Big, \bigg, and \Bigg; for example: