In mathematical notation, the absolute value symbol is used to represent the distance of a number from zero, regardless of its sign. This symbol is essential for expressing a wide range of mathematical concepts from basic algebra to advanced calculus.

This article will explore different ways how to typeset the absolute value symbol in LaTeX so you can include it in your document according to its context.

Using the pipe character

There are several ways to typeset the absolute value symbol in LaTeX:

Using the pipe character.
Using the \left| and \right| notation.
Using the \lvert and \rvert notation.
Using the \vert notation.
Using the \abs notation.

The basic way to write the absolute value symbol in LaTeX is to use the pipe character (|) found just right above the Enter key of your keyboard.

You can also use a keyboard shortcut Alt+124. All you have to do is to turn on the numeric keypad, hold Alt and then press 1, 2, and 4.

Using the \left| and \right| notation

This way of typesetting the absolute value symbol will use the \left and \right commands. You do not need to use any package to use these commands.

What’s nice about this notation is that they set the size of the absolute value symbol based on the contents inside the symbol.

This becomes useful when you want to typeset the absolute value of an expression that may change in size, such as an equation. The adjustment in size ensures that the symbol is always the appropriate size.

Note: It is crucial to make sure that the left and right delimiters match properly, as this can affect the visual appearance of the equation.

Using the \lvert and \rvert notation

This is another way of writing the absolute value symbol in LaTeX. The \lvert and \rvert are basic LaTeX commands that can be used without the need to load any additional packages.

This notation will not automatically adjust the symbol accordingly to fit the contents inside. Thus, this is commonly used in text mode.

Using the \vert notation

The \vert notation is similar to \lvert notation, but it does not adjust the size of the symbol based on the contents inside.

This notation is commonly used in text mode where the absolute value symbol will be the same size as the text.

Using the \abs notation

This notation uses the \abs command which is provided by the amsmath package. Again, this is another way of including the absolutely value symbol in your LaTeX document.

The \abs notation is the most semantic way of typesetting the absolute value notation if you’re using it in a mathematical equation. The issue is that it does not automatically typeset the bar symbol because if you come to think of it, the bar symbol is not always the best way to represent the absolute value.

Use this notation in conjunction with the different notations we mentioned above.

Seeing it in action

Here’s an example code to put everything that we have in this article.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\section*{Using the pipe character}
A simple inline example of an absolute value function is $|x+y|$. \\
A slightly complicated example is $|\frac{x+1}{x^2+1}|$.

\begin{equation}
    |\frac{x+1}{x^2+1}|
\end{equation}

\section*{Using the left notation}
A simple inline example of an absolute value function is $\left| x+y \right|$. \\
A slightly complicated example is $\left| \frac{x+1}{x^2+1} \right|$.

\begin{equation}
    \left| \frac{x+1}{x^2+1} \right|
\end{equation}

\section*{Using the lvert notation}
A simple inline example of an absolute value function is $\lvert x+y \rvert$. \\
A slightly complicated example is $\lvert \frac{x+1}{x^2+1} \rvert$.

\begin{equation}
    \lvert \frac{x+1}{x^2+1} \rvert
\end{equation}

\section*{Using the vert notation}
A simple inline example of an absolute value function is $\vert x+y \vert$. \\
A slightly complicated example is $\vert \frac{x+1}{x^2+1} \vert$.

\begin{equation}
    \vert \frac{x+1}{x^2+1} \vert
\end{equation}

\end{document}

Final thoughts

It’s important to note that the size of the absolute value symbol may need to be adjusted according to its context. While we can use any of the notations we have outlined in this article, it’s always good to choose one and be consistent when using it throughout your LaTeX document.