Aligning equations with amsmath

The amsmath package provides a handful of options for displaying equations. You can choose the layout that better suits your document, even if the equations are really long, or if you have to include several equations in the same line.

Introduction

The standard LaTeX tools for equations may lack some flexibility, causing overlapping or even trimming part of the equation when it's too long. We can surpass these difficulties with amsmath. Let's check an example:

\begin{equation} \label{eq1}
\begin{split}
A & = \frac{\pi r^2}{2} \\
 & = \frac{1}{2} \pi r^2
\end{split}
\end{equation}

You have to wrap your equation in the equation environment if you want it to be numbered, use equation* (with an asterisk) otherwise. Inside the equation environment, use the split environment to split the equations into smaller pieces, these smaller pieces will be aligned accordingly. The double backslash works as a newline character. Use the ampersand character &, to set the points where the equations are vertically aligned.

  Open an example of the amsmath package in Overleaf

Including the amsmath package

This is a simple step, if you use LaTeX frequently surely you already know this. In the preamble of the document include the code:

\usepackage{amsmath}

  Open an example of the amsmath package in Overleaf

Writing a single equation

To display a single equation, as mentioned in the introduction, you have to use the equation* or equation environment, depending on whether you want the equation to be numbered or not. Additionally, you might add a label for future reference within the document.

\begin{equation} \label{eu_eqn}
e^{\pi i} + 1 = 0
\end{equation}

The beautiful equation \ref{eu_eqn} is known as the Euler equation

  Open an example of the amsmath package in Overleaf

Displaying long equations

For equations longer than a line use the multline environment. Insert a double backslash to set a point for the equation to be broken. The first part will be aligned to the left and the second part will be displayed in the next line and aligned to the right.

Again, the use of an asterisk * in the environment name determines whether the equation is numbered or not.

\begin{multline*}
p(x) = 3x^6 + 14x^5y + 590x^4y^2 + 19x^3y^3\\ 
- 12x^2y^4 - 12xy^5 + 2y^6 - a^3b^3
\end{multline*}

  Open an example of the amsmath package in Overleaf

Splitting and aligning an equation

Split is very similar to multline. Use the split environment to break an equation and to align it in columns, just as if the parts of the equation were in a table. This environment must be used inside an equation environment. For an example check the introduction of this document.

Aligning several equations

If there are several equations that you need to align vertically, the align environment will do it:

\begin{align*} 
2x - 5y &=  8 \\ 
3x + 9y &=  -12
\end{align*}

Usually the binary operators (>, < and =) are the ones aligned for a nice-looking document.

As mentioned before, the ampersand character & determines where the equations align. Let's check a more complex example:

\begin{align*}
x&=y           &  w &=z              &  a&=b+c\\
2x&=-y         &  3w&=\frac{1}{2}z   &  a&=b\\
-4 + 5x&=2+y   &  w+2&=-1+w          &  ab&=cb
\end{align*}

Here we arrange the equations in three columns. LaTeX assumes that each equation consists of two parts separated by a &; also that each equation is separated from the one before by an &.

Again, use * to toggle the equation numbering. When numbering is allowed, you can label each row individually.

  Open an example of the amsmath package in Overleaf

Grouping and centering equations

If you just need to display a set of consecutive equations, centered and with no alignment whatsoever, use the gather environment. The asterisk trick to set/unset the numbering of equations also works here.

\begin{gather*} 
2x - 5y =  8 \\ 
3x^2 + 9y =  3a + c
\end{gather*}

  Open an example of the amsmath package in Overleaf

Further reading

For more information see

• Mathematical expressions
• Brackets and Parentheses
• Subscripts and superscripts
• Spacing in math mode
• Display style in math mode
• Mathematical fonts
• List of Greek letters and math symbols
• Operators
• Fractions and Binomials
• amsmath package documentation