LaTeX Equation Numbering and Referencing: \label, \eqref, \tag and align

LaTeX numbers every equation environment automatically, and a \label inside it lets you cite that number anywhere in the text with \eqref. That is the whole system for a single-line equation. The questions start with everything else: how to number equations per section, how to break a long equation onto a new line, how to number a multi-line derivation once or on every line, how to write (1a) and (1b), how to replace the number with a custom tag, and how to turn numbering off. This guide answers all of them with amsmath and cleveref.

Numbered and Unnumbered Equations

The equation environment produces a centered, numbered display. Its starred twin equation*, provided by amsmath, produces the same display without a number, and \[ ... \] is a shorthand for it. Load amsmath in every document that contains math; almost everything in this guide depends on it.

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{equation}
  E = mc^2
\end{equation}

\begin{equation*}
  a^2 + b^2 = c^2
\end{equation*}

\[ F = ma \]

\end{document}

The first display is “(1)”; the other two are unnumbered. The rule of thumb used by most journals: number an equation only if you refer to it somewhere. Avoid the plain TeX $$ ... $$ form; it has wrong spacing with amsmath and does not support \tag or \label properly.

Referencing an Equation: \label, \ref and \eqref

Put \label anywhere inside the numbered environment. Three commands read it back:

\begin{equation}
  \label{eq:energy}
  E = mc^2
\end{equation}

Equation~\ref{eq:energy} ...      % prints: Equation 1
Equation~(\ref{eq:energy}) ...    % prints: Equation (1)
Equation~\eqref{eq:energy} ...    % prints: Equation (1), with amsmath
on page~\pageref{eq:energy}        % prints: on page 4

• \ref prints the bare number. You add the parentheses yourself.
• \eqref (amsmath) prints the number with parentheses, in upright text even inside italics, exactly as the equation itself shows it. Use it for equations.
• The tilde ~ is a non-breaking space; it stops “Equation” and “(1)” from landing on different lines.

Labels are resolved on the next compilation run, so the first build after adding a label shows ?? and the warning Label(s) may have changed. Rerun to get cross-references right. Compile twice, or use latexmk, which reruns as needed.

Pick a naming convention and keep it: eq: for equations, fig: for figures, tab: for tables, sec: for sections. The prefix is only a convention, but it makes \ref commands readable and prevents an equation and a figure from sharing a label by accident.

cleveref: \cref and \Cref

The cleveref package writes the word “equation” for you and handles lists and ranges. Load it after hyperref if you use that, and after amsmath:

\usepackage{amsmath}
\usepackage{hyperref}
\usepackage{cleveref}

See \cref{eq:energy}.                      % eq. (1)
See \Cref{eq:energy}.                      % Equation (1), at sentence start
See \cref{eq:energy,eq:momentum}.          % eqs. (1) and (2)
See \crefrange{eq:first}{eq:last}.         % eqs. (1) to (5)

% Change the wording once in the preamble
\crefname{equation}{Eq.}{Eqs.}
\Crefname{equation}{Equation}{Equations}

With hyperref, every reference becomes a clickable link to the equation. See LaTeX Hyperlinks for the loading order and link colors.

Numbering Within Sections or Chapters

In article, equations are numbered 1, 2, 3 through the whole document. In book and report they are numbered per chapter: (2.1), (2.2). To number per section in any class, use \numberwithin from amsmath:

\usepackage{amsmath}
\numberwithin{equation}{section}   % (1.1), (1.2), (2.1), ...

% In book/report, per section instead of per chapter:
\numberwithin{equation}{section}   % (1.1.1), (1.1.2), ...

% Change only the printed form, keeping the counter global
\renewcommand{\theequation}{\Roman{equation}}       % (I), (II), ...
\renewcommand{\theequation}{\thesection-\arabic{equation}}  % (1-1), (1-2)

\numberwithin both resets the equation counter at each section and prefixes the section number. The kernel command \counterwithin does the same without amsmath, and \counterwithout undoes it, which is how you get document-wide numbering in a book: \counterwithout{equation}{chapter}.

Numbers on the left

Equation numbers sit at the right margin by default. The leqno option moves them to the left, and fleqn left-aligns the equations themselves instead of centering them. Both are class options that amsmath also accepts:

\documentclass[leqno]{article}      % numbers on the left
\documentclass[fleqn]{article}      % equations flush left
\usepackage[leqno, fleqn]{amsmath}  % same, as package options

Custom Tags: \tag and \tag*

\tag replaces the automatic number with any text for that one equation. The equation counter is not advanced, so the next automatic number continues as if the tagged equation were not there. \tag* prints the tag without parentheses:

\begin{equation}
  \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \tag{Gauss}
\end{equation}

\begin{equation}
  x^2 + y^2 = r^2 \tag*{(circle)}
\end{equation}

% Tags work in the starred environments too
\begin{align*}
  f(x) &= x^2 \tag{A} \\
  g(x) &= 2x \tag{B} \label{eq:B}
\end{align*}

% Reuse an earlier number, e.g. when repeating an equation
\begin{equation}
  E = mc^2 \tag{\ref{eq:energy}}
\end{equation}

A tagged equation can carry a \label, and \eqref then prints the tag. For a primed repeat of equation (3), write \tag{\ref{eq:energy}$'$} to get (3′).

Suppressing Numbers: \nonumber, \notag and Starred Environments

There are three levels of control. For a whole display, use the starred environment (equation*, align*, gather*). For single lines in a multi-line environment, put \notag (or its older synonym \nonumber) before the line break:

\begin{align}
  (a+b)^2 &= (a+b)(a+b) \notag \\
          &= a^2 + ab + ba + b^2 \notag \\
          &= a^2 + 2ab + b^2 \label{eq:binomial}
\end{align}

Only the last line gets a number, (1), and the label refers to it. This is the most common pattern in derivations: intermediate steps unnumbered, the result numbered.

Multi-Line Equations: align, split, multline and gather

amsmath offers several environments for displays with more than one line. The choice depends on two things: whether the lines should be aligned on a symbol, and whether you want one number for the whole block or one per line.

align: a number on every line

\begin{align}
  x + y &= 10 \label{eq:sum} \\
  x - y &= 2  \label{eq:diff}
\end{align}

Adding \eqref{eq:sum} and \eqref{eq:diff} gives $x = 6$.

The & marks the alignment point (usually just before =), and \\ ends each line except the last. A second pair of columns can be added with more ampersands: a &= b & c &= d sets two equations side by side.

split: one number for a broken equation

\begin{equation}
  \label{eq:long}
  \begin{split}
    (a + b)^4 &= a^4 + 4a^3b + 6a^2b^2 \\
              &\quad + 4ab^3 + b^4
  \end{split}
\end{equation}

The number is centered vertically on the whole block, and the label goes on the outer equation. The \quad at the start of the continuation line is the conventional indent that shows the line is a continuation, not a new equation.

multline: long equations without an alignment point

\begin{multline}
  \label{eq:series}
  1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}
  + \frac{1}{7} + \frac{1}{8} \\
  + \frac{1}{9} + \frac{1}{10} + \dots + \frac{1}{n} = H_n
\end{multline}

gather: centered lines, each numbered

\begin{gather}
  a = b + c \\
  d + e + f + g = h \notag \\
  x = y
\end{gather}

aligned and cases inside equation

aligned and gathered are building blocks, not full displays: they take no number of their own and can sit next to other material in an equation. cases is the same idea with a left brace:

\begin{equation}
  \label{eq:abs}
  |x| =
  \begin{cases}
    x  & \text{if } x \geq 0 \\
    -x & \text{if } x < 0
  \end{cases}
\end{equation}

\begin{equation}
  \left.
  \begin{aligned}
    u &= x + y \\
    v &= x - y
  \end{aligned}
  \right\} \quad \text{(change of variables)}
\end{equation}

Never nest align inside equation: both are top-level displays and amsmath stops with erroneous nesting of equation structures. Use split or aligned inside, and align on its own.

New Line in an Equation: Line Breaks in Long Equations

\\ does not work inside a plain equation; the environment is a single line by design. To start a new line, switch to one of the multi-line environments above. The decision is simple:

• One equation, one number, lines aligned on = → split inside equation.
• One equation, one number, no alignment → multline.
• Several equations or derivation steps → align, with \notag on lines that should not be numbered.

Two related tools: \intertext inserts a line of normal text between aligned lines without breaking the alignment, and \allowdisplaybreaks allows a page break inside a multi-line display, which amsmath forbids by default:

\allowdisplaybreaks   % in the preamble, or in a group around one display

\begin{align}
  f(x) &= x^2 + 2x + 1 \\
  \intertext{which factors as}
  f(x) &= (x+1)^2
\end{align}

To permit a break at one specific line instead, put \displaybreak just before that line's \\. The mathtools package adds \shortintertext, which uses less vertical space than \intertext.

If you would rather not choose break points by hand, the breqn package provides a dmath environment that breaks and aligns long equations automatically. It is powerful but interacts badly with some other packages, so try it on a copy of the document first.

Subequations: (1a), (1b), (1c)

Wrap any numbered environment in subequations and the lines are numbered with the parent number plus a letter. A label on the wrapper refers to the group:

\begin{subequations}
  \label{eq:maxwell}
  \begin{align}
    \nabla \cdot \mathbf{E}  &= \frac{\rho}{\varepsilon_0} \label{eq:gauss} \\
    \nabla \cdot \mathbf{B}  &= 0 \label{eq:nomonopole} \\
    \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \label{eq:faraday}
  \end{align}
\end{subequations}

Maxwell's equations \eqref{eq:maxwell} ...  % (1)
Gauss's law \eqref{eq:gauss} ...            % (1a)

The letter style comes from \theequation inside the group; for roman numerals or another separator, redefine it right after \begin{subequations}: \renewcommand{\theequation}{\theparentequation.\roman{equation}} gives (1.i), (1.ii).

Referencing From the Text

Two conventions are common. Mathematics journals and most physics journals write the number alone in parentheses: “substituting (3) into (5)”. Engineering, computer science and many theses spell it out: “as shown in Equation (3)” or “Eq. (3)”. Either way, \eqref provides the parentheses, so do not add a second pair:

Substituting \eqref{eq:sum} into \eqref{eq:diff} ...   % (1) into (2)
As shown in Equation~\eqref{eq:sum} ...                % Equation (1)
As shown in Eq.~\eqref{eq:sum} ...                     % Eq. (1)
As shown in \cref{eq:sum} ...                          % eq. (1), cleveref
\Cref{eq:sum} shows ...                                % Equation (1), cleveref

With cleveref the wording lives in one place (\crefname), so a journal's request to switch from “Eq.” to “Equation” is a one-line change. Avoid \autoref from hyperref for equations: it prints “Equation 3” without parentheses, which is inconsistent with \eqref elsewhere.

Manual numbering with \refstepcounter

Occasionally you need an equation number in a place amsmath does not number, such as one line of an align*. Step the counter yourself and use the result as a tag; \refstepcounter (not \stepcounter) is what makes the following \label pick up the new value:

\begin{align*}
  a &= b + c \\
  \refstepcounter{equation}
  d &= e + f \tag{\theequation} \label{eq:manual}
\end{align*}

Only the second line is numbered, as \eqref{eq:manual}.

Common Errors

Complete Example

\documentclass{article}
\usepackage{amsmath}
\usepackage[hidelinks]{hyperref}
\usepackage{cleveref}

\numberwithin{equation}{section}
\crefname{equation}{Eq.}{Eqs.}
\Crefname{equation}{Equation}{Equations}

\begin{document}

\section{Kinematics}

A body with constant acceleration satisfies
\begin{equation}
  \label{eq:velocity}
  v = v_0 + at
\end{equation}
and
\begin{equation}
  \label{eq:position}
  x = x_0 + v_0 t + \tfrac{1}{2} a t^2 .
\end{equation}
Eliminating $t$ between \cref{eq:velocity,eq:position}:
\begin{align}
  t   &= \frac{v - v_0}{a} \notag \\
  x - x_0 &= v_0 \frac{v - v_0}{a} + \frac{(v - v_0)^2}{2a} \notag \\
  v^2 &= v_0^2 + 2a(x - x_0). \label{eq:torricelli}
\end{align}
\Cref{eq:torricelli} contains no time variable.

\section{Field equations}

\begin{subequations}
  \label{eq:maxwell}
  \begin{align}
    \nabla \cdot \mathbf{E}  &= \rho / \varepsilon_0 \label{eq:gauss} \\
    \nabla \cdot \mathbf{B}  &= 0 \label{eq:nomono}
  \end{align}
\end{subequations}
Together, \eqref{eq:maxwell} are two of Maxwell's equations;
\eqref{eq:gauss} alone is Gauss's law.

A long identity with a single number:
\begin{equation}
  \label{eq:binom}
  \begin{split}
    (a+b)^4 &= a^4 + 4a^3 b + 6a^2 b^2 \\
            &\quad + 4ab^3 + b^4 .
  \end{split}
\end{equation}

A named equation instead of a number:
\begin{equation}
  e^{i\pi} + 1 = 0 \tag{Euler}
\end{equation}

The piecewise function
\begin{equation*}
  |x| =
  \begin{cases}
    x  & \text{if } x \ge 0, \\
    -x & \text{otherwise}
  \end{cases}
\end{equation*}
is not numbered because it is never referenced; \cref{eq:binom} is.

\end{document}

Compile twice. The equations are numbered (1.1), (1.2), (1.3), (2.1a), (2.1b), (2.2) and (Euler), and every \cref and \eqref resolves to the right one.

Quick Reference

Next Steps

Numbering under control? Continue with the rest of the math toolkit:

• Mathematical Expressions – Fractions, roots, operators and the amsmath environments in detail
• Integrals, Sums & Limits – Big operators, limits above and below, and multi-line sums
• Theorems, Lemmas and Proofs – amsthm, \newtheorem and the QED symbol, with the same \label/\cref workflow
• Matrices in LaTeX – pmatrix, bmatrix and augmented matrices inside numbered equations
• Greek Letters & Math Symbols – Every symbol used in the examples above
• LaTeX Hyperlinks – Make equation references clickable with hyperref

Free LaTeX Tools

• Math to LaTeX Converter – Turn handwritten or typed math into LaTeX
• LaTeX Preview – Check equation numbering with a live PDF preview
• Math to LaTeX – Convert handwritten equations to LaTeX
• LaTeX Symbols Reference – Browse math operators and special characters