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Building on the math basics, this guide covers advanced equation formatting, multi-line equations, alignment, and professional mathematical typesetting.
Prerequisites: Familiarity with basic math mode ($...$ and \[...\]). See our Mathematics Basics guide if needed.Related topics: Mathematical symbols | Text formatting in math | Cross-referencing equations

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Single Equations

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Basic Display Equations

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

% Simple display equation
\[ E = mc^2 \]

% With equation number
\begin{equation}
  E = mc^2
\end{equation}

% Without equation number
\begin{equation*}
  E = mc^2
\end{equation*}

% Reference an equation
\begin{equation}\label{eq:energy}
  E = mc^2
\end{equation}
As shown in Equation \ref{eq:energy}, energy and mass are related.

% Using \eqref for parentheses
As shown in Equation \eqref{eq:energy}...

\end{document}

Rendered Output

Display equation: E=mc2E = mc^2Numbered equation: E = mc^2 \tag{1}

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Equation Numbering Control

% Suppress numbering for specific equation
\begin{equation}
  a^2 + b^2 = c^2 \nonumber
\end{equation}

% Custom numbering
\begin{equation}
  F = ma \tag{Newton's 2nd Law}
\end{equation}

% Numbered with custom tag
\begin{equation}
  e^{i\pi} + 1 = 0 \tag{$\star$}
\end{equation}

% Subequations
\begin{subequations}
\begin{equation}
  x + y = 5
\end{equation}
\begin{equation}
  2x - y = 1
\end{equation}
\end{subequations}

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Multi-line Equations

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Split Environment

For single equations that are too long: 
\documentclass{article}
\usepackage{amsmath}
\begin{document}

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

% Left-aligned split
\begin{equation}
\begin{split}
  \text{LHS} &= \text{some long expression} \\
  &\quad + \text{continuation} \\
  &\quad + \text{more terms} \\
  &= \text{RHS}
\end{split}
\end{equation}

\end{document}
Rendered Output (a + b)^4 &= (a + b)^2(a + b)^2 \\ &= (a^2 + 2ab + b^2)(a^2 + 2ab + b^2) \\ &= a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 \end{split} \tag{2}$$ ### Multline Environment For very long single equations: <CodeGroup> ```latex multline-environment.tex \begin{multline} \int_0^1 \biggl\{ \sum_{i=1}^n x_i^2 + \sum_{j=1}^m y_j^2 + \sum_{k=1}^p z_k^2 \biggr\} \, dx \\ + \int_1^2 \biggl\{ \sum_{i=1}^n x_i^3 + \sum_{j=1}^m y_j^3 + \sum_{k=1}^p z_k^3 \biggr\} \, dx \\ = \text{some complicated result} \end{multline} % Control positioning \begin{multline} \text{First line flush left} \\ \text{Middle lines centered} \\ \shoveleft{\text{This line shoved left}} \\ \shoveright{\text{This line shoved right}} \\ \text{Last line flush right} \end{multline} ``` </CodeGroup> ## Aligned Equations ### Align Environment The most versatile environment for multiple equations: <CodeGroup> ```latex align-environment.tex \documentclass{article} \usepackage{amsmath} \begin{document} % Basic alignment \begin{align} 2x + 3y &= 7 \\ 5x - 2y &= 4 \end{align} % Multiple alignment points \begin{align} x &= a + b &\qquad y &= c + d \\ 2x &= 2(a + b) &\qquad 3y &= 3(c + d) \end{align} % Without numbering \begin{align*} \sin^2\theta + \cos^2\theta &= 1 \\ 1 + \tan^2\theta &= \sec^2\theta \\ 1 + \cot^2\theta &= \csc^2\theta \end{align*} % Selective numbering \begin{align} a &= b + c \\ d &= e + f \nonumber \\ g &= h + i \end{align} \end{document} ``` </CodeGroup> <Card title="Rendered Output" icon="eye"> **Aligned equations (numbered):** $$\begin{align} 2x + 3y &= 7 \tag{3}\\ 5x - 2y &= 4 \tag{4} \end{align}$$ **Without numbering:** $$\begin{aligned} \sin^2\theta + \cos^2\theta &= 1 \\ 1 + \tan^2\theta &= \sec^2\theta \\ 1 + \cot^2\theta &= \csc^2\theta \end{aligned}$$ </Card> ### Aligned Within Equation <CodeGroup> ```latex aligned-within.tex % For alignment within a single equation number \begin{equation} \begin{aligned} f(x) &= (x+a)(x+b) \\ &= x^2 + (a+b)x + ab \end{aligned} \end{equation} % Multiple aligned blocks \begin{equation} \left\{ \begin{aligned} x + y + z &= 1 \\ 2x - y + 3z &= 0 \\ x - 2y - z &= 4 \end{aligned} \right. \end{equation} ``` </CodeGroup> ## Equation Arrays ### Eqnarray (Deprecated) <Warning> **Note**: `eqnarray` is deprecated. Use `align` instead. Shown here for reference only. </Warning> ### Array Environment For complex layouts: <CodeGroup> ```latex array-equations.tex \begin{equation} \begin{array}{lcl} f(x) &=& (x+1)^2 \\ &=& x^2 + 2x + 1 \end{array} \end{equation} % Multiple columns \begin{equation} \begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array} \end{equation} ``` </CodeGroup> ## Cases and Piecewise Functions ### Cases Environment <CodeGroup> ```latex cases-environment.tex \documentclass{article} \usepackage{amsmath} \begin{document} % Basic cases \begin{equation} f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x^2 & \text{if } x < 0 \end{cases} \end{equation} % Multiple conditions \begin{equation} \text{sgn}(x) = \begin{cases} 1 & \text{if } x > 0 \\ 0 & \text{if } x = 0 \\ -1 & \text{if } x < 0 \end{cases} \end{equation} % Nested cases \begin{equation} f(x,y) = \begin{cases} \begin{cases} 1 & \text{if } y > x \\ 0 & \text{if } y = x \end{cases} & \text{if } x \geq 0 \\ -1 & \text{if } x < 0 \end{cases} \end{equation} % Left cases \begin{equation} \begin{rcases} x^2 + y^2 = 1 \\ x + y = 0 \end{rcases} \text{defines a curve} \end{equation} \end{document} ``` </CodeGroup> <Card title="Rendered Output" icon="eye"> **Piecewise function:** $$f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x^2 & \text{if } x < 0 \end{cases} \tag{5}$$ **Sign function:** $$\text{sgn}(x) = \begin{cases} 1 & \text{if } x > 0 \\ 0 & \text{if } x = 0 \\ -1 & \text{if } x < 0 \end{cases} \tag{6}$$ </Card> ## Gathered and Centered Equations <CodeGroup> ```latex gathered-equations.tex % Multiple centered lines with one number \begin{equation} \begin{gathered} (a + b)^2 = a^2 + 2ab + b^2 \\ (a - b)^2 = a^2 - 2ab + b^2 \\ (a + b)(a - b) = a^2 - b^2 \end{gathered} \end{equation} % Within text The identities $\begin{gathered} \sin^2\theta + \cos^2\theta = 1 \\ \tan\theta = \frac{\sin\theta}{\cos\theta} \end{gathered}$ are fundamental. ``` </CodeGroup> ## Advanced Alignment ### Complex Alignment Patterns <CodeGroup> ```latex complex-alignment.tex % Aligning equals signs and operators \begin{align} f(x) &= x^2 + 2x + 1 \\ &= (x + 1)^2 \\ &> 0 \quad \text{for all } x \neq -1 \end{align} % Multiple columns \begin{align} a_1 &= b_1 + c_1 & a_2 &= b_2 + c_2 \\ d_1 &= e_1 + f_1 & d_2 &= e_2 + f_2 \end{align} % Alignment with text \begin{align} 2x + 3 &= 7 & &\text{(given)} \\ 2x &= 4 & &\text{(subtract 3)} \\ x &= 2 & &\text{(divide by 2)} \end{align} ``` </CodeGroup> ### Intertext and Shortintertext <CodeGroup> ```latex intertext.tex \begin{align} a &= b + c \\ &= d + e + f \intertext{Now we substitute the known values:} &= 1 + 2 + 3 \\ &= 6 \end{align} % Shorter spacing \begin{align} x^2 + y^2 &= r^2 \shortintertext{and} x &= r\cos\theta \\ y &= r\sin\theta \end{align} ``` </CodeGroup> ## Boxed and Highlighted Equations <CodeGroup> ```latex boxed-equations.tex % Simple box \begin{equation} \boxed{E = mc^2} \end{equation} % Colored box \usepackage{xcolor} \begin{equation} \colorbox{yellow}{$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$} \end{equation} % Framed important result \begin{equation} \boxed{ \int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi} } \end{equation} % Highlight part of equation \begin{equation} f(x) = \underbrace{x^2 + 2x}_{\text{quadratic}} + \overbrace{3x + 4}^{\text{linear}} \end{equation} ``` </CodeGroup> ## Equation Spacing ### Manual Spacing in Equations <CodeGroup> ```latex equation-spacing.tex % Spacing commands \begin{align} f(x) &= x^2+2x+1 \\ % No space f(x) &= x^2 + 2x + 1 \\ % Normal space f(x) &= x^2\,+\,2x\,+\,1 \\ % Thin space f(x) &= x^2\:+\:2x\:+\:1 \\ % Medium space f(x) &= x^2\;+\;2x\;+\;1 \\ % Thick space f(x) &= x^2\quad+\quad2x\quad+\quad1 % Quad space \end{align} % Negative space \begin{equation} \int\!\!\!\int f(x,y) \, dx \, dy % Bring integral signs closer \end{equation} ``` </CodeGroup> ## Best Practices <Tip> **Equation guidelines:** 1. **Consistency**: Use the same alignment style throughout 2. **Readability**: Don't over-align; prioritize clarity 3. **References**: Label important equations for cross-referencing 4. **Spacing**: Use `\,` before differentials in integrals 5. **Breaking**: Break long equations at operators (+, -, =) 6. **Grouping**: Use `subequations` for related equations </Tip> ## Common Patterns ### System of Equations <CodeGroup> ```latex system-equations.tex % Using array \begin{equation} \left\{ \begin{array}{rcrcrcr} 2x & + & 3y & - & z & = & 4 \\ x & - & y & + & 2z & = & 1 \\ 3x & + & y & - & z & = & 0 \end{array} \right. \end{equation} % Using aligned \begin{equation} \left\{ \begin{aligned} 2x + 3y - z &= 4 \\ x - y + 2z &= 1 \\ 3x + y - z &= 0 \end{aligned} \right. \end{equation} ``` </CodeGroup> <Card title="Rendered Output" icon="eye"> $$\left\{ \begin{aligned} 2x + 3y - z &= 4 \\ x - y + 2z &= 1 \\ 3x + y - z &= 0 \end{aligned} \right. \tag{7}$$ </Card> ### Derivations <CodeGroup> ```latex derivations.tex \begin{align} (x + y)^2 &= (x + y)(x + y) \\ &= x(x + y) + y(x + y) \\ &= x^2 + xy + yx + y^2 \\ &= x^2 + 2xy + y^2 \end{align} ``` </CodeGroup> <Card title="Rendered Output" icon="eye"> $$\begin{aligned} (x + y)^2 &= (x + y)(x + y) \\ &= x(x + y) + y(x + y) \\ &= x^2 + xy + yx + y^2 \\ &= x^2 + 2xy + y^2 \end{aligned}$$ </Card> ## Quick Reference | Environment | Purpose | Numbering | |------------|---------|-----------| | `equation` | Single equation | Yes | | `equation*` | Single equation | No | | `align` | Multiple aligned equations | Yes (each) | | `align*` | Multiple aligned equations | No | | `split` | Split long equation | One number | | `multline` | Very long equation | One number | | `gather` | Centered equations | Yes (each) | | `cases` | Piecewise functions | Within equation | --- <Info> **Next**: Explore [Mathematical symbols](/learn/latex/mathematics/symbols) for a comprehensive guide to mathematical notation in LaTeX. </Info>