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Math Equations

Render beautiful mathematical equations in your documentation using KaTeX

Overview

KaTeX is a fast, easy-to-use JavaScript library for rendering TeX math notation on the web. This site integrates KaTeX to enable beautiful mathematical equations in documentation.

Features

  • Fast rendering - KaTeX is significantly faster than MathJax
  • High quality - Produces crisp output at any zoom level
  • Self-contained - No dependencies on external fonts or stylesheets
  • Server-side rendering - Works without JavaScript enabled
  • TeX/LaTeX syntax - Familiar notation for mathematicians

Basic Usage

Inline Math

Wrap inline equations with single dollar signs $...$:

The Pythagorean theorem states that $c = \pm\sqrt{a^2 + b^2}$ for a right triangle.

The Pythagorean theorem states that c=±a2+b2c = \pm\sqrt{a^2 + b^2} for a right triangle.

Block Math

Use code blocks with the math language identifier or wrap with double dollar signs $$...$$:

```math
c = \pm\sqrt{a^2 + b^2}
```
c=±a2+b2c = \pm\sqrt{a^2 + b^2}

Or using double dollar signs:

$$
E = mc^2
$$
E=mc2E = mc^2

Common Examples

Algebra

Quadratic Formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Binomial Theorem:

(x+y)n=∑k=0n(nk)xn−kyk(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k

Calculus

Fundamental Theorem of Calculus:

∫abf(x) dx=F(b)−F(a)\int_a^b f(x) \, dx = F(b) - F(a)

Partial Derivatives:

∂2f∂x∂y=∂2f∂y∂x\frac{\partial^2 f}{\partial x \partial y} = \frac{\partial^2 f}{\partial y \partial x}

Limit Definition:

lim⁡x→∞(1+1x)x=e\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x = e

Linear Algebra

Matrix Multiplication:

[abcd][efgh]=[ae+bgaf+bhce+dgcf+dh]\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e & f \\ g & h \end{bmatrix} = \begin{bmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{bmatrix}

Determinant:

det⁡(A)=∣abcd∣=ad−bc\det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

Statistics & Probability

Normal Distribution:

f(x)=1σ2πe−12(x−μσ)2f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

Bayes' Theorem:

P(A∣B)=P(B∣A)⋅P(A)P(B)P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}

Complex Analysis

Taylor Series Expansion:

The Taylor expansion expresses a holomorphic function f(z)f(z) as a power series:

Tf(z)=∑k=0∞(z−c)k2πi∫γf(w)(w−c)k+1 dw=12πi∫γf(w)w−c∑k=0∞(z−cw−c)k dw=12πi∫γf(w)w−c(11−z−cw−c) dw=12πi∫γf(w)w−z dw=f(z),\displaystyle {\begin{aligned}T_{f}(z)&=\sum _{k=0}^{\infty }{\frac {(z-c)^{k}}{2\pi i}}\int _{\gamma }{\frac {f(w)}{(w-c)^{k+1}}}\,dw\\&={\frac {1}{2\pi i}}\int _{\gamma }{\frac {f(w)}{w-c}}\sum _{k=0}^{\infty }\left({\frac {z-c}{w-c}}\right)^{k}\,dw\\&={\frac {1}{2\pi i}}\int _{\gamma }{\frac {f(w)}{w-c}}\left({\frac {1}{1-{\frac {z-c}{w-c}}}}\right)\,dw\\&={\frac {1}{2\pi i}}\int _{\gamma }{\frac {f(w)}{w-z}}\,dw=f(z),\end{aligned}}

Euler's Formula:

eix=cos⁡(x)+isin⁡(x)e^{ix} = \cos(x) + i\sin(x)

Physics

Schrödinger Equation:

iℏ∂∂tΨ(r,t)=H^Ψ(r,t)i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat{H}\Psi(\mathbf{r},t)

Maxwell's Equations:

∇⋅E=ρϵ0∇⋅B=0∇×E=−∂B∂t∇×B=μ0J+μ0ϵ0∂E∂t\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t} \end{aligned}

Lagrangian Mechanics:

The action functional SS is defined as:

S[q]=∫abL(t,q(t),q˙(t)) dt.\displaystyle S[{\boldsymbol {q}}]=\int _{a}^{b}L(t,{\boldsymbol {q}}(t),{\dot {\boldsymbol {q}}}(t))\,dt.

Advanced Features

Multi-line Equations

Use aligned environment for aligned equations:

f(x)=(x+a)(x+b)=x2+(a+b)x+ab\begin{aligned} f(x) &= (x+a)(x+b) \\ &= x^2 + (a+b)x + ab \end{aligned}

Cases and Piecewise Functions

f(x)={x2if x≥0−x2if x<0f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x^2 & \text{if } x < 0 \end{cases}

Fractions and Continued Fractions

11+12+13+14\frac{1}{\displaystyle 1+\frac{1}{\displaystyle 2+\frac{1}{\displaystyle 3+\frac{1}{4}}}}

Greek Letters and Symbols

Common symbols used in mathematics:

  • Greek: α,β,γ,δ,ϵ,θ,λ,μ,π,σ,ω\alpha, \beta, \gamma, \delta, \epsilon, \theta, \lambda, \mu, \pi, \sigma, \omega
  • Operators: ∑,∏,∫,∮,∇,∂\sum, \prod, \int, \oint, \nabla, \partial
  • Relations: ≤,≥,≠,≈,≡,∝\leq, \geq, \neq, \approx, \equiv, \propto
  • Sets: ∈,∉,⊂,⊆,∪,∩,∅\in, \notin, \subset, \subseteq, \cup, \cap, \emptyset
  • Logic: ∀,∃,¬,∧,∨,  ⟹  ,  ⟺  \forall, \exists, \neg, \land, \lor, \implies, \iff

Subscripts and Superscripts

x1,x2,…,xnanda2+b2=c2x_1, x_2, \ldots, x_n \quad \text{and} \quad a^2 + b^2 = c^2

Large Operators

Summation:

∑i=1ni=n(n+1)2\sum_{i=1}^{n} i = \frac{n(n+1)}{2}

Product:

∏i=1ni=n!\prod_{i=1}^{n} i = n!

Integration:

∫−∞∞e−x2 dx=π\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}

Special Formatting

Colored Equations

KaTeX supports color through the \textcolor and \colorbox commands:

F=maandE=mc2\textcolor{red}{F = ma} \quad \text{and} \quad \colorbox{yellow}{$E = mc^2$}

Sizing

Control the size of your equations:

tinysmallnormallargeLargeLARGEhuge\tiny{tiny} \quad \small{small} \quad \normalsize{normal} \quad \large{large} \quad \Large{Large} \quad \LARGE{LARGE} \quad \huge{huge}

Spacing

Fine-tune spacing in equations:

a ⁣ba ba ba  ba bababa\!b \quad a\,b \quad a\:b \quad a\;b \quad a\ b \quad a\quad b \quad a\qquad b

Best Practices

Keep It Readable

Use clear variable names and proper spacing:

P(X=k)=(nk)pk(1−p)n−kP(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

Cramped or unclear notation:

P(X=k)=(nk)pk(1−p)n−kP(X=k)=\binom{n}{k}p^k(1-p)^{n-k}

Use Display Style for Complex Equations

For complex fractions and large operators, use \displaystyle:

∑i=1n1i2=π26\displaystyle \sum_{i=1}^{n} \frac{1}{i^2} = \frac{\pi^2}{6}

Break Long Equations

For very long equations, use multiple lines with aligned:

(a+b)3=(a+b)(a+b)2=(a+b)(a2+2ab+b2)=a3+3a2b+3ab2+b3\begin{aligned} (a + b)^3 &= (a + b)(a + b)^2 \\ &= (a + b)(a^2 + 2ab + b^2) \\ &= a^3 + 3a^2b + 3ab^2 + b^3 \end{aligned}

Label Important Equations

Use text annotations to explain components:

eiπ⏟Euler’s identity+1=0\underbrace{e^{i\pi}}_{\text{Euler's identity}} + 1 = 0

Common Syntax Reference

Basic Operations

SyntaxResultDescription
x + yx+yx + yAddition
x - yx−yx - ySubtraction
x \times yx×yx \times yMultiplication
x \div yx÷yx \div yDivision
\frac{x}{y}xy\frac{x}{y}Fraction
x^yxyx^ySuperscript
x_yxyx_ySubscript
\sqrt{x}x\sqrt{x}Square root
\sqrt[n]{x}xn\sqrt[n]{x}nth root

Delimiters

SyntaxResultDescription
(x)(x)(x)Parentheses
[x][x][x]Brackets
\{x\}{x}\{x\}Braces
\langle x \rangle⟨x⟩\langle x \rangleAngle brackets
\lvert x \rvert∣x∣\lvert x \rvertAbsolute value
\lVert x \rVert∥x∥\lVert x \rVertNorm

Troubleshooting

Equation Not Rendering

  • Check that katex/dist/katex.css is imported in your layout
  • Verify the TeX syntax is valid
  • Ensure remark-math and rehype-katex are configured correctly
  • Use the KaTeX Live Demo to test syntax

Missing Symbols

  • Not all LaTeX commands are supported by KaTeX
  • Check the KaTeX Support Table
  • Consider using alternative notation

Escaping Special Characters

Use backslash to escape special characters:

Use \$ for a dollar sign, not $\$$ in math mode.

Pro Tip

You can copy equations from Wikipedia - they're already in LaTeX format and work directly with KaTeX!

Try it: Visit any Wikipedia math article, right-click an equation, and select "Copy LaTeX code".

Resources

Next Steps

On this page

OverviewFeaturesBasic UsageInline MathBlock MathCommon ExamplesAlgebraCalculusLinear AlgebraStatistics & ProbabilityComplex AnalysisPhysicsAdvanced FeaturesMulti-line EquationsCases and Piecewise FunctionsFractions and Continued FractionsGreek Letters and SymbolsSubscripts and SuperscriptsLarge OperatorsSpecial FormattingColored EquationsSizingSpacingBest PracticesKeep It ReadableUse Display Style for Complex EquationsBreak Long EquationsLabel Important EquationsCommon Syntax ReferenceBasic OperationsDelimitersTroubleshootingEquation Not RenderingMissing SymbolsEscaping Special CharactersResourcesNext Steps