LaTeX Math

Write beautiful mathematical formulas using LaTeX syntax, rendered with KaTeX.

Inline Math

Use single $ for inline formulas:

The famous equation $E = mc^2$ changed physics.

The famous equation $E = mc^2$ changed physics.

More examples:

• Area of circle: $A = \pi r^2$
• Pythagorean theorem: $a^2 + b^2 = c^2$
• Quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Block Math

Use double $$ for centered, block-level formulas:

$$
\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}
$$

$$\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$$

Basic Syntax

Superscripts and Subscripts

Syntax	Result
x^2	$x^2$
x_i	$x_i$
x_i^2	$x_i^2$
x^{10}	$x^{10}$

Fractions

$$
\frac{a}{b} \quad \frac{1}{2} \quad \frac{x+1}{y-1}
$$

$$\frac{a}{b} \quad \frac{1}{2} \quad \frac{x+1}{y-1}$$

Square Roots

$$
\sqrt{2} \quad \sqrt{x+y} \quad \sqrt[3]{8}
$$

$$\sqrt{2} \quad \sqrt{x+y} \quad \sqrt[3]{8}$$

Greek Letters

Letter	Syntax	Letter	Syntax
$\alpha$	\alpha	$\beta$	\beta
$\gamma$	\gamma	$\delta$	\delta
$\pi$	\pi	$\sigma$	\sigma
$\theta$	\theta	$\lambda$	\lambda
$\Omega$	\Omega	$\Sigma$	\Sigma

Operators

Sums and Products

$$
\sum_{i=1}^{n} x_i \quad \prod_{i=1}^{n} x_i
$$

$$\sum_{i=1}^{n} x_i \quad \prod_{i=1}^{n} x_i$$

Integrals

$$
\int_a^b f(x)dx \quad \iint_D f(x,y)dxdy \quad \oint_C f(z)dz
$$

$$\int_a^b f(x)dx \quad \iint_D f(x,y)dxdy \quad \oint_C f(z)dz$$

Limits

$$
\lim_{x \to \infty} \frac{1}{x} = 0
$$

$$\lim_{x \to \infty} \frac{1}{x} = 0$$

Matrices

$$
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\quad
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6
\end{bmatrix}
$$

$$\begin{pmatrix} a & b \\ c & d \end{pmatrix} \quad \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$$

Equations

Aligned Equations

$$
\begin{aligned}
(a+b)^2 &= a^2 + 2ab + b^2 \\
(a-b)^2 &= a^2 - 2ab + b^2
\end{aligned}
$$

$$\begin{aligned} (a+b)^2 &= a^2 + 2ab + b^2 \\ (a-b)^2 &= a^2 - 2ab + b^2 \end{aligned}$$

Cases

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

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

Common Formulas

Statistics

Standard deviation:

$$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2}$$

Calculus

Taylor series:

$$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots$$

Physics

Maxwell’s equations:

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$$

Tips

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