How to Write Math Equations in Markdown: A Complete KaTeX Guide

KaTeX is a fast, lightweight JavaScript library that renders mathematical notation in web browsers. Originally developed by Khan Academy, KaTeX translates LaTeX-style math commands into beautifully typeset equations without requiring any server-side processing or plugins.

Unlike full LaTeX — which is a complete document preparation system requiring compilation — KaTeX focuses on one thing: rendering math expressions quickly in HTML. While LaTeX might take seconds to compile a document, KaTeX renders individual equations in under a millisecond, making it ideal for live-editing environments like the Prescosoft Markdown Editor.

The syntax for math in Markdown is simple:

• Inline math: Wrap expressions in single dollar signs: $E = mc^2$ renders within a sentence.
• Display math: Wrap expressions in double dollar signs on their own line for centered, standalone equations.

Most modern Markdown processors — including GitHub, Obsidian, Notion, and the Prescosoft editor — support KaTeX math notation natively or through plugins.

Start with the fundamentals: arithmetic operators, exponents, subscripts, fractions, and square roots. These building blocks combine to express virtually any mathematical idea.

Arithmetic

Standard operators work as you'd expect. For multiplication and division symbols, use \times and \div:

$$a + b - c = d \times e \div f$$

Renders: $a + b - c = d \times e \div f$

Exponents and Subscripts

Use ^ for superscripts and _ for subscripts. Wrap multi-character expressions in braces:

$$x^{2n+1} + y_{i,j} = z^3_0$$

Renders: $x^{2n+1} + y_{i,j} = z^3_0$

Fractions

The \frac command takes two arguments — numerator and denominator:

$$\frac{a + b}{c - d} + \frac{1}{2}$$

Renders: $$\frac{a + b}{c - d} + \frac{1}{2}$$

Square Roots

Use \sqrt for square roots, and \sqrt[n] for nth roots:

$$\sqrt{x^2 + y^2} \quad \sqrt[3]{27} = 3$$

Renders: $$\sqrt{x^2 + y^2} \quad \sqrt[3]{27} = 3$$

Greek Alphabet

Greek letters are essential in physics, engineering, statistics, and pure mathematics. Each letter has a lowercase and uppercase version. Capitalize the command name for uppercase variants:

Uppercase variants use capitalized names: \Gamma ($\Gamma$), \Delta ($\Delta$), \Sigma ($\Sigma$), \Omega ($\Omega$).

Mathematical Operators

Large operators like summation, product, integral, and limit accept bounds using subscript and superscript notation:

For display mode, these operators render with limits above and below instead of as subscripts, creating the classic textbook appearance. See Advanced GitHub Flavored Markdown for more on display mode options.

Matrices and Arrays

Matrices use environment names that specify the type of bracket. Separate columns with & and rows with \\:

Parentheses (pmatrix):

$$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$

Renders: $$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$

Square brackets (bmatrix):

$$\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$$

Renders: $$\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$$

Vertical bars / determinant (vmatrix):

$$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$$

Renders: $$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$$

Calculus Notation

KaTeX supports the full range of calculus notation — derivatives, partial derivatives, single and multiple integrals:

Derivatives:

$$\frac{dy}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$

Renders: $$\frac{dy}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$

Partial derivatives:

$$\frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} = 0$$

Renders: $$\frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} = 0$$

Definite integrals:

$$\int_a^b f(x)\, dx = F(b) - F(a)$$

Renders: $$\int_a^b f(x)\, dx = F(b) - F(a)$$

Double integrals:

$$\iint_D f(x,y)\, dA = \int_a^b \int_{g(x)}^{h(x)} f(x,y)\, dy\, dx$$

Renders: $$\iint_D f(x,y)\, dA = \int_a^b \int_{g(x)}^{h(x)} f(x,y)\, dy\, dx$$

Common Academic Formulas

These frequently-used formulas appear across mathematics, physics, and engineering. Each is written in KaTeX notation you can copy directly into your Markdown documents:

Quadratic Formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Renders: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Pythagorean Theorem:

$$a^2 + b^2 = c^2$$

Renders: $$a^2 + b^2 = c^2$$

Euler's Identity:

$$e^{i\pi} + 1 = 0$$

Renders: $$e^{i\pi} + 1 = 0$$

Binomial Theorem:

$$(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k$$

Renders: $$(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k$$

These examples demonstrate that even complex academic formulas can be expressed clearly with KaTeX. For additional formatting techniques like tables and task lists, check out our guide on Advanced GitHub Flavored Markdown.

Inline Math in Paragraphs

Inline math flows naturally within a sentence. Use single dollar signs around short expressions that you reference in passing. For example, you might write "the area of a circle is $A = \pi r^2$" directly in your paragraph text. Keep inline expressions brief — if an equation is complex, promote it to display mode instead.

Display Math for Standalone Equations

Display math gets its own line, centered on the page, with larger symbols and properly-positioned limits. Use double dollar signs on separate lines. This is ideal for equations you want to emphasize, reference, or discuss. Display mode also renders fractions at full size rather than the compressed inline version.

Mixing Math with Regular Text

Effective mathematical writing alternates between prose and notation. Introduce a concept in plain language, then formalize it with an equation. For example: "By the chain rule, the derivative of a composite function is the product of the derivatives." Then show: $$\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)$$

This pattern — explain in words, then show in symbols — makes your writing accessible to readers at different levels of mathematical sophistication.

Best Practices for Readability

• Add spacing: Use \, or \quad to add space in expressions like \int f(x)\, dx
• Number important equations: Use \tag{1} at the end of display math to label equations for cross-reference
• Align multi-line equations: Use the aligned environment to line up equals signs across multiple lines
• Preview as you write: Always use a live-rendering editor like the Prescosoft Markdown Editor to verify your equations render correctly before publishing
• Keep source readable: Add spaces around operators in your source code for easier editing, even though KaTeX ignores extra whitespace

Whether you're writing homework solutions, research papers, or technical blog posts, mastering math notation in Markdown saves time and produces publication-quality output. The Prescosoft Markdown Editor makes this process seamless with instant KaTeX rendering, export to HTML, and a distraction-free writing environment. If you want to explore more advanced Markdown features beyond math, our Advanced GFM guide covers tables, task lists, and footnotes.