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Markdown LaTeX Math Formula Reference & Interactive Sandbox

Searchable formula cheat sheet and live KaTeX equation reference for calculus, physics, algebra, and discrete mathematics.

Live Equation Sandbox & Quick CopyKaTeX / MathJax syntax

Formula Reference Cards (8)

Einstein Mass-Energy EquivalencePhysics

E = mc^2

Fundamental relativistic relationship between mass and energy.

Quadratic FormulaAlgebra

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

Closed-form solution for general quadratic polynomial roots.

Euler's IdentityCalculus

e^{i\pi} + 1 = 0

Profound relation connecting five fundamental mathematical constants.

Gaussian Normal DistributionStatistics

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

Probability density function for the standard bell curve.

Definite Integral (Fundamental Theorem)Calculus

\int_{a}^{b} f(x)\,dx = F(b) - F(a)

Relates differentiation and Riemann integration.

Pythagorean TheoremGeometry

a^2 + b^2 = c^2

Fundamental metric relation among sides of a right triangle.

2x2 Matrix DeterminantLinear Algebra

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

Determinant calculation for a two-dimensional square matrix.

Summation of SeriesDiscrete Math

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

Sum of the first n positive natural numbers.

Markdown Documentation TableLive GFM

# 📐 LaTeX Math Reference & Formula Guide

| Category | Formula Name | LaTeX Code | Preview Syntax | Description |
|:---|:---|:---|:---:|:---|
| **Physics** | Einstein Mass-Energy Equivalence | `$E = mc^2$` | $$E = mc^2$$ | Fundamental relativistic relationship between mass and energy. |
| **Algebra** | Quadratic Formula | `$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$` | $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ | Closed-form solution for general quadratic polynomial roots. |
| **Calculus** | Euler's Identity | `$e^{i\pi} + 1 = 0$` | $$e^{i\pi} + 1 = 0$$ | Profound relation connecting five fundamental mathematical constants. |
| **Statistics** | Gaussian Normal Distribution | `$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$` | $$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$$ | Probability density function for the standard bell curve. |
| **Calculus** | Definite Integral (Fundamental Theorem) | `$\int_{a}^{b} f(x)\,dx = F(b) - F(a)$` | $$\int_{a}^{b} f(x)\,dx = F(b) - F(a)$$ | Relates differentiation and Riemann integration. |
| **Geometry** | Pythagorean Theorem | `$a^2 + b^2 = c^2$` | $$a^2 + b^2 = c^2$$ | Fundamental metric relation among sides of a right triangle. |
| **Linear Algebra** | 2x2 Matrix Determinant | `$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$` | $$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$$ | Determinant calculation for a two-dimensional square matrix. |
| **Discrete Math** | Summation of Series | `$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$` | $$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$ | Sum of the first n positive natural numbers. |

### 💡 Usage Note
> Use single dollar signs `$E=mc^2$` for inline formulas, and double dollar signs `$$...$$` for centered display block formulas.

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Complete Guide & Overview

Markdown LaTeX Math Formula Reference & Interactive Sandbox

Searchable formula cheat sheet and live KaTeX equation builder for mathematical expressions, calculus integrals, and Greek symbols in Markdown.

How to Use the Markdown LaTeX Math Formula Reference & Interactive Sandbox

Input Content

Paste or compose your markdown or source data into the input editor.

Customize Settings

Select formatting options, syntax modes, or display options.

Copy or Download

Copy the processed output to your clipboard or download the generated file.

Key Features & Capabilities

Instant Equation Sandbox: Test raw LaTeX formulas and copy inline ($) or block ($$) snippets in one click.

Categorized Reference: Fast filters for Calculus, Physics, Linear Algebra, Probability, and Discrete Mathematics.

GitHub & KaTeX Compliant: Fully compatible with GitHub native math rendering, Obsidian, Hugo, and Astro.

100% Client-Side Privacy: Formulas execute strictly inside your local browser without third-party requests.

Frequently Asked Questions

How does GitHub render LaTeX math equations?

GitHub natively renders math expressions delimited by single dollar signs `$E=mc^2$` for inline math and double dollar signs `$$...$$` on separate lines for centered display blocks.

Does this require MathJax or KaTeX installed locally?

Most modern Markdown processors (Obsidian, GitHub, GitLab, Fumadocs, Nextra) bundle KaTeX or MathJax automatically. You simply copy the markdown table or raw equation tags.

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