Math Equation Inventory

Ready-to-use LaTeX equations for Markdown

A curated catalog of algebra, calculus, linear-algebra, statistics, trigonometry, physics, discrete-math, and logic equation templates — rendered live with KaTeX. Copy as inline ( $…$ ), block ($$…$$), or raw LaTeX. Works on GitHub, GitLab, Notion, Docusaurus, MkDocs, Obsidian, and any platform with a math renderer in its pipeline.

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Filter by name or category. Pick a copy format (inline, block, or raw LaTeX), then click Copy on any card. Equations render live with KaTeX.

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59 of 59

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

Quadratic formula

Roots of ax² + bx + c = 0.

a^2 + b^2 = c^2

Pythagorean theorem

Relationship between the sides of a right triangle.

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

Binomial theorem

Expansion of (x + y) to the nth power.

S_n = \sum_{k=0}^{n-1} a r^k = a \frac{1 - r^n}{1 - r}, \quad r \neq 1

Geometric series (finite)

Closed form for a + ar + ar² + … + arⁿ⁻¹.

\log_b(xy) = \log_b x + \log_b y

Logarithm of a product

Sum-of-logs identity.

f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}

Derivative (limit definition)

Difference quotient as h → 0.

\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)

Chain rule

Derivative of a composition.

(fg)' = f'g + fg'

Product rule

Derivative of a product of two functions.

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

Fundamental theorem of calculus

Integration and differentiation are inverse operations.

f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x - a)^n

Taylor series

Series expansion of f around the point a.

e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n

Euler's number from a limit

Continuous compounding limit.

\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^{n} a_i b_i

Dot product

Sum of element-wise products.

A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}

2×2 matrix

Inline matrix with bracket delimiters.

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

2×2 determinant

ad − bc.

A \mathbf{v} = \lambda \mathbf{v}

Eigenvalue equation

Definition of an eigenvector and eigenvalue.

\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i

Arithmetic mean

Sum of values divided by count.

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

Variance (population)

Mean squared deviation from the mean.

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

Standard deviation

Square root of variance.

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

Normal distribution (PDF)

Probability density of the Gaussian.

P(A \mid B) = \frac{P(B \mid A) \, P(A)}{P(B)}

Bayes' theorem

Posterior in terms of likelihood, prior, evidence.

z = \frac{x - \mu}{\sigma}

Z-score

Standardized distance from the mean.

\sin^2 \theta + \cos^2 \theta = 1

Pythagorean identity

sin²θ + cos²θ = 1.

\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta

Sine sum formula

Expansion of sin(α + β).

c^2 = a^2 + b^2 - 2ab \cos C

Law of cosines

Generalized Pythagorean theorem.

e^{i\theta} = \cos \theta + i \sin \theta

Euler's formula

e^{iθ} = cos θ + i sin θ.

E = mc^2

Mass–energy equivalence

Einstein's famous equation.

\mathbf{F} = m \mathbf{a}

Newton's second law

Force equals mass times acceleration.

i \hbar \frac{\partial}{\partial t} \Psi = \hat{H} \Psi

Schrödinger equation (time-dependent)

Wavefunction evolution under a Hamiltonian.

\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}

Wave equation

Generic 1D wave equation.

a^{p-1} \equiv 1 \pmod{p}

Fermat's little theorem

If p is prime and gcd(a, p) = 1.

\binom{n}{k} = \frac{n!}{k!(n-k)!}

Binomial coefficient

Number of ways to choose k from n.

(A \cup B)^c = A^c \cap B^c, \quad (A \cap B)^c = A^c \cup B^c

De Morgan's laws (sets)

Complement of union and intersection.

(P \rightarrow Q) \land P \vdash Q

Modus ponens

If P implies Q and P holds, then Q holds.

ax^2 + bx + c = a\left(x + \frac{b}{2a}\right)^2 + c - \frac{b^2}{4a}

Completing the square

Rewrite a quadratic in vertex form.

S_n = \frac{n}{2} \bigl(2a + (n-1)d\bigr)

Arithmetic series sum

Sum of the first n terms.

a^m \cdot a^n = a^{m+n}

Exponent product rule

Multiplying powers of the same base.

f(x) = (x - a) \, q(x) + f(a)

Polynomial remainder theorem

f(a) is the remainder of f(x) ÷ (x − a).

\lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}

L'Hôpital's rule

Indeterminate forms 0/0 or ∞/∞.

\int u \, dv = uv - \int v \, du

Integration by parts

∫ u dv = uv − ∫ v du.

\left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2}

Quotient rule

Derivative of f/g.

e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}

Maclaurin series for eˣ

Power series around 0.

(AB)_{ij} = \sum_{k=1}^{n} A_{ik} B_{kj}

Matrix multiplication entry

(AB)_{ij} as a sum over k.

\dim(V) = \operatorname{rank}(T) + \operatorname{nullity}(T)

Rank–nullity theorem

dim(domain) = rank + nullity.

(AB)^{\top} = B^{\top} A^{\top}

Transpose of a product

(AB)ᵀ = BᵀAᵀ.

\rho_{X,Y} = \frac{\operatorname{Cov}(X, Y)}{\sigma_X \sigma_Y}

Pearson correlation

Covariance normalized by standard deviations.

\hat{\beta} = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x})^2}

OLS slope

Slope of the least-squares regression line.

P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}

Poisson distribution

Probability mass function with rate λ.

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

Binomial distribution

PMF for n trials with success probability p.

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Law of sines

Side / sine ratio is constant in any triangle.

\cos(2\theta) = 1 - 2 \sin^2 \theta

Cosine double-angle

cos(2θ) = 1 − 2sin²θ.

E_k = \tfrac{1}{2} m v^2

Kinetic energy

Energy of a moving object.

F = G \, \frac{m_1 m_2}{r^2}

Newtonian gravity

Force between two point masses.

F = k_e \, \frac{q_1 q_2}{r^2}

Coulomb's law

Electrostatic force between two charges.

V = I R

Ohm's law

V = I · R.

\mathbf{p} = m \mathbf{v}

Linear momentum

p = m · v.

P(n, k) = \frac{n!}{(n-k)!}

Permutations of k from n

Ordered selection without replacement.

\varphi(n) = n \prod_{p \mid n} \left(1 - \frac{1}{p}\right)

Euler's totient

Multiplicative on coprime arguments.

(P \rightarrow Q) \equiv (\lnot Q \rightarrow \lnot P)

Contrapositive

An implication is equivalent to its contrapositive.

\lnot (P \land Q) \equiv \lnot P \lor \lnot Q, \quad \lnot (P \lor Q) \equiv \lnot P \land \lnot Q

De Morgan's laws (logic)

Negation distributes over ∧ and ∨ by swapping them.

How math equations work in Markdown

Markdown ships unmodified — write $e^{i\pi} + 1 = 0$ and your renderer prints those exact characters. To turn LaTeX into pretty mathematical notation you need a math renderer wired into your pipeline. Two libraries dominate, both speak standard LaTeX:

KaTeX — fast, server-side renderable, slightly smaller subset of LaTeX. Used by GitLab, our editor, Notion (limited), Docusaurus, MkDocs Material, and most modern docs frameworks.
MathJax — broader feature coverage, including elaborate macros and accessibility tree generation. Used by GitHub, Stack Overflow, Wikipedia, and most academic publishers.

For 95% of equations the source is identical between the two — the catalog below works on both.

The two flavors of delimiter

Inline math: $E = mc^2$ flows with the surrounding sentence.

Block math (centered on its own lines):

$$
\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}
$$

Both use $ for inline and $$ for block. Pick block for important, complex equations; inline for short fragments inside prose. Each template ships with a recommended mode in the catalog — short expressions like a^2 + b^2 = c^2 default to inline, complex ones like the normal distribution PDF default to block.

Where it renders

Platform	Math renderer	Notes
GitHub README / issues / PRs	MathJax (built-in)	Live since 2022
GitLab	KaTeX (built-in)	Default
Markdown Viewer editor	KaTeX (live)	Re-renders as you type
Notion	KaTeX (limited)	`/equation` block
Obsidian	MathJax (built-in)	No setup required
Joplin	KaTeX (built-in)	Same UX as Obsidian
Docusaurus	KaTeX or MathJax	`@docusaurus/theme-mermaid` not required
MkDocs Material	MathJax / KaTeX	`pymdownx.arithmatex` extension
Hugo	KaTeX	Themed shortcodes

Quick LaTeX pointers

Greek letters. \alpha \beta \gamma \Delta \Omega → α β γ Δ Ω. Capitalize the command for uppercase.
Fractions. \frac{a}{b} for a/b. \tfrac for inline-sized fractions.
Powers & subscripts. x^2, x_i, x^{2n+1}, x_{i,j}. Always brace multi-character indices.
Roots. \sqrt{x}, \sqrt[3]{x} for cube root.
Sums, products, integrals. \sum_{i=1}^{n}, \prod_{i=1}^{n}, \int_a^b.
Matrices. Wrap rows separated by \\ inside \begin{bmatrix} … \end{bmatrix} (square brackets) or pmatrix (parens), vmatrix (vertical bars, for determinants).
Operators. \cdot (centered dot), \times, \pm, \leq, \geq, \neq, \approx.
Sets & logic. \in, \subset, \cup, \cap, \rightarrow, \forall, \exists.
Vectors & bold. \mathbf{v} for bold vector. \vec{v} for arrow notation.
Spacing. \, thin space, \; medium, \quad em-quad, \qquad double em-quad.

Common gotchas

Backslash escapes inside JSON or YAML double up: write \\frac{a}{b} in a YAML front-matter string for the renderer to receive \frac{a}{b}.
Smart quotes break math. Paste from Word or Notion and KaTeX rejects the equation. Run the source through the Typography Cleaner first.
$ in plain prose can false-trigger math mode on GitHub if the surrounding text looks math-shaped. Escape with \$ or wrap in backticks.

Why use templates instead of writing from scratch?

Writing LaTeX from scratch every time is slow and error-prone — most teams hit the same dozen equations over and over. The catalog below covers the common cases:

Algebra: quadratic, Pythagorean, binomial, geometric series, logarithms.
Calculus: derivative, integral, chain rule, product rule, fundamental theorem, Taylor series.
Linear algebra: dot product, matrices, determinants, eigenvalue equation.
Statistics: mean, variance, standard deviation, normal PDF, Bayes' theorem, z-score.
Trigonometry: Pythagorean identity, sum/difference formulas, law of cosines, Euler's formula.
Physics: E = mc², F = ma, Schrödinger, wave equation.
Discrete & set/logic: Fermat's little theorem, binomial coefficient, De Morgan, modus ponens.

Workflow tips

Live-edit in our editor. The Markdown Editor preview pane renders KaTeX as you type. Way faster than the GitHub edit-commit-refresh loop.
Pair with diagrams. For technical content combining equations and architecture sketches, see the Mermaid Diagram Inventory.
Audit your prose. Use the Markdown Word Counter and Reading Time Estimator to make sure your math-heavy section is paced well.
Clean up smart quotes with the Typography Cleaner before posting to GitHub — copy-paste from Word frequently introduces curly quotes that break KaTeX parsing.

Companion tools

Markdown Editor — math renders live, side by side.
Mermaid Diagram Inventory — same idea, for diagrams.
Markdown Code Block Extractor — pull all math fences out of a document.
Markdown Typography Cleaner — strip smart quotes that break math parsing.
GFM Compliance Checklist — confirm overall document health before publish.

Frequently asked questions

What is this math equation inventory?

A curated library of 59 production-quality LaTeX equation templates rendered with KaTeX. Covers algebra, calculus, linear algebra, statistics, trigonometry, physics, discrete math, and set theory / logic. Each card shows the live-rendered equation plus a description. Copy as inline ($…$), block ($$…$$), or raw LaTeX with no delimiters — pick whichever format your downstream renderer expects.

How do I use a template?

Pick the desired format at the top: Recommended (each equation's best fit), Inline ($…$), Block ($$…$$), or Raw LaTeX. Click Copy on any card to put it on your clipboard, then paste into your Markdown document. The wrapping delimiters are included automatically.

Which renderers support these equations?

KaTeX and MathJax both parse standard LaTeX. Our editor uses KaTeX. GitHub renders math in READMEs, issues, and PRs since 2022 via MathJax. Notion, Obsidian, Joplin, Docusaurus, MkDocs Material, Hugo, Astro, and Jekyll all support either KaTeX or MathJax through plugins — the LaTeX source itself is identical.

What's the difference between inline and block math?

Inline math like `$a^2 + b^2 = c^2$` flows with surrounding text and uses a compact layout. Block math like `$$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$` sits on its own lines, centered, with larger glyphs — better for important or complex equations. Each template ships with a recommended mode used by the Recommended copy option; you can override with Inline or Block in the dropdown.

Why do equations look like raw text in my Markdown?

Markdown by itself doesn't render LaTeX — you need KaTeX, MathJax, or another math plugin in your render pipeline. Our editor handles this out of the box. For static-site generators, look for math plugins (e.g., remark-math + rehype-katex for unified-based tooling, docusaurus-mathjax for Docusaurus, the mathjax extension for MkDocs Material).

Where does GitHub support math?

GitHub renders math in README files, issue/PR descriptions, comments, and discussions. Inline math uses `$…$`. Block math uses `$$…$$`. The renderer is GitHub-flavored MathJax — supports most KaTeX equations one-to-one. Inline math containing a dollar sign in regular prose can occasionally false-positive trigger math mode; wrap with backticks or escape with `\$` to disambiguate.

How do I write LaTeX from scratch?

Common building blocks: `\frac{a}{b}` for fractions, `x^2` for superscript, `x_i` for subscript, `\sqrt{x}` for roots, `\sum_{i=1}^n` for summation, `\int_a^b` for integration, `\alpha \beta \gamma` for Greek letters, `\begin{bmatrix} … \end{bmatrix}` for matrices. Wrap groups with `{ }`. Use `\\` for line breaks inside matrices and aligned environments.

Why do some templates use \\ inside matrices?

In LaTeX, `\\` separates rows in matrix and aligned environments. Inside a JavaScript string literal you'd see `\\\\` (escaped twice). When you copy from the inventory, the clipboard receives the correct `\\` so it pastes into your Markdown intact.

Is there a picker inside the editor too?

Yes. Open the [Markdown Editor](/editor) and click the math (Σ) icon — the same templates appear in a modal with live KaTeX preview. Click a card to insert at the cursor.

Can I contribute a new equation template?

Open an issue or pull request on our [GitHub repository](https://github.com/saifurrahmanshochib/markdown-viewer). Templates live in `lib/markdown-math-templates.ts` — one entry per equation with title, description, category, LaTeX source, and a preferred render mode. The inventory page and editor picker both pick it up automatically.

One copy. An equation anywhere Markdown is rendered.

Free for any project — personal, commercial, internal. No signup, no API key, no attribution required.

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