The formula notebook
Start with a working formula. Browse LaTeX examples for matrices, fractions, integrals, probability, and multiline equations, then turn them into PNG, SVG, or JPG images.
Browse 30 examples, search by name or command, then copy the source or open it in the converter. Each example includes editing tips and a link you can share. New equations start as transparent PNG at 2× scale.
Search English or Chinese names and LaTeX commands. Category filters also apply.
30 examples
Every preview includes editable LaTeX source.
Algebra & fractions
Use grouped braces for the numerator, denominator, and the expression under the square root.
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Algebra & fractions
Combine a summation with a binomial coefficient. Change n to suit your expression.
(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k
Algebra & fractions
A starter fraction for ratios and algebraic expressions.
\frac{a+b}{c+d}
Algebra & fractions
Show a fraction inside another fraction, as used in continued fractions.
\frac{1}{1+\frac{1}{x}}
Algebra & fractions
Combine a square root, a power, and a multi-character subscript in a recurrence.
x_{n+1} = \sqrt{x_n^2 + a_n^2}
Calculus
Place lower and upper bounds on the integral, with a small space before the differential.
\int_0^\infty e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}
Calculus
Use the limit operator and a fraction to keep the approach value and ratio legible.
\lim_{x \to 0} \frac{\sin x}{x} = 1
Calculus
Write an ordinary derivative using a fraction and a power.
\frac{d}{dx} x^n = n x^{n-1}
Calculus
Differentiate a function of two variables with respect to x.
f(x,y)=x^2y \qquad \frac{\partial f}{\partial x}=2xy
Calculus
Express integration over the unit square as two iterated integrals.
\iint_{[0,1]^2} xy\,dA = \int_0^1 \int_0^1 xy\,dx\,dy
Matrices
The bmatrix environment adds square brackets. Use & between columns and two backslashes between rows.
A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
Matrices
The vmatrix environment uses vertical bars around the entries of a determinant.
\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad-bc
Matrices
Display nine entries with round matrix brackets.
A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}
Matrices
Stack three components in a single column.
\mathbf{v} = \begin{bmatrix} x \\ y \\ z \end{bmatrix}
Matrices
Use horizontal, vertical, and diagonal dots to indicate omitted entries.
A = \begin{bmatrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{m1} & \cdots & a_{mn} \end{bmatrix}
Multiline & cases
Align both lines at the equals sign using &. Each pair of backslashes starts a new row.
\begin{aligned}
(a+b)^2 &= (a+b)(a+b) \\
&= a^2 + 2ab + b^2
\end{aligned}
Multiline & cases
The cases environment places values beside their conditions under a single left brace.
|x| = \begin{cases}
x & x \ge 0 \\
-x & x < 0
\end{cases}
Multiline & cases
Group two equations under a single left brace.
\begin{cases}
2x+y=5 \\
x-y=1
\end{cases}
Multiline & cases
Define the sign function with negative, zero, and positive branches.
\operatorname{sgn}(x) = \begin{cases}
-1 & x<0 \\
0 & x=0 \\
1 & x>0
\end{cases}
Multiline & cases
Split a wide polynomial expansion into readable aligned lines.
\begin{aligned}
(a+b+c)^2 &= a^2+b^2+c^2 \\
&\quad +2ab+2ac+2bc
\end{aligned}
Probability
Use a conditional bar inside each probability. This identity assumes P(B) is greater than zero.
P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}
Probability
Nested fractions, Greek letters, and an exponent describe the density for a positive standard deviation.
f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}
Probability
Use an overbar and a summation to show the average of n observations.
\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i
Probability
Use blackboard-bold expectation symbols and paired scalable brackets.
\operatorname{Var}(X) = \mathbb{E}\!\left[(X-\mathbb{E}[X])^2\right]
Probability
Show the probability of k successes in n independent Bernoulli trials.
P(X=k) = \binom{n}{k} p^k(1-p)^{n-k}
Symbols & sets
A short example of superscripts and the Greek letter pi. Group the full exponent in braces.
e^{i\pi}+1=0
Symbols & sets
Use escaped braces for a visible set, membership symbols, and a text command for words.
A \cap B = \{x \mid x \in A \text{ and } x \in B\}
Symbols & sets
A compact reference for parameters used in mathematics and science.
\alpha,\ \beta,\ \gamma,\ \theta,\ \lambda,\ \mu,\ \sigma,\ \Omega
Symbols & sets
Combine “for all”, “there exists”, membership, and logical conjunction.
\forall x \in \mathbb{R},\quad x^2 \ge 0 \quad \land \quad \exists y \in \mathbb{R}: y^2=2
Symbols & sets
Compare blackboard bold, calligraphic, bold Latin, and bold Greek styles.
\mathbb{R}\quad \mathcal{F}\quad \mathbf{v}\quad \boldsymbol{\alpha}Edit a grid of up to 10 × 10 cells and export the matrix as an image.
Open matrix generator →Build tabular or booktabs source from cells or CSV. The preview shows the layout; this tool exports table code.
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