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LaTeX math cheat sheet: fractions, roots, integrals, Greek letters
This cheat sheet collects the LaTeX math commands you need most often, grouped by topic. Every command goes inside math mode, so wrap it in $…$ for inline math or \[…\] for a displayed formula.
Most commands are part of core LaTeX. Some come from the amsmath or amssymb packages; they are marked in the tables. In a full LaTeX document, load them in the preamble with \usepackage{amsmath} and \usepackage{amssymb}. Many formula editors and web renderers include these commands out of the box.
Fractions, roots, powers and indices
Braces group everything that belongs together. x^2 works for a single character, but x^{10} needs braces, otherwise only the 1 is raised. The same applies to subscripts and to the arguments of \frac and \sqrt.
| What | Command | Example / note |
|---|---|---|
| Superscript | x^{2} | x squared |
| Subscript | a_{n} | a with index n |
| Fraction | \frac{a}{b} | a over b |
| Fraction, display size (amsmath) | \dfrac{a}{b} | large fraction inline |
| Fraction, text size (amsmath) | \tfrac{1}{2} | small fraction |
| Square root | \sqrt{x} | root of x |
| n-th root | \sqrt[n]{x} | cube root: \sqrt[3]{8} |
| Binomial coefficient (amsmath) | \binom{n}{k} | n choose k |
| Text in a formula (amsmath) | \text{if } x > 0 | upright words |
| Multiplication dot | a \cdot b | centered dot |
| Times sign | a \times b | cross |
| Plus/minus | \pm | x = \pm 1 |
Greek letters
Lowercase Greek letters are written as their name with a backslash. For uppercase letters, capitalize the first letter of the command – but only where the uppercase letter looks different from a Latin one. Uppercase alpha, beta and the others are just the Latin letters A, B and so on; there is no \Alpha in standard LaTeX. There is no \omicron either; use a plain o.
Variant forms: \varepsilon, \vartheta, \varphi, \varrho, \varsigma and \varpi. Many people prefer \varepsilon and \varphi because they match handwriting.
| Letter | Lowercase | Uppercase |
|---|---|---|
| Alpha | \alpha | plain A |
| Beta | \beta | plain B |
| Gamma | \gamma | \Gamma |
| Delta | \delta | \Delta |
| Epsilon | \epsilon | plain E |
| Zeta | \zeta | plain Z |
| Eta | \eta | plain H |
| Theta | \theta | \Theta |
| Iota | \iota | plain I |
| Kappa | \kappa | plain K |
| Lambda | \lambda | \Lambda |
| Mu | \mu | plain M |
| Nu | \nu | plain N |
| Xi | \xi | \Xi |
| Pi | \pi | \Pi |
| Rho | \rho | plain P |
| Sigma | \sigma | \Sigma |
| Tau | \tau | plain T |
| Upsilon | \upsilon | \Upsilon |
| Phi | \phi | \Phi |
| Chi | \chi | plain X |
| Psi | \psi | \Psi |
| Omega | \omega | \Omega |
Sums, integrals, limits and functions
Limits of sums, products and integrals are written as subscript and superscript. In display math they appear above and below the symbol, inline they move to the side. The small space \, before dx is a typographic convention that separates the differential from the integrand.
| What | Command | Example / note |
|---|---|---|
| Sum | \sum_{i=1}^{n} a_i | sum from i = 1 to n |
| Product | \prod_{i=1}^{n} a_i | product |
| Integral | \int_{a}^{b} f(x)\,dx | definite integral |
| Double integral (amsmath) | \iint_{D} f\,dA | area integral |
| Triple integral (amsmath) | \iiint_{V} f\,dV | volume integral |
| Contour integral | \oint_{C} \vec{F} \cdot d\vec{r} | closed curve |
| Limit | \lim_{x \to 0} \frac{\sin x}{x} | limit |
| Infinity | \infty | \sum_{n=1}^{\infty} |
| Partial derivative | \frac{\partial f}{\partial x} | partial |
| Nabla | \nabla f | gradient |
| Functions | \sin x, \cos x, \ln x, \log x, \exp x | upright function names |
| Own operator (amsmath) | \operatorname{sgn}(x) | upright, correct spacing |
Do it with TexletLearn more →Relations, sets, logic and arrows
\le and \ge are short forms of \leq and \geq, \ne is a short form of \neq. amsmath additionally offers \implies and \iff, which add extra space around the arrows.
| What | Command |
|---|---|
| Less or equal | \leq |
| Greater or equal | \geq |
| Not equal | \neq |
| Approximately | \approx |
| Identical / congruent | \equiv |
| Proportional | \propto |
| Element of | \in |
| Not an element of | \notin |
| Subset | \subset |
| Subset or equal | \subseteq |
| Union / intersection | \cup, \cap |
| For all / exists | \forall, \exists |
| Empty set | \emptyset |
| Arrow (short form \to) | \rightarrow |
| Implies | \Rightarrow |
| If and only if | \Leftrightarrow |
| Maps to | \mapsto |
| Logical and / or / not | \land, \lor, \neg |
Accents and math fonts
Accents apply to the next character or group. For accents across several letters, use the wide forms \widehat{…} and \widetilde{…} or \overline{…}.
| What | Command |
|---|---|
| Vector arrow | \vec{v} |
| Hat | \hat{x} |
| Bar (mean) | \bar{x} |
| Long bar | \overline{AB} |
| Tilde | \tilde{a} |
| Dot / double dot (derivative) | \dot{x}, \ddot{x} |
| Bold (upright) | \mathbf{v} |
| Bold Greek (amsmath) | \boldsymbol{\alpha} |
| Upright | \mathrm{d}x |
| Number sets (amssymb) | \mathbb{R}, \mathbb{N}, \mathbb{Z} |
| Calligraphic | \mathcal{L} |
Brackets, dots and spacing
Plain parentheses keep their size. \left and \right make a pair of delimiters grow with the content between them; they must always come in pairs. If you only need one side, use a dot as an invisible partner: \left. … \right|.
| What | Command |
|---|---|
| Growing parentheses | \left( \frac{a}{b} \right) |
| Braces | \{ x \mid x > 0 \} |
| Angle brackets | \langle u, v \rangle |
| Absolute value (amsmath) | \lvert x \rvert |
| Norm (amsmath) | \lVert v \rVert |
| Floor / ceiling | \lfloor x \rfloor, \lceil x \rceil |
| Dots on the baseline / centered | \ldots, \cdots |
| Small / medium / large space | \, \; \quad |
Trying the commands without a setup
The quickest way to learn these commands is to type them and watch the result. Texlet shows a live preview of your formula as you write, works offline, and has building blocks above the keyboard for fractions, roots, superscripts and subscripts, Greek letters, sums, integrals, relations, arrows and brackets. The app also includes a LaTeX guide with examples, and with Texlet Pro you can copy a finished formula as an image or export it as PDF or PNG.
Frequently asked questions
How do I write a fraction in LaTeX?
Use \frac{numerator}{denominator}, for example \frac{a}{b}. With amsmath, \dfrac{a}{b} forces a large fraction and \tfrac{a}{b} a small one.
How do I write a square root or an n-th root?
\sqrt{x} gives the square root; the optional argument in square brackets sets the degree, for example \sqrt[3]{x} for the cube root.
Why does \mathbb{R} not work?
\mathbb is defined in the amssymb package (or amsfonts). Add \usepackage{amssymb} to the preamble of your document. Many formula editors load it automatically.
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