Unlike word processors that focus on visual formatting, LaTeX is markup-based document preparation system. It is widely used in academia, science, engineering, and mathematics for producing high-quality, structured documents. You write plain text with embedded commands that describe the structure and meaning of the content, and the system compiles it into a professionally typeset document. This approach is especially powerful for handling complex elements like equations, references, bibliographies, and large documents such as theses or research papers.
LaTeX Mathematical Symbols
One of LaTeX’s core strengths is its mathematical typesetting capability. Mathematical symbols in LaTeX are written using specific commands inside math mode, which is activated using delimiters like $…$ , \[ ... \] , or \begin{equation} ... \end{equation} . Instead of manually formatting symbols, users write semantic commands such as \alpha for α, \sum for summation (∑), or \int for integrals (∫). LaTeX then renders these symbols with proper spacing, alignment, and sizing, ensuring consistency and readability.
LaTeX supports a vast range of mathematical symbols, including Greek letters , operators, relations, arrows , and specialized notation for advanced fields like linear algebra, calculus, and logic. Additional packages such as amsmath and amssymb extend this functionality further, enabling complex structures like multi-line equations, matrices, and aligned formulas. This makes LaTeX the standard tool for anyone who needs precise and elegant representation of mathematical content.
1. Greek Letters
Symbol Code Function α \alpha Lowercase alpha β \beta Lowercase beta γ \gamma Lowercase gamma δ \delta Lowercase delta ε \epsilon Lowercase epsilon ϵ \varepsilon Variant epsilon ζ \zeta Lowercase zeta η \eta Lowercase eta θ \theta Lowercase theta ϑ \vartheta Variant theta ι \iota Lowercase iota κ \kappa Lowercase kappa λ \lambda Lowercase lambda μ \mu Lowercase mu ν \nu Lowercase nu ξ \xi Lowercase xi ο \omicron Lowercase omicron π \pi Lowercase pi ϖ \varpi Variant pi ρ \rho Lowercase rho ϱ \varrho Variant rho σ \sigma Lowercase sigma ς \varsigma Variant sigma (end form) τ \tau Lowercase tau υ \upsilon Lowercase upsilon φ \phi Lowercase phi φ \varphi Variant phi (often identical) χ \chi Lowercase chi ψ \psi Lowercase psi ω \omega Lowercase omega Γ \Gamma Uppercase Gamma Δ \Delta Uppercase Delta Θ \Theta Uppercase Theta Λ \Lambda Uppercase Lambda Ξ \Xi Uppercase Xi Π \Pi Uppercase Pi Σ \Sigma Uppercase Sigma Υ \Upsilon Uppercase Upsilon Φ \Phi Uppercase Phi Ψ \Psi Uppercase Psi Ω \Omega Uppercase Omega
2. Binary Operators
Symbol Code Function + + Addition − – Subtraction ± \pm Plus-minus ∓ \mp Minus-plus ⋅ \cdot Centered dot × \times Multiplication (cross) ÷ \div Division ∗ \ast Asterisk operator ⋆ \star Star operator ∘ \circ Composition/circle ∙ \bullet Bullet operator ∩ \cap Set intersection ∪ \cup Set union ⊔ \sqcup Square union ⊓ \sqcap Square intersection ∨ \vee Logical OR (join) ∧ \wedge Logical AND (meet) ⊕ \oplus Direct sum / circled plus ⊖ \ominus Circled minus ⊗ \otimes Tensor product / circled times ⊘ \oslash Circled division ⊙ \odot Circled dot ⊎ \uplus Multiset union ⋄ \diamond Diamond operator ◇ \Diamond Large diamond (amssymb) △ \triangle Triangle ▽ \bigtriangleup Big triangle up ▼ \bigtriangledown Big triangle down ◃ \triangleleft Triangle left ▹ \triangleright Triangle right ⋉ \ltimes Left semidirect product ⋊ \rtimes Right semidirect product ⋋ \leftthreetimes Left threetimes ⋌ \rightthreetimes Right threetimes ⋏ \curlywedge Curly wedge ⋎ \curlyvee Curly vee ∐ \amalg Amalgamation/coproduct
3. Relation Symbols
Symbol Code Function = = Equals ≠ \neq or \ne Not equal < < Less than > > Greater than ≤ \leq or \le Less than or equal ≥ \geq or \ge Greater than or equal ≪ \ll Much less than ≫ \gg Much greater than ≈ \approx Approximately equal ≅ \cong Congruent / isomorphic ≃ \simeq Similar / asymptotic equal ∼ \sim Similar to / tilde operator ≁ \nsim Not similar ≉ \not\approx Not approximately equal ≡ \equiv Identically equal / equivalence ≢ \not\equiv Not identical ⊂ \subset Proper subset ⊃ \supset Proper superset ⊆ \subseteq Subset or equal ⊇ \supseteq Superset or equal ⊄ \not\subset Not subset ⊈ \nsubseteq Not subset or equal ⊉ \nsupseteq Not superset or equal ⊊ \subsetneq Proper subset (strict) ⊋ \supsetneq Proper superset (strict) ∈ \in Element of ∋ \ni or \owns Contains as member ∉ \notin Not element of ∌ \not\ni Does not contain ⊢ \vdash Provable / turnstile ⊣ \dashv Reverse turnstile ⊧ \models Models ∣ \mid Divides / such that ∤ \nmid Does not divide ∥ \parallel Parallel ∦ \nparallel Not parallel ⊥ \perp Perpendicular ≐ \doteq Doted equal ∝ \propto Proportional to ≺ \prec Precedes ≻ \succ Succeeds ⪯ \preceq Precedes or equal ⪰ \succeq Succeeds or equal ⊀ \not\prec Does not precede ⊁ \not\succ Does not succeed
4. Arrows
Symbol Code Function ⟶ \dashleftarrow Dashed left arrow ⟵ \dashrightarrow Dashed right arrow ⇇ \leftleftarrows Double left arrows ⇉ \rightrightarrows Double right arrows ⇊ \downdownarrows Double down arrows ⇈ \upuparrows Double up arrows ⇔ \Leftrightarrow Double arrow (iff) ⇀ \downharpoonright Down harpoon right ⇃ \downharpoonleft Down harpoon left ⇓ \Downarrow Down double arrow ↓ \downarrow Down arrow ↞ \twoheadleftarrow Two-headed left arrow ↠ \twoheadrightarrow Two-headed right arrow ⇚ \Lleftarrow Double long left arrow ↰ \Lsh Left shift arrow ↱ \Rsh Right shift arrow ← \leftarrow Left arrow ↢ \leftarrowtail Left arrow with tail ⇐ \Leftarrow Left double arrow ⟵ \longleftarrow Long left arrow ⟸ \Longleftarrow Long left double arrow ↩ \hookleftarrow Hook left arrow ↪ \hookrightarrow Hook right arrow ⇄ \leftrightarrows Left-right arrows ↔ \leftrightarrow Left-right arrow ⟷ \longleftrightarrow Long left-right arrow ↭ \leftrightsquigarrow Left-right squiggle arrow ⇋ \leftrightharpoons Harpoons both directions ⇌ \rightleftharpoons Right-left harpoons ⇄ \rightleftarrows Right-left arrows ⇋ \rightleftharpoons Right-left harpoons ⇝ \leadsto Leads to ↶ \curvearrowleft Curved left arrow ↷ \curvearrowright Curved right arrow ↺ \circlearrowleft Circular left arrow ↻ \circlearrowright Circular right arrow ↺ \looparrowleft Looping left arrow ↻ \looparrowright Looping right arrow ↦ \mapsto Mapsto ⟼ \longmapsto Long mapsto ⊸ \multimap Multimap ↗ \nearrow North-east arrow ↖ \nwarrow North-west arrow ↘ \searrow South-east arrow ↙ \swarrow South-west arrow → \rightarrow Right arrow ↣ \rightarrowtail Right arrow with tail ⇒ \Rightarrow Right double arrow ⟶ \longrightarrow Long right arrow ⟹ \Longrightarrow Long right double arrow ⇀ \rightharpoonup Right harpoon up ⇁ \rightharpoondown Right harpoon down ↝ \rightsquigarrow Right squiggle arrow ↼ \leftharpoonup Left harpoon up ↽ \leftharpoondown Left harpoon down ⇑ \Uparrow Up double arrow ↑ \uparrow Up arrow ↕ \updownarrow Up-down arrow ⇕ \Updownarrow Up-down double arrow ↿ \upharpoonleft Up harpoon left ⇀ \upharpoonright Up harpoon right ↚ \nleftarrow Not left arrow ↛ \nrightarrow Not right arrow ⇍ \nLeftarrow Not left double arrow ⇏ \nRightarrow Not right double arrow ↮ \nleftrightarrow Not left-right arrow ⇎ \nLeftrightarrow Not double arrow
5. Delimiters and Brackets
Symbol Code Function ( ( Left parenthesis ) ) Right parenthesis [ [ Left bracket ] ] Right bracket { \{ Left curly brace } /} Right curly brace ⌊ \lfloor Left floor ⌋ \rfloor Right floor ⌈ \lceil Left ceiling ⌉ \rceil Right ceiling ⟨ \langle Left angle bracket ⟩ \rangle Right angle bracket / / Forward slash \ \backslash Backslash | | Pipeline
6. Miscellaneous Symbols
Symbol Code Function ∞ \infty Infinity ∇ \nabla Nabla (gradient) ∂ \partial Partial derivative ℓ \ell Script l ℏ \hbar Reduced Planck constant ∅ \emptyset Empty set ı \imath Dotless i ȷ \jmath Dotless j ℘ \wp Weierstrass P ℜ \Re Real part ℑ \Im Imaginary part ∀ \forall For all ∃ \exists There exists ¬ \neg Logical not ∧ \land Logical and ∨ \lor Logical or ⊻ \veebar Exclusive or ∴ \therefore Therefore ∵ \because Because a/b \frac{a}{b} Fraction √a \sqrt{a} Square root ⁿ√ab \sqrt[n]{ab} Nth root ∠ \angle Angle ∡ \measuredangle Measured angle ∢ \sphericalangle Spherical angle ⊥ \bot Bottom / false / perpendicular ⊤ \top Top / true ⊢ \vdash Turnstile (provable) ⊣ \dashv Reverse turnstile ∎ \Box Square (end of proof) ◇ \Diamond Diamond △ \triangle Triangle ▽ \bigtriangledown Big triangle down □ \square Hollow square ♯ \sharp Sharp (music) ♭ \flat Flat ♮ \natural Natural % % Percent sign § \S Section sign ¶ \P Paragraph sign … \dots or \ldots Ellipsis (low) ⋯ \cdots Centered ellipsis ⋮ \vdots Vertical ellipsis ⋱ \ddots Diagonal ellipsis
7. Accents and Decorations
Symbol Code Function â \hat{a} Hat (circumflex) ȧ \dot{a} Single dot derivative ä \ddot{a} Double dot a⃛ \dddot{a} Triple dot (amsmath) a⃜ \ddddot{a} Four dots (amsmath) ā \bar{a} Bar over one character a̅b̅ \overline{ab} Overline (multiple chars) a̲ \underline{a} Underline →a \vec{a} Vector arrow ã \tilde{a} Tilde ãbc \widetilde{abc} Wide tilde ǎ \check{a} Check (caron) ă \breve{a} Breve à \grave{a} Grave accent á \acute{a} Acute accent å \mathring{a} Ring
8. Operators and Large Symbols
Symbol Code Function ∑ \sum Summation (large) ∏ \prod Product ∐ \coprod Coproduct ∫ \int Integral ∬ \iint Double integral ∭ \iiint Triple integral ∮ \oint Contour integral ⋂ \bigcap Big intersection ⋃ \bigcup Big union ⨆ \bigsqcup Big square union ⨁ \bigoplus Big direct sum ⨂ \bigotimes Big tensor product ⨀ \bigodot Big dot product ⋁ \bigvee Big logical or ⋀ \bigwedge Big logical and ⨄ \biguplus Big multiset union lim \lim Limit max \max Maximum min \min Minimum sup \sup Supremum inf \inf Infimum arg \arg Argument det \det Determinant dim \dim Dimension exp \exp Exponential function gcd \gcd Greatest common divisor hom \hom Homomorphism inf \inf Infimum ker \ker Kernel lg \lg Base-2 logarithm lim \lim Limit liminf \liminf Limit inferior limsup \limsup Limit superior ln \ln Natural logarithm log \log Logarithm max \max Maximum min \min Minimum Pr \Pr Probability sup \sup Supremum
9. Special Functions and Named Operators
Symbol Code Function sin \sin Sine cos \cos Cosine tan \tan Tangent csc \csc Cosecant sec \sec Secant cot \cot Cotangent arcsin \arcsin Inverse sine arccos \arccos Inverse cosine arctan \arctan Inverse tangent sinh \sinh Hyperbolic sine cosh \cosh Hyperbolic cosine tanh \tanh Hyperbolic tangent coth \coth Hyperbolic cotangent mod \bmod Binary modulo (a mod b) mod \pmod{m} Parenthesized modulo gcd \gcd Greatest common divisor lcm \lcm Least common multiple (define) arg \arg Argument (complex) deg \deg Degree
10. Mathematical Alphabets
Style Code Roman (default) (none) Bold \mathbf{} Italic \mathit{} Bold italic \bm{} Sans-serif \mathsf{} Bold sans-serif \mathsf{} (with bold) Typewriter \mathtt{} Calligraphic \mathcal{} Script \mathscr{} Blackboard bold \mathbb{} Fraktur \mathfrak{}
Example usage: \mathbb{R} will make ℝ \mathbb{R} ℒ \mathcal{L}
Conclusion
This guide covers the vast majority of mathematical symbols you will need when typesetting mathematics in LaTeX. For any symbol not listed here, consult the comprehensive symbol list (texdoc comprehensive in your terminal) or use Detexify (an online tool where you draw the symbol and it suggests LaTeX code).
