A comprehensive collection of mathematical symbols with their names, meanings, and examples. Click any symbol to copy it instantly!
Mathematical symbols are specialized characters used to represent mathematical concepts, operations, relations, and quantities. They form the universal language of mathematics, enabling precise communication of complex ideas across cultures and languages.
From basic arithmetic operators like + and − to advanced notation in calculus and set theory, these symbols have evolved over centuries. This comprehensive maths symbols chart covers all mathematical symbols with their names and meanings, organized by category for easy reference.
Whether you're a student, teacher, engineer, or researcher, this all mathematical symbols guide serves as your complete reference for mathematical notation.
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| + | Plus | Addition | 3 + 5 = 8 |
| − | Minus | Subtraction | 9 − 4 = 5 |
| × | Times | Multiplication | 4 × 3 = 12 |
| ÷ | Division | Division | 12 ÷ 4 = 3 |
| / | Slash | Division / Fraction | 6/2 = 3 |
| = | Equals | Equality | 2 + 2 = 4 |
| ≠ | Not Equal | Inequality | 5 ≠ 3 |
| < | Less Than | Comparison | 3 < 5 |
| > | Greater Than | Comparison | 7 > 4 |
| ≤ | Less Than or Equal | Comparison | x ≤ 10 |
| ≥ | Greater Than or Equal | Comparison | y ≥ 0 |
| ± | Plus-Minus | Both positive and negative | x = ±5 |
| ∓ | Minus-Plus | Opposite of plus-minus | 3 ± 2 = 5 ∓ 2 |
| % | Percent | Per hundred | 50% = 0.5 |
| ‰ | Per Mille | Per thousand | 5‰ = 0.005 |
| . | Decimal Point | Decimal separator | 3.14 |
| √ | Square Root | Square root | √9 = 3 |
| ∛ | Cube Root | Cube root | ∛8 = 2 |
| ∜ | Fourth Root | Fourth root | ∜16 = 2 |
| ^ | Caret | Exponentiation | 2^3 = 8 |
| ! | Factorial | Factorial | 5! = 120 |
| |x| | Absolute Value | Distance from zero | |−5| = 5 |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| x, y, z | Variables | Unknown values | x + 2 = 5 |
| ≈ | Approximately Equal | Approximation | π ≈ 3.14 |
| ≡ | Identical To | Identical / Congruent | x ≡ y (mod n) |
| ∝ | Proportional To | Proportionality | y ∝ x |
| ∞ | Infinity | Unbounded quantity | lim x→∞ |
| ∑ | Summation | Sum of sequence | ∑(i=1 to n) i |
| ∏ | Product | Product of sequence | ∏(i=1 to n) i = n! |
| ( ) | Parentheses | Grouping | (2 + 3) × 4 |
| [ ] | Brackets | Grouping / Interval | [0, 1] |
| { } | Braces | Set notation | {1, 2, 3} |
| ⌊ ⌋ | Floor | Greatest integer ≤ x | ⌊3.7⌋ = 3 |
| ⌈ ⌉ | Ceiling | Smallest integer ≥ x | ⌈3.2⌉ = 4 |
| f(x) | Function | Function notation | f(x) = x² |
| f⁻¹ | Inverse Function | Inverse of f | f⁻¹(f(x)) = x |
| ° | Degree | Degree of polynomial/angle | 90° |
| ⁿ | Superscript n | Exponent | xⁿ |
| ₙ | Subscript n | Index | aₙ |
| log | Logarithm | Logarithm base 10 | log(100) = 2 |
| ln | Natural Log | Logarithm base e | ln(e) = 1 |
| e | Euler's Number | ≈ 2.71828 | e¹ ≈ 2.718 |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ∠ | Angle | Angle | ∠ABC = 45° |
| ∟ | Right Angle | 90 degree angle | ∟ABC |
| ° | Degree | Angle measurement | 360° |
| ′ | Prime / Minute | Arc minute / feet | 45° 30′ |
| ″ | Double Prime / Second | Arc second / inches | 45° 30′ 15″ |
| ⊥ | Perpendicular | Perpendicular lines | AB ⊥ CD |
| ∥ | Parallel | Parallel lines | AB ∥ CD |
| ∦ | Not Parallel | Not parallel | AB ∦ CD |
| ≅ | Congruent | Same shape and size | △ABC ≅ △DEF |
| ~ | Similar | Same shape, different size | △ABC ~ △DEF |
| △ | Triangle | Triangle shape | △ABC |
| □ | Square | Square / Rectangle | □ABCD |
| ○ | Circle | Circle shape | ○O |
| ⊙ | Circle with Center | Circle with center point | ⊙O |
| π | Pi | Ratio of circumference to diameter | π ≈ 3.14159 |
| rad | Radian | Angle unit | π rad = 180° |
| ⌢ | Arc | Curved line segment | ⌢AB |
| ↔ | Line | Infinite line | ↔AB |
| → | Ray | Half-line | →AB |
| — | Line Segment | Segment between points | AB |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ∫ | Integral | Integration | ∫f(x)dx |
| ∬ | Double Integral | Integration over area | ∬f(x,y)dA |
| ∭ | Triple Integral | Integration over volume | ∭f(x,y,z)dV |
| ∮ | Contour Integral | Line integral over closed curve | ∮f(z)dz |
| ∂ | Partial Derivative | Partial differentiation | ∂f/∂x |
| d/dx | Derivative | Differentiation | d/dx(x²) = 2x |
| f′ | Prime Notation | First derivative | f′(x) |
| f″ | Double Prime | Second derivative | f″(x) |
| ẋ | Dot Notation | Time derivative | ẋ = dx/dt |
| ẍ | Double Dot | Second time derivative | ẍ = d²x/dt² |
| lim | Limit | Limit of function | lim(x→0) sin(x)/x = 1 |
| ∇ | Nabla / Del | Gradient operator | ∇f |
| ∆ | Delta | Change / Difference | ∆x = x₂ − x₁ |
| δ | Lowercase Delta | Infinitesimal change | δx |
| ε | Epsilon | Small positive number | |x − a| < ε |
| ∞ | Infinity | Unbounded limit | lim x→∞ |
| dx | Differential | Infinitesimal change in x | ∫ydx |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| { } | Set Braces | Set notation | {1, 2, 3} |
| ∈ | Element Of | Is member of set | 3 ∈ {1,2,3} |
| ∉ | Not Element Of | Is not member of set | 4 ∉ {1,2,3} |
| ∋ | Contains | Set contains element | {1,2,3} ∋ 2 |
| ⊂ | Proper Subset | Proper subset of | {1,2} ⊂ {1,2,3} |
| ⊃ | Proper Superset | Proper superset of | {1,2,3} ⊃ {1,2} |
| ⊆ | Subset | Subset or equal | A ⊆ B |
| ⊇ | Superset | Superset or equal | B ⊇ A |
| ⊄ | Not Subset | Is not subset of | {1,4} ⊄ {1,2,3} |
| ∪ | Union | Set union | A ∪ B |
| ∩ | Intersection | Set intersection | A ∩ B |
| ∖ | Set Minus | Set difference | A ∖ B |
| ∅ | Empty Set | Set with no elements | A ∩ B = ∅ |
| ℕ | Natural Numbers | {1, 2, 3, ...} | 5 ∈ ℕ |
| ℤ | Integers | {..., -1, 0, 1, ...} | −3 ∈ ℤ |
| ℚ | Rational Numbers | Fractions p/q | ½ ∈ ℚ |
| ℝ | Real Numbers | All real numbers | π ∈ ℝ |
| ℂ | Complex Numbers | a + bi form | 3+2i ∈ ℂ |
| |A| | Cardinality | Number of elements | |{1,2,3}| = 3 |
| 𝒫(A) | Power Set | Set of all subsets | 𝒫({1,2}) |
| × | Cartesian Product | Set of ordered pairs | A × B |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ∧ | Logical And | Conjunction | p ∧ q |
| ∨ | Logical Or | Disjunction | p ∨ q |
| ¬ | Negation | Not | ¬p |
| ~ | Tilde | Negation (alternate) | ~p |
| → | Implication | If...then | p → q |
| ⇒ | Implies | Logical implication | p ⇒ q |
| ↔ | Biconditional | If and only if | p ↔ q |
| ⇔ | Equivalent | Logical equivalence | p ⇔ q |
| ∀ | For All | Universal quantifier | ∀x: P(x) |
| ∃ | There Exists | Existential quantifier | ∃x: P(x) |
| ∃! | Unique Existence | There exists exactly one | ∃!x: P(x) |
| ∴ | Therefore | Logical conclusion | ∴ x = 5 |
| ∵ | Because | Reason follows | ∵ x > 0 |
| ⊤ | Tautology | Always true | p ∨ ¬p = ⊤ |
| ⊥ | Contradiction | Always false | p ∧ ¬p = ⊥ |
| ⊕ | XOR | Exclusive or | p ⊕ q |
| ⊻ | XOR (alternate) | Exclusive or | p ⊻ q |
| ⊢ | Turnstile | Proves / Derives | Γ ⊢ φ |
| ⊨ | Double Turnstile | Models / Satisfies | Γ ⊨ φ |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| P(A) | Probability | Probability of event A | P(A) = 0.5 |
| P(A|B) | Conditional Probability | Probability of A given B | P(A|B) |
| P(A∩B) | Joint Probability | Probability of A and B | P(A∩B) |
| P(A∪B) | Union Probability | Probability of A or B | P(A∪B) |
| μ | Mu | Population mean | μ = 50 |
| x̄ | X-bar | Sample mean | x̄ = 48.5 |
| σ | Sigma | Standard deviation (population) | σ = 5 |
| σ² | Sigma Squared | Variance (population) | σ² = 25 |
| s | S | Standard deviation (sample) | s = 4.8 |
| s² | S Squared | Variance (sample) | s² = 23 |
| ∑ | Summation | Sum of values | ∑xᵢ |
| n | Sample Size | Number in sample | n = 100 |
| N | Population Size | Number in population | N = 10000 |
| E(X) | Expected Value | Expected value of X | E(X) = μ |
| Var(X) | Variance | Variance of X | Var(X) = σ² |
| ρ | Rho | Correlation coefficient | ρ = 0.85 |
| r | R | Sample correlation | r = 0.82 |
| nCr | Combination | n choose r | 5C2 = 10 |
| nPr | Permutation | n permute r | 5P2 = 20 |
| ! | Factorial | Product of integers | 5! = 120 |
| ~ | Distribution | Follows distribution | X ~ N(μ,σ²) |
| N(μ,σ²) | Normal Distribution | Gaussian distribution | X ~ N(0,1) |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| α | Alpha | Angle, coefficient | α = 30° |
| β | Beta | Angle, coefficient | β = 60° |
| γ | Gamma | Angle, Euler constant | γ ≈ 0.5772 |
| Γ | Gamma (upper) | Gamma function | Γ(n) = (n-1)! |
| δ | Delta | Small change | δx |
| Δ | Delta (upper) | Change, discriminant | Δ = b² - 4ac |
| ε | Epsilon | Small positive number | ε > 0 |
| ζ | Zeta | Riemann zeta function | ζ(s) |
| η | Eta | Efficiency, coordinate | η = 0.95 |
| θ | Theta | Angle | θ = 45° |
| Θ | Theta (upper) | Big-Theta notation | Θ(n²) |
| ι | Iota | Index, inclusion | ι: A → B |
| κ | Kappa | Curvature | κ = 1/R |
| λ | Lambda | Eigenvalue, wavelength | λ = 2 |
| Λ | Lambda (upper) | Diagonal matrix | Λ = diag(λ₁,λ₂) |
| μ | Mu | Mean, micro | μ = 100 |
| ν | Nu | Frequency | ν = 50 Hz |
| ξ | Xi | Random variable | ξ ~ N(0,1) |
| Ξ | Xi (upper) | Cascade particle | Ξ⁰ |
| π | Pi | Circle constant ≈ 3.14159 | C = 2πr |
| Π | Pi (upper) | Product notation | Π(i=1 to n) |
| ρ | Rho | Correlation, density | ρ = 0.9 |
| σ | Sigma | Standard deviation | σ = 5 |
| Σ | Sigma (upper) | Summation | Σ(i=1 to n) |
| τ | Tau | Time constant, 2π | τ = 2π |
| υ | Upsilon | Frequency | υ |
| φ | Phi | Golden ratio ≈ 1.618 | φ = (1+√5)/2 |
| Φ | Phi (upper) | CDF of normal dist. | Φ(z) |
| χ | Chi | Chi-square test | χ² |
| ψ | Psi | Wave function | ψ(x) |
| Ψ | Psi (upper) | Digamma function | Ψ(x) |
| ω | Omega | Angular velocity | ω = 2πf |
| Ω | Omega (upper) | Ohm, sample space | R = 10Ω |
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ℵ | Aleph | Cardinality of infinite sets | ℵ₀ |
| ℵ₀ | Aleph Null | Countable infinity | |ℕ| = ℵ₀ |
| ℵ₁ | Aleph One | First uncountable cardinal | ℵ₁ |
| ℶ | Beth | Beth numbers | ℶ₁ = 2^ℵ₀ |
| ∇ | Nabla | Gradient/Del operator | ∇f = grad f |
| ∇² | Laplacian | Laplace operator | ∇²f |
| ∇× | Curl | Curl of vector field | ∇×F |
| ∇· | Divergence | Divergence of vector field | ∇·F |
| ⊗ | Tensor Product | Tensor/Kronecker product | A ⊗ B |
| ⊕ | Direct Sum | Direct sum of spaces | V ⊕ W |
| ⊖ | Symmetric Difference | Set symmetric difference | A ⊖ B |
| ⊙ | Hadamard Product | Element-wise product | A ⊙ B |
| † | Dagger | Hermitian conjugate | A† |
| * | Asterisk | Convolution, conjugate | f * g |
| ∘ | Composition | Function composition | (f ∘ g)(x) |
| ⟨ ⟩ | Angle Brackets | Inner product, expectation | ⟨u, v⟩ |
| ‖ ‖ | Norm | Vector/matrix norm | ‖v‖ = √(v·v) |
| det | Determinant | Matrix determinant | det(A) |
| tr | Trace | Matrix trace | tr(A) |
| rank | Rank | Matrix rank | rank(A) |
| dim | Dimension | Vector space dimension | dim(V) |
| ker | Kernel | Null space | ker(T) |
| im | Image | Range of transformation | im(T) |
| ℓ | Ell | Sequence space | ℓ² |
| ℏ | H-bar | Reduced Planck constant | ℏ = h/2π |
| ∂ | Boundary | Boundary operator | ∂S |
| ⋃ | Big Union | Union of many sets | ⋃(i=1 to n) Aᵢ |
| ⋂ | Big Intersection | Intersection of many sets | ⋂(i=1 to n) Aᵢ |
| ≃ | Homotopy | Homotopy equivalent | X ≃ Y |
| ≅ | Isomorphic | Isomorphism | G ≅ H |
| ≜ | Defined As | Definition | f(x) ≜ x² |
| := | Definition | Is defined as | n := 5 |
| ⌀ | Diameter | Diameter symbol | ⌀ = 10cm |
| ∡ | Measured Angle | Measured angle | ∡ABC = 45° |
| ∢ | Spherical Angle | Spherical angle | ∢ABC |
There are hundreds of mathematical symbols used across different branches of mathematics. This comprehensive page covers over 150 essential symbols from arithmetic, algebra, geometry, calculus, set theory, logic, statistics, and advanced mathematics. New symbols continue to be introduced as mathematics evolves.
Advanced math symbols include Greek letters (α, β, γ, π), calculus notations (∫, ∂, ∇), set theory symbols (∈, ⊂, ∪), logic operators (∧, ∨, ⇒), and special mathematical constants and functions used in higher mathematics like linear algebra, topology, and abstract algebra.
Most mathematical symbols are internationally standardized and used universally. However, some notations may vary by region. For example, some countries use a comma instead of a period for decimals, and multiplication may be shown as × or ·. The symbols listed here follow international mathematical conventions recognized by mathematicians worldwide.
You can type mathematical symbols using keyboard shortcuts (Alt codes on Windows), character maps, LaTeX notation, or simply copy and paste from reference pages like this one. Click any symbol on this page to copy it to your clipboard instantly for use in documents, emails, or code.
The equals sign (=) is considered the most used mathematical symbol, introduced by Robert Recorde in 1557. Other commonly used symbols include the plus (+), minus (−), multiplication (×), and division (÷) signs. In advanced mathematics, the integral sign (∫) and summation symbol (∑) are also extensively used.