Math Symbols Reference Sheet
A quick reference guide to the most common mathematical symbols — their names, meanings, and examples. Print-friendly.
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➕ Arithmetic 8 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| + | Plus | Addition | 3 + 4 = 7 |
| − | Minus | Subtraction | 9 − 2 = 7 |
| × | Times / Multiply | Multiplication | 4 × 3 = 12 |
| ⋅ | Dot / Multiply | Multiplication (alternate) | a ⋅ b = ab |
| ÷ | Divide / Obelus | Division | 12 ÷ 4 = 3 |
| / | Slash / Fraction bar | Division (alternate) | 10 / 2 = 5 |
| ± | Plus-Minus | Both plus and minus | x = −b ± √(b²−4ac) / 2a |
| % | Percent | Per hundred (÷ 100) | 25% = 0.25 |
⚖️ Comparison 9 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| = | Equals | Equal to | 2 + 2 = 4 |
| ≠ | Not equal | Not equal to | 3 ≠ 4 |
| ≈ | Approximately | Roughly equal to | π ≈ 3.1416 |
| ≅ | Congruent | Identical in shape/size | △ABC ≅ △DEF |
| ≡ | Equivalent | Identical; modular congruence | 7 ≡ 2 (mod 5) |
| < | Less than | Smaller than | 2 < 5 |
| > | Greater than | Larger than | 7 > 3 |
| ≤ | Less/equal | At most | x ≤ 10 |
| ≥ | Greater/equal | At least | y ≥ 0 |
√ Algebra & Functions 10 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| √ | Square root | Principal square root | √16 = 4 |
| ∛ | Cube root | Third root | ∛27 = 3 |
| ∜ | Fourth root | Fourth root | ∜16 = 2 |
| ∞ | Infinity | Unbounded / limitless | lim 1/x² = ∞ |
| ∑ | Sigma (sum) | Sum of terms | ∑ᵢ₌₁ⁿ i = n(n+1)/2 |
| ∏ | Pi (product) | Product of terms | n! = ∏ₖ₌₁ⁿ k |
| ∂ | Partial derivative | Derivative w.r.t. one variable | ∂f/∂x |
| ∆ | Delta / change | Change; discriminant | Δ = b² − 4ac |
| ∇ | Nabla / del | Gradient operator | ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z) |
| d | Differential | Infinitesimal change | dy/dx (derivative) |
∫ Calculus & Analysis 6 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ∫ | Integral | Area under a curve | ∫₀¹ x² dx = ⅓ |
| ∬ | Double integral | Integral over 2D area | ∬_R f(x,y) dA |
| ∭ | Triple integral | Integral over 3D volume | ∭_V ρ dV |
| ∮ | Contour integral | Integral along a closed loop | ∮_C f(z) dz |
| lim | Limit | Value as input approaches point | lim_{x→0} sin x/x = 1 |
| → | Approaches | Tends to | x → ∞ |
△ Geometry 8 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ∠ | Angle | Figure formed by two rays | ∠ABC = 90° |
| ∡ | Measured angle | Angle with a specific measure | ∡ABC = 45° |
| ⊥ | Perpendicular | At right angle (90°) | AB ⊥ CD |
| ∥ | Parallel | Never intersect | AB ∥ CD |
| ° | Degree | Unit of angle measure | Right angle = 90° |
| △ | Triangle | Three-sided polygon | △ABC |
| π | Pi | Circle constant ≈ 3.1416 | C = 2πr |
| ∼ | Similar | Same shape, different size | △ABC ∼ △DEF |
∈ Set Theory 10 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ∈ | Element of | Belongs to a set | 5 ∈ ℕ |
| ∉ | Not element of | Does not belong | −1 ∉ ℕ |
| ⊂ | Subset | Every element in A is also in B | ℕ ⊂ ℤ |
| ⊆ | Subset or equal | Subset (allows equality) | A ⊆ B |
| ∪ | Union | All elements in A or B | {1,2} ∪ {2,3} = {1,2,3} |
| ∩ | Intersection | Elements in both A and B | {1,2} ∩ {2,3} = {2} |
| ∅ | Empty set | Set with no elements | A ∩ A' = ∅ |
| ∀ | For all | Universal quantifier | ∀x > 0, x² > 0 |
| ∃ | There exists | Existential quantifier | ∃x : x² = 4 |
| ∄ | There does not exist | No element satisfies | ∄x : x² = −1 (in ℝ) |
🧮 Logic 8 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ∧ | AND (conjunction) | Both true | A ∧ B |
| ∨ | OR (disjunction) | At least one true | A ∨ B |
| ¬ | NOT (negation) | Flips truth value | ¬(2+2=5) |
| ⇒ | Implies | If P then Q | Rain ⇒ wet ground |
| ⇔ | Iff / equivalent | If and only if | x+1=5 ⇔ x=4 |
| ⊤ | Top / true | Always true (tautology) | A ∨ ¬A ≡ ⊤ |
| ⊥ | Bottom / false | Always false (contradiction) | A ∧ ¬A ≡ ⊥ |
| ∴ | Therefore | Logical conclusion | All men mortal ∴ Socrates mortal |
α Greek Letters in Math 12 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| α | Alpha | Angles; significance level | α = 0.05 |
| β | Beta | Regression coefficients; angles | y = β₀ + β₁x |
| γ | Gamma | Gamma function; Lorentz factor | Γ(n) = (n−1)! |
| δ | Delta | Small change | δx (small change in x) |
| ε | Epsilon | Small positive quantity | ε → 0 |
| θ | Theta | Angle in trigonometry | sin²θ + cos²θ = 1 |
| λ | Lambda | Eigenvalue; wavelength | Av = λv |
| μ | Mu | Population mean; micro- | μ = (1/n)∑xᵢ |
| π | Pi | Circle constant ≈ 3.1416 | C = 2πr |
| ρ | Rho | Density; correlation | ρ = Cov/σ_Xσ_Y |
| σ | Sigma | Standard deviation | 68% in μ ± σ |
| φ | Phi | Golden ratio; totient | φ = (1+√5)/2 |
📐 Vectors & Matrices 6 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| → | Vector (arrow) | Vector quantity | v = (v₁, v₂, v₃) |
| |v| | Magnitude | Length of a vector | |v| = √(v₁²+v₂²) |
| · | Dot product | Scalar product of vectors | u · v = |u||v|cosθ |
| × | Cross product | Vector product in 3D | a × b = |a||b|sinθ n̂ |
| ⊤ | Transpose | Matrix transpose | (A⊤)ᵢⱼ = Aⱼᵢ |
| det | Determinant | Scalar from a square matrix | det(A) = ad − bc |
📊 Statistics & Probability 8 symbols
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| x̄ | Sample mean | Average of a sample | x̄ = (1/n)∑xᵢ |
| σ | Standard deviation | Spread of data | σ = √(∑(x−x̄)²/n) |
| σ² | Variance | Square of std dev | σ² = variance |
| P(A) | Probability of A | Chance event A occurs | P(heads) = 0.5 |
| E(X) | Expected value | Mean of random variable | E(X) = ∑x·P(x) |
| ∼ | Distributed as | Probabilistic distribution | X ∼ N(μ, σ²) |
| corr | Correlation | Linear relationship strength | corr(X,Y) ∈ [−1, 1] |
| ! | Factorial | Product of 1 to n | 5! = 120 |