Math Symbols
A practical guide to common math symbols, including arithmetic signs, comparison marks, set notation, logic symbols, calculus notation, geometry signs, and commonly confused characters.
31 symbol guides available
What Are Math Symbols?
Math symbols are characters used to represent numbers, operations, relationships, sets, logical statements, geometric ideas, and other mathematical concepts. A single symbol can replace an entire phrase: + means addition, ≠ means “not equal to,” ∞ represents infinity, and ∈ means that an element belongs to a set.
Some mathematical symbols are familiar from basic arithmetic, while others appear mainly in algebra, geometry, calculus, logic, set theory, statistics, or advanced mathematics. The exact meaning of a symbol can also depend on context. For example, the vertical bar | can represent absolute value, divisibility, conditional probability, set-builder notation, or other relationships.
This guide groups common mathematical symbols by how they are typically used and explains their most widely recognized meanings.
Basic Arithmetic Symbols
Arithmetic symbols represent familiar mathematical operations such as addition, subtraction, multiplication, and division.
| Symbol | Name | Common meaning | Example |
|---|---|---|---|
| + | Plus sign | Addition; positive value | 3 + 2 = 5 |
| − | Minus sign | Subtraction; negative value | 5 − 2 = 3 |
| ± | Plus-minus sign | Either a positive or negative value | x = 5 ± 1 |
| ∓ | Minus-plus sign | Paired counterpart of ± | a ± b ∓ c |
| × | Multiplication sign | Multiplication | 4 × 3 = 12 |
| ÷ | Division sign | Division | 12 ÷ 3 = 4 |
| · | Middle dot | Used for multiplication and other notation in some contexts | 2 · 4 = 8 |
| ⋅ | Dot operator | Mathematical dot operator, including multiplication or related operations | a ⋅ b |
| / | Slash | Division or fraction notation | 6 / 2 = 3 |
| % | Percent sign | Parts per hundred | 25% = 0.25 |
| ! | Factorial sign | Factorial when placed after a number or expression | 5! = 120 |
Equality and Comparison Symbols
Comparison symbols describe relationships between values or expressions. They indicate whether quantities are equal, unequal, greater, smaller, approximately equal, or related in another way.
| Symbol | Name | Meaning |
|---|---|---|
| = | Equals sign | Two expressions have the same value |
| ≠ | Not equal to | Two expressions do not have the same value |
| < | Less-than sign | The value on the left is smaller |
| > | Greater-than sign | The value on the left is larger |
| ≤ | Less-than or equal to | Smaller than or equal to |
| ≥ | Greater-than or equal to | Larger than or equal to |
| ≈ | Almost equal to | Approximately equal values |
| ≡ | Identical to / equivalent to | Identity or equivalence, depending on context |
| ≅ | Approximately equal to / congruent to | Often used for geometric congruence |
| ∼ | Tilde operator | Similarity, equivalence, distribution, or another context-dependent relation |
| ∝ | Proportional to | One quantity varies proportionally with another |
| ≪ | Much less than | A quantity is much smaller than another |
| ≫ | Much greater than | A quantity is much larger than another |
Powers, Roots, and Related Notation
Powers and roots are frequently written using superscript notation, radical signs, or plain-text substitutes.
| Symbol | Name | Meaning |
|---|---|---|
| √ | Square root sign | Square root |
| ∛ | Cube root | Cube root |
| ∜ | Fourth root | Fourth root |
| ² | Superscript two | Squared |
| ³ | Superscript three | Cubed |
| ^ | Caret | Used for exponentiation in some calculators, plain-text conventions, and software systems; in many programming languages it has other meanings such as XOR |
The caret ^ is highly context-dependent. In professionally typeset mathematics, exponents are normally displayed as raised characters, while calculators, programming languages, and plain-text systems may use a caret or another operator.
Set Theory Symbols
Set theory uses symbols to describe collections of objects and relationships between those collections.
| Symbol | Name | Meaning |
|---|---|---|
| ∅ | Empty set | A set containing no elements |
| ∈ | Element of | An object belongs to a set |
| ∉ | Not an element of | An object does not belong to a set |
| ∋ | Contains as member | A set contains a particular element |
| ⊂ | Subset of | One set is a subset of another; conventions about strictness can vary |
| ⊆ | Subset of or equal to | Every member of one set belongs to another set |
| ⊃ | Superset of | One set contains another set |
| ⊇ | Superset of or equal to | A set contains all elements of another set |
| ∪ | Union | Elements belonging to either or both sets |
| ∩ | Intersection | Elements shared by two or more sets |
| ∖ | Set minus | Elements in one set that are not in another |
The mathematical set-minus symbol ∖ is a distinct Unicode character from the keyboard backslash , although a backslash is sometimes used as a plain-text substitute.
A power set is commonly written using notation such as P(A) or a script capital P such as 𝒫(A). The character ℘ should not be treated as a generic power-set symbol; it is associated with the Weierstrass elliptic function.
Logic Symbols
Mathematical logic uses compact notation to describe statements, conditions, implications, and quantifiers.
| Symbol | Name | Common meaning |
|---|---|---|
| ¬ | Logical NOT | Negation |
| ∧ | Logical AND | Both statements are true |
| ∨ | Logical OR | At least one statement is true |
| ⊕ | Exclusive OR | Exclusive alternative in many logical contexts |
| ⇒ | Rightwards double arrow | Implies |
| ⇔ | Left-right double arrow | If and only if; logical equivalence |
| ∀ | For all | Universal quantifier |
| ∃ | There exists | Existential quantifier |
| ∄ | There does not exist | Negated existential quantifier |
| ∴ | Therefore | Introduces a conclusion |
| ∵ | Because | Introduces a reason |
Calculus and Analysis Symbols
Calculus and mathematical analysis introduce symbols for limits, derivatives, integrals, sums, products, and changes in quantities.
| Symbol | Name | Common meaning |
|---|---|---|
| ∑ | Summation sign | Sum of a sequence of terms |
| ∏ | Product sign | Product of a sequence of terms |
| ∫ | Integral sign | Integration |
| ∬ | Double integral | Integration over two dimensions or variables |
| ∭ | Triple integral | Integration over three dimensions or variables |
| ∮ | Contour integral | Integral around a closed path |
| ∂ | Partial differential | Partial derivative |
| ∇ | Nabla / del | Gradient, divergence, curl, or related vector-calculus operations |
| Δ | Capital delta | Change or difference in a quantity in many mathematical contexts |
| ∞ | Infinity | A quantity without a finite bound |
Do not rely on appearance alone when identifying delta-like characters. Unicode contains both Greek capital delta Δ and the visually similar increment character ∆.
Geometry Symbols
| Symbol | Name | Common meaning |
|---|---|---|
| ∠ | Angle | An angle |
| ∟ | Right angle | A right angle |
| ⊥ | Perpendicular | Lines or objects meeting at a right angle |
| ∥ | Parallel to | Parallel lines, planes, or directions |
| ≅ | Congruent to | Geometric figures with the same shape and size in common notation |
| ∼ | Similar to | Geometrically similar figures in many contexts |
| ° | Degree sign | Angular measurement |
| ′ | Prime | Arcminutes or other mathematical notation |
| ″ | Double prime | Arcseconds or other mathematical notation |
Common Greek Letters Used in Mathematics
| Symbol | Name | Common mathematical uses |
|---|---|---|
| α | Alpha | Angles, coefficients, parameters |
| β | Beta | Angles, coefficients, parameters |
| γ | Gamma | Angles, functions, constants |
| Δ | Capital delta | Change or difference |
| δ | Lowercase delta | Small changes, variations, or parameters |
| θ | Theta | Angles |
| λ | Lambda | Parameters, eigenvalues, wavelength in applied contexts |
| μ | Mu | Means, parameters, coefficients |
| π | Pi | The circle constant; approximately 3.14159 |
| ρ | Rho | Density, correlation, parameters |
| σ | Sigma | Standard deviation and other parameters |
| Σ | Capital sigma | Greek capital letter used as a variable or symbol in mathematical notation |
| φ | Phi | Angles, functions, and the golden ratio in some notation |
| ω | Omega | Angular quantities and other variables |
| Ω | Capital omega | Sets, asymptotic notation, and other context-specific meanings |
The Greek capital letter sigma Σ is not the same Unicode character as the mathematical summation operator ∑. They can look similar, but ∑ is the dedicated symbol used for n-ary summation.
Symbols That Are Easy to Confuse
Minus Sign − vs Hyphen-Minus -
The mathematical minus sign − is not the same Unicode character as the keyboard hyphen-minus -. The hyphen-minus is commonly substituted when typing plain text, but professionally typeset mathematics normally uses the true minus sign.
Multiplication Sign × vs Letter x
The multiplication sign × is a mathematical operator. The letters x and X are alphabetic characters. In algebra, the letter x is also commonly used as a variable, so context is important.
Empty Set ∅ vs Ø vs 0
The empty set symbol ∅, the letter Ø, and the digit 0 are different characters. They can look similar in certain fonts but should not be treated as interchangeable.
Vertical Bar |
The vertical bar is especially ambiguous. Depending on context, |x| can indicate absolute value, a | b can mean that a divides b, P(A | B) can represent conditional probability, and the same character also appears in set-builder notation and programming languages.
Approximately Equal ≈ vs Identical ≡
≈ normally indicates approximate equality, while ≡ can indicate identity, equivalence, or congruence modulo a value depending on context. They are not simply decorative alternatives to the equals sign.
Parallel ∥ vs Double Vertical Line ‖ vs Two Vertical Bars ||
The mathematical parallel relation ∥, the Unicode double vertical line ‖, and two keyboard vertical bars || are not the same encoded text. They may look nearly identical in some fonts but have different Unicode identities and uses.
Why the Same Symbol Can Have Different Meanings
Mathematical notation is highly context-dependent. There is not always a one-to-one relationship between a character and a single definition.
For example, an asterisk * can indicate multiplication, convolution, a special operation, or another operator defined by an author. A tilde ~ can indicate similarity, approximation, equivalence, asymptotic behavior, or a statistical distribution. A caret ^ may represent exponentiation in one system but a completely different operation in another.
Math Symbols and Unicode
Modern mathematical notation includes many Unicode characters. Unicode assigns each encoded character a distinct code point, making it possible to store, search, copy, and exchange mathematical symbols as text.
Visually similar characters are not necessarily the same Unicode character. This matters when copying formulas, searching for a symbol, writing software, preparing documents, or comparing text programmatically.
Fonts can also change how a symbol looks. The same Unicode character may appear slightly different across browsers, operating systems, applications, and typefaces.
How to Identify an Unknown Math Symbol
Start by looking at the character itself and then examine how it is being used. Is it placed between two numbers? Does it appear before a set? Is it surrounding an expression? Is it part of a logical statement or calculus formula?
These clues can help distinguish an operator from a relation, a set-theory symbol, a logical connective, a geometric mark, or a character that only happens to look mathematical.
WITS provides individual symbol guides for mathematical characters as they are added to the symbol library. Those guides can provide more detail about a symbol's name, Unicode identity, common uses, similar-looking characters, and context-specific meanings.