Math Symbols Reference Chart
Below you'll find a list of all mathematical symbols together with their meaning and examples.
Basic Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| equals sign | equality between two expressions | ||
| not equal sign | inequality between two expressions | ||
| approximately equal | very similar to but not exactly equal due to | ||
| strict inequality | less than | ||
| strict inequality | greater than | ||
| inequality | greater than or equal to | ||
| inequality | less than or equal to | ||
| parentheses | calculations in parentheses are performed first | ||
| brackets | calculations in brackets are performed first | ||
| plus | addition | ||
| minus | subtraction | ||
| plus - minus | both plus and minus operations in one equation | ||
| minus - plus | both plus and minus operations in one equation | ||
| times | multiplication | ||
| asterisk | multiplication | ||
| obelus | division | ||
| slash | division | ||
| vinculum | fraction bar | ||
| modulo | remainder operator | ||
| interpunct / dot product | multiplication | ||
| power | exponent | ||
| caret | exponent | ||
| radical | square root | ||
| cube root | number which produces a given number when cubed | ||
| fourth root | a number, which when multiplied four times by itself the original number will be obtained | ||
| n-th root (radical) | nth root of a number x, where n is a positive integer, is any of the n real or complex numbers r whose nth power is x | ||
| percent | by a specified amount in or for every hundred | ||
| per-mille | by a specified amount in every thousand | ||
| per-million | by a specified amount in every million | ||
| per-billion | by a specified amount in every billion | ||
| per-trillion | by a specified amount in every trillion |
Geometry Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| angle | geometrical figure formed when two rays meet at a common point called vertex | ||
| measured angle | an angle with a known size | ||
| spherical angle | angle formed by three great circles on a sphere | ||
| right angle | if two straight lines intersect each other at 90˚ they form a right angle | ||
| degree | represents degrees of an arc | ||
| degree | represents degrees of an arc | ||
| prime | arcminute | ||
| double prime | arcsecond | ||
| line | infinite line | ||
| line segment | line from point A to point B | ||
| ray | line that starts at point A | ||
| arc | arc from point A to point B | ||
| perpendicular | perpendicular lines | ||
| parallel | parallell lines | ||
| congruent to | equivalence of geometric size and shape | ||
| similarity | same shape but not same size | ||
| triangle | closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices | ||
| distance | distance between points x and y | ||
| pi constant | ratio between the circumference and diameter of a circle | ||
| radians | one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius | ||
| radians | one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius | ||
| gradians / gons | unit of angular measure in which the angle of an entire circle is 400 gradians | ||
| gradians / gons | unit of angular measure in which the angle of an entire circle is 400 gradians |
Algebra Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| x variable | An unknown or variable value | ||
| Equivalence | Identical to | ||
| Equal by definition | Equal by definition | ||
| Equal by definition | Equal by definition | ||
| Approximately equal | Approximation | ||
| Approximately equal | Asymptotic equivalence | ||
| Proportional to | Proportional to | ||
| Lemniscate | Infinity | ||
| Much less-than | Much less-than | ||
| Much greater-than | Much greater-than | ||
| parentheses | calculations in parentheses are performed first | ||
| brackets | calculations in brackets are performed first | ||
| braces | Defines a set | ||
| delta | difference | ||
| discriminant | parameter of an object or system calculated as an aid to its classification or solution | ||
| sigma | summation of the numbers indicated | ||
| sigma | double summation of the numbers indicated | ||
| floor brackets | rounds the number down to the lower integer | ||
| ceiling brackets | rounds the number up to the higher integer | ||
| factorial | product of all integer values up to the provided number | ||
| absolute value | the distance from zero that a number is on the number line, without considering direction | ||
| function of x | calculate the value of the function substituting x with the provided value | ||
| functional composition | The result of function f is passed to function g | ||
| open interval | interval that doesn't include its endpoints | ||
| closed interval | interval that includes its endpoints | ||
| capital pi | product of all the numbers indicated | ||
| Euler's number | The irrational number represented by the letter e | ||
| Euler's constant / Euler-Mascheroni constant | The limiting difference between the harmonic series and the natural logarithm. Approximately 0.5772156649. | ||
| golden ratio | Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Approximately 1.618033988749894 | ||
| pi constant | The ratio of a circle's circumference to its diameter. Approximately 3.14159. |
Linear Algebra Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| dot | scalar product | ||
| multiplication / times | multiplication of vectors | ||
| tensor product | multiplication of vectors | ||
| inner product | how much of one vector is pointing in the direction of another one | ||
| parentheses | matrix of values | ||
| brackets | matrix of values | ||
| determinant | scalar value or number calculated using a square matrix | ||
| determinant | scalar value or number calculated using a square matrix | ||
| double vertical bars | norm | ||
| transpose | transposed matrix A | ||
| Hermitian matrix | conjugate transposition of matrix A | ||
| Hermitian matrix | conjugate transposition of matrix A | ||
| inverse matrix | |||
| matrix rank | rank of the matrix | ||
| dimension | dimension of the matrix |
Statistics & Probability Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| probability function | the probability of event A | ||
| probability of intersection of events | the probability of events A and B | ||
| probability of union of events | the probability of events A or B | ||
| conditional probability | the probability of event a given event B | ||
| probability density function | |||
| cumulative distribution function | |||
| population mean (mu) | mean of population values | ||
| expectation value | expected value of a random variable X | ||
| considitional expectation | expected value of a random variable X given value Y | ||
| variance | variance of a random value X | ||
| variance | variance of a population of values | ||
| standard deviation | the amount of variation of a set of values | ||
| standard deviation | the amount of variation of a set of values | ||
| median | the middle value in an ordered set of numbers | ||
| covariance | covariance of variables X and Y | ||
| correlation | correlation of variables X and Y | ||
| pearson correlation | pearson correlation of variables X and Y | ||
| summation | sum of all values in the denoted series | ||
| double summation | double summation | ||
| mode | value that occurs most frequently in a population | ||
| mid-range | |||
| sample median | the value separating the higher half from the lower half of a data sample | ||
| first quartile | 25% of the population is below the first quartile | ||
| second quartile | 50% of the population is below the second quartile | ||
| third quartile | 75% of the population is below the third quartile | ||
| sample mean | arithmetic mean / average | ||
| sample variance | estimates the variance in a sample | ||
| sample standard deviation | estimates the standard deviation in a sample | ||
| standard score | |||
| distribution of X | distribution of X | ||
| normal distribution | guassian distribution | ||
| uniform distribution | equal probability in the range [a,b] | ||
| exponential distribution | exponential distribution | ||
| chi-square definition | chi-square definition | ||
| F-distribution | F-distribution | ||
| binomial distribution | binomial distribution | ||
| Poisson distribution | Poisson distribution | ||
| geometric distribution | geometric distribution | ||
| hypergeometric distribution | hypergeometric distribution | ||
| bernoulli distributions | discrete probability distribution where every experiment conducted asks a question that can be answered only in yes or no. |
Combinatorics Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| factorial | product of all integer values up to the provided number | ||
| permutation | an arrangement of its members into a sequence or linear order | ||
| combination | selection of items from a set that has distinct members, such that the order of selection does not matter |
Set Theory Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| set | collection of elements | ||
| intersection | elements that belong to both sets A and B | ||
| union | elements that belong to sets A or B | ||
| subset | set A is a subset of, or equal to set B | ||
| strict subset | set A is a subset of, but not equal to set B | ||
| not a subset | set A is a not a subset of set B | ||
| strict superset | set A is a superset of, or equal to set B | ||
| superset | set A is a superset of, but not equal to set B | ||
| not superset | set A is not a superset of set B | ||
| power set | all subsets of S | ||
| power set | all subsets of S | ||
| equality | A and B have the same members | ||
| complement | the set of objects that do not belong to set A | ||
| relative complement | the set of objects that belong to set A but not to set B | ||
| relative complement | the set of objects that belong to set A but not to set B | ||
| symmetric difference | the set of objects that belong to set A or set B but not their intersection | ||
| symmetric difference | the set of objects that belong to set A or set B but not their intersection | ||
| set membership | an element x belongs to set A | ||
| no set membership | an element x does not belong to set A | ||
| ordered pair | a collection of 2 ordered elements | ||
| cartesian product | set of all ordered pairs from sets A and B | ||
| cardinality | the number of elements in set A | ||
| cardinality | the number of elements in set A | ||
| vertical bar | such that | ||
| aleph-null | infinite cardinality of the set of natural numbers | ||
| aleph-one | cardinality of countable ordinal set of numbers | ||
| empty set | empty set | ||
| universal set | set of all possible values | ||
| all natural numbers including zero | |||
| all natural numbers excluding zero | |||
| set of all integers | |||
| set of all rational numbers | |||
| set of all real numbers | |||
| set of all complex numbers |
Logic Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| and | conjunction operator | ||
| circumflex / caret | conjunction operator | ||
| and | conjunction operator | ||
| plus | or operator | ||
| inverse circumflex / caret | or operator | ||
| vertical line | or operator | ||
| prime | negation | ||
| bar | negation | ||
| not | negation | ||
| not | negation | ||
| circled plus | xor / exclusive or | ||
| tilde | negation | ||
| implies | logically implies | ||
| equivalent | if and only if | ||
| equivalent | if and only if | ||
| for all | for any; for each | ||
| there exists | there exists | ||
| therefore | logical consequence | ||
| because | signals reasoning | ||
| Domain of discourse | Domain of predicate |
Calculus Math Symbols
| Symbol | Name | Description | Example / Definition |
|---|---|---|---|
| limit | limit value of a function | ||
| epsilon | a very small, near zero value | ||
| Euler's constant | e ≈ 2.7182818284 | ||
| derivative | derivative using Lagrange's notation | ||
| second derivative | derivative of a derivative using Lagrange's notation | ||
| nth derivative | derivative applied n-times using Lagrange's notation | ||
| derivative | derivative using Leibniz's notation | ||
| second derivative | second derivative using Leibniz's notation | ||
| nth derivative | nth derivative using Leibniz's notation | ||
| time derivative | time derivative using Newton's notation | ||
| second time derivative | second time derivative using Newton's notation | ||
| nth time derivative | nth time derivative using Newton's notation | ||
| derivative | derivative using Euler's notation | ||
| second derivative | second derivative using Euler's notation | ||
| partial derivative | derivative of a function of two or more variables with respect to one variable | ||
| integral | opposite operation to derivation | ||
| double integral | the integral of a function of two variables | ||
| triple integral | the integral of a function of three variables | ||
| line integral / closed integral | integral where the function to be integrated is evaluated along a curve | ||
| closed surface integral | generalization of multiple integrals to integration over surfaces | ||
| closed volume integral | integral over a 3-dimensional domain | ||
| closed interval | |||
| open interval | |||
| imaginary unit | |||
| complex conjugate | |||
| complex conjugate | |||
| real part of a complex number | |||
| imaginary part of a complex number | |||
| absolute value / magnitude of a complex number | |||
| argument of a complex number | the angle of the radius in the complex plane | ||
| nabla / del | gradient operator / divergence operator | ||
| vector | a quantity that has both magnitude and direction | ||
| unit vector | vector which has a magnitude of one | ||
| convolution | operation on two functions that produces a third function that expresses how the shape of one is modified by the other | ||
| Laplace transform | converts differential equations into purely algebraic equations | ||
| Fourier transform | function derived from a given function and representing it by a series of sinusoidal functions | ||
| delta function | tool for the normalization of state vectors | ||
| lemniscate | infinity symbol |