Math Symbols | All Mathematical Symbols with Examples (2024)

Mathematical symbols are used to perform various operations. The symbols make it easier to refer Mathematical quantities. It is interesting to note that Mathematics is completely based on numbers and symbols. The math symbols not only refer to different quantities but also represent the relationship between two quantities. Allmathematical symbols are mainly used to perform mathematical operations under various concepts.

As we know, the full name of Maths is Mathematics. It is defined as the science of calculating, measuring, quantity, shape, and structure. It is based on logical thinking, numerical calculations, and the study of shapes. Algebra, trigonometry, geometry, and number theory are examples of mathematical dimensions, and the concept of Maths is purely dependent on numbers and symbols.

There are many symbols used in Maths that have some predefined values. To simplify the expressions, we can use those kinds of values instead of those symbols. Some of the examples are the pi symbol (π),which holds the value 22/7 or 3.14. The pi symbol is a mathematical constant which is defined as the ratio of circumference of a circle to its diameter. In Mathematics, pi symbol is also referred to as Archimedes constant. Also,e-symbol in Mathswhich holds the value e= 2.718281828….This symbol is known as e-constant or Euler’s constant. The table provided below has a list of all the common symbols in Maths with meaning and examples.

There are so many mathematical symbols that are very important to students. To understand this in an easier way, the list of mathematical symbols are noted here with definition and examples. There are numerous signs and symbols, ranging from the simple addition concept sign to the complex integration concept sign. Here, the list of mathematical symbols is provided in a tabular form, and those notations are categorized according to the concept.

List of Mathematical Symbols

  • Basic Math Symbols
  • Logic Symbols
  • Calculus and Analysis Symbols
  • Combinatorics Symbols
  • Greek Alphabets
  • Common Numeral Symbols
  • Importance
  • FAQs

Basic Mathematical Symbols With Name, Meaning and Examples

The basic mathematical symbols used in Maths help us to work with mathematical concepts in a theoretical manner. In simple words, without symbols, we cannot do maths. The mathematical signs and symbols are considered as representative of the value. The basic symbols in maths are used to express mathematical thoughts. The relationship between the sign and the value refers to the fundamental need of mathematics. With the help of symbols, certain concepts and ideas are clearly explained. Here is a list of commonly used mathematical symbols with names and meanings. Also, an example is provided to understand the usage of mathematical symbols.

SymbolSymbol Name in MathsMath Symbols MeaningExample
not equal signinequality10 ≠ 6
=equal signequality3 = 1 + 2
<strict inequalityless than7 < 10
>strict inequalitygreater than6 > 2
inequalityless than or equal tox ≤ y, means, y = x or y > x, but not vice-versa.
inequalitygreater than or equal toa ≥ b, means, a = b or a > b, but vice-versa does not hold true.
[ ]bracketscalculate expression inside first[ 2×5] + 7 = 10 + 7 = 17
( )parenthesescalculate expression inside first3 × (3 + 7) = 3× 10 = 30
minus signsubtraction5 − 2 = 3
+plus signaddition4 + 5 = 9
minus – plusboth minus and plus operations1 ∓ 4 = -3 and 5
±plus – minusboth plus and minus operations5 ± 3 = 8 and 2
×times signmultiplication4 × 3 = 12
*asteriskmultiplication2 * 3 = 6
÷division sign / obelusdivision15 ÷ 5 = 3
multiplication dotmultiplication2 ∙ 3 = 6
horizontal linedivision / fraction8/2 = 4
/division slashdivision6 ⁄ 2 = 3
modmoduloremainder calculation7 mod 3 = 1
abpowerexponent24= 16
.perioddecimal point, decimal separator4.36 = 4 +(36/100)
asquare root√a · √a = a√9 = ±3
a^bcaretexponent2 ^ 3 = 8
4√afourth root4√a·4√a·4√a·4√a = a4√16= ± 2
3√acube root3√a·3√a·3√a= a3√343 = 7
%percent1% = 1/10010% × 30 = 3
n√an-th root (radical)n√a·n√a···n times = afor n=3, n√8 = 2
ppmper-million1 ppm = 1/100000010ppm × 30 = 0.0003
per-mille1‰ = 1/1000 = 0.1%10‰ × 30 = 0.3
pptper-trillion1ppt = 10-1210ppt × 30 = 3×10-10
ppbper-billion1 ppb = 1/100000000010 ppb × 30 = 3×10-7

Maths Logic symbols With Meaning

SymbolSymbol Name in MathsMath Symbols MeaningExample
^caret / circumflexandx ^ y
·andandx · y
+plusorx + y
&ampersandandx & y
|vertical lineorx | y
reversed caretorx ∨ y
barnot – negation
x’single-quotenot – negationx’
!Exclamation marknot – negation! x
¬notnot – negation¬ x
~tildenegation~ x
circled plus / oplusexclusive or – xorx ⊕ y
equivalentif and only if (iff)p: this year has 366 days
q: this is a leap year
p ⇔ q
impliesImplicationp: a number is a multiple of 4

q: the number is even

p ⇒ q

Belong to/is an element ofSet membershipA = {1, 2, 3}
2 ∈ A
Not element ofNegation of set membershipA={1, 2, 3}
0 ∉ A
for allUniversal Quantifier2n is even ∀ n ∈ N

where N is a set of Natural Numbers

equivalentif and only if (iff)p: x is an even number

q: x is divisible by 2

p ↔ q

there does not existNegation of existential quantifierb is not divisible by a, then ∄ n ∈ N such that b = na
there existsExistential quantifierb is divisible by a, then ∃ n ∈ N such that b = na
because / sinceBecause shorthanda = b, b = c

⇒ a = c (∵ a = b)

thereforeTherefore shorthand (Logical consequence)x + 6 = 10

∴ x = 4

Calculus and Analysis Symbol Names in Maths

In calculus, we have come across different math symbols. All mathematical symbols with names and meanings are provided here. Go through the all mathematical symbols used in calculus.

SymbolSymbol Name in MathsMath Symbols MeaningExample
εepsilonrepresents a very small number, near-zeroε → 0
limx→alimitlimit value of a functionlimx→a(3x+1)= 3 × a + 1 = 3a + 1
y derivativederivative – Lagrange’s notation(5x3)’ = 15x2
ee constant / Euler’s numbere = 2.718281828…e = lim (1+1/x)x , x→∞
y(n)nth derivativen times derivationnth derivative of 3xn = 3 n (n-1)(n-2)….(2)(1)= 3n!
y”second derivativederivative of derivative(4x3)” = 24x

\(\begin{array}{l}\frac{d^2 y}{d x^2}\end{array} \)

second derivativederivative of derivative

\(\begin{array}{l}\frac{d^2 }{d x^2}(6x^{3}+x^{2}+3x+1) = 36x + 1\end{array} \)

dy/dxderivativederivative – Leibniz’s notation

\(\begin{array}{l}\frac{d }{d x}(5x) = 5\end{array} \)

\(\begin{array}{l}\frac{d^n y}{d x^n}\end{array} \)

nth derivativen times derivation

\(\begin{array}{l}\frac{d^{n}x}{dx^{n}}(x^{n})=n!\end{array} \)

\(\begin{array}{l}\ddot{y}= \frac{d^{2} y}{dt^{2}}\end{array} \)

Second derivative of timederivative of derivativeIf y = 4t2, then

\(\begin{array}{l}\ddot{y}= \frac{d^{2}y}{dt^{2}}=4\frac{d^{2}}{dt^{2}}(t^{2})=8\end{array} \)

\(\begin{array}{l}\dot{y}\end{array} \)

Single derivative of timederivative by time – Newton’s notationy = 5t, then

\(\begin{array}{l}\dot{y}= \frac{dy}{dt}=5\frac{d}{dt}(t)=5\end{array} \)

D2xsecond derivativederivative of derivativey” + 2y + 1 = 0

⇒ D2y + 2Dy + 1 = 0

Dxderivativederivative – Euler’s notationdy/x – 1 = 0

⇒ Dy – 1 = 0

integralopposite to derivation∫xn dx = xn + 1/n + 1 + C

\(\begin{array}{l}\frac{\partial f(x,y)}{\partial x}\end{array} \)

partial derivativeDifferentiating a function with respect to one variable considering the other variables as constant∂(x2+y2)/∂x = 2x
triple integralintegration of the function of 3 variables

\(\begin{array}{l}\int_{1}^{2}\int_{2}^{3} \int_{0}^{1}(xyz) \:dz\;dx\;dy\end{array} \)

double integralintegration of the function of 2 variables∬(x3+y3)dx dy
closed surface integralDouble integral over a closed surfaceV (⛛.F)dV = ∯S (F.n̂) dS
closed contour / line integralLine integral over closed curveC 2/z dz
[a,b]closed interval[a,b] = {x | a ≤ x ≤ b}sin x ∈ [ – 1, 1]
closed volume integralVolume integral over a closed three-dimensional domain∰ (x2 + y2 + z2) dx dy dz
(a,b)open interval(a,b) = {x | a < x < b}f is continuous within (0, 1)
z*complex conjugatez = a+bi → z*=a-biIf z = 3 + 2i then z* = 3 – 2i
iimaginary uniti ≡ √-1z = 3 + 2i
nabla / delgradient / divergence operator∇f (x,y,z)

\(\begin{array}{l}\vec{x}\end{array} \)

vectorA quantity with magnitude and direction

\(\begin{array}{l}\overrightarrow{V}= x\hat{i}+y\hat{j}+z\hat{k}\end{array} \)

x * yconvolutionModification in a function due to the other function.y(t) = x(t) * h(t)
lemniscateinfinity symbol3x ≥ 0; x ∈ (0, ∞)
δdelta functionDirac Delta function

\(\begin{array}{l}\delta(x)=\left\{\begin{matrix}0 & if\:x\neq0 \\ \infty& if\:x=0 \\\end{matrix}\right. \end{array} \)

  • Algebra Symbols
  • Geometry Symbols
  • Probability and Statistics Symbols
  • Set Theory Symbols

Combinatorics Symbols Used in Maths

The different Combinatorics symbols used in maths concern the study of the combination of finite discrete structures. Some of the most important combinatorics symbols used in maths are as follows:


Symbol Name

Meaning or Definition



\(\begin{array}{l}^{n}P_{k}= \frac{n!}{(n-k)!}\end{array} \)

\(\begin{array}{l}^{5}P_{3}= \frac{5!}{(5-3)!} = 60\end{array} \)

n!Factorialn! = 1×2×3×…×n5! = 1×2×3×4×5 = 120

\(\begin{array}{l}^{n}C_{k}= \frac{n!}{k!(n-k)!} \end{array} \)

\(\begin{array}{l}^{5}C_{3}= \frac{5!}{3!(5-3)!}=10\end{array} \)

Greek Alphabet Letters Used in Maths

Mathematicians frequently use Greek alphabets in their work to represent the variables, constants, functions and so on. Some of the commonly used Greek symbols name in Maths are listed below:

Greek SymbolGreek Letter NameEnglish EquivalentPronunciation
Upper Case
Lower Case

Common Numeral Symbols Used in Maths

The roman numerals are used in many applications and can be seen in our real-life activities. The common Roman numeral symbols used in Maths are as follows.

one hundred100C١٠٠ק

These are some of the most important and commonly used symbols in mathematics. It is important to get completely acquainted with all the maths symbols to be able to solve maths problems efficiently. It should be noted that without knowing maths symbols, it is extremely difficult to grasp certain concepts on a universal scale. Some of the key importance of maths symbols are summarized below.

Importance of Mathematical Symbols

  • Helps in denoting quantities
  • Establishes relationships between quantities
  • Helps to identify the type of operation
  • Makes reference easier
  • Maths symbols are universal and break the language barrier

Frequently Asked Questions on Math Symbols


What is the pi symbol in Maths?

The pi symbol is a mathematical constant, which is approximately equal to 3.14. The symbol of pi is π and it is a Greek alphabet. Pi is an irrational number which is defined as the ratio of circle circumference to its diameter.


What is e symbol in mathematics?

The “e” symbol in maths represents Euler’s number which is approximately equal to 2.71828…It is considered as one of the most important numbers in mathematics. It is an irrational number and it cannot be represented as a simple fraction


Write down the symbols for basic arithmetic operations.

The symbols for basic arithmetic operations are addition (+), subtraction (-), Multiplication (×), Division(÷).


Why do we use mathematical symbols?

Mathematics is a universal language and the basics of maths are the same everywhere in the universe. Mathematical symbols play a major role in this. The definition and the value of the symbols are constant. For example, the Roman letter X represents the value 10 everywhere around us.


Mention the logic symbols in maths.

The logic symbols in maths are:
AND (^)
OR (∨)
NOT (¬)
Implies (⇒)
Equivalent (⇔)
For all (∀)
There exists (∃)

Keep visiting BYJU’S – The Learning App to get more such maths topics and concepts. Also, register at BYJU’S and download the app to access various video lessons and practice tests on different maths topics.

Math Symbols | All Mathematical Symbols with Examples (2024)


Math Symbols | All Mathematical Symbols with Examples? ›

The 11 basic symbols essential for writing mathematical equations are the plus (+), minus (-), equals (=), does not equal (≠), multiplication (×), division (÷), greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), fraction (/), decimal (.) and percent (%) symbols.

What are the 5 mathematical symbols? ›

The 11 basic symbols essential for writing mathematical equations are the plus (+), minus (-), equals (=), does not equal (≠), multiplication (×), division (÷), greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), fraction (/), decimal (.) and percent (%) symbols.

What does ∑ mean in math? ›

The symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern. For example, the sum of the first 4 squared integers, 12+22+32+42, follows a simple pattern: each term is of the form i2, and we add up values from i=1 to i=4.

What does the Ø mean in math? ›

The letter "Ø" is sometimes used in mathematics as a replacement for the symbol "∅" (Unicode character U+2205), referring to the empty set as established by Bourbaki, and sometimes in linguistics as a replacement for same symbol used to represent a zero.

What does ∈ mean in math? ›

The symbol ∈ indicates set membership and means “is an element of” so that the statement x∈A means that x is an element of the set A. In other words, x is one of the objects in the collection of (possibly many) objects in the set A.

What is the 8 symbol in math? ›

The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, after the lemniscate curves of a similar shape studied in algebraic geometry, or "lazy eight", in the terminology of livestock branding.

What does "u" and "upside-down you" mean? ›

In math, the symbol U represents the union of two sets, while upside-down U represents the intersection of the sets.

What symbol is this δ? ›

Greek Alphabet
20 more rows

What is the sideways M in math? ›

The Sigma notation is another way to say 'sum. ' It is also referred to as summation notation. This notation looks like a big sideways M. On the bottom of the symbol, we have little letters that tell us our beginning point. On the top of the symbol, there is a little number that tells us our end point.

What does ≠ mean in math? ›

The mathematical symbol "≠" represents "not equal to" or "is not equal to." It is used to indicate that two values or expressions are not the same. When you see "≠" between two entities, it means that they are distinct or different from each other. It is the negation of the equality symbol "=".

What does θ mean in math? ›

Theta (θ) is a letter from the Greek alphabet. In Mathematics and Physics it is customary to designate variables with letters. The symbol θ usually represents the angular position of a vector.

What is the weird O symbol in math? ›

big O (𝒪) represents an upper bound to a function, f = 𝒪(g) means that g(x) ≥ f(x) after some value x₁, and it's defined as: f = 𝒪(g) if ∃M>0 in with 0 ≤ f ≤ Mg ⇔ f/g ≤ M.

What is this symbol φ in math? ›

Phi is an irrational mathematical constant, approximately 1.618.., and is often denoted by the Greek letter φ. Other commonly used names for Phi are: Golden Mean, Extreme and Mean Ratio, Divine Proportion and Golden Ratio. Phi is a naturally occurring ratio which exhibits aesthetically pleasing properties.

What does ⊆ mean? ›

In set theory, a subset is denoted by the symbol ⊆ and read as 'is a subset of'. Using this symbol we can express subsets as follows: A ⊆ B; which means Set A is a subset of Set B. Note: A subset can be equal to the set. That is, a subset can contain all the elements that are present in the set.

What does ∧ mean in math? ›

∧ is (most often) the mathematical symbol for logical conjunction, which is equivalent to the AND operator you're used to. Similarly ∨ is (most often) logical disjunction, which would be equivalent to the OR operator.

What is the z symbol in math? ›

Integers. The letter (Z) is the symbol used to represent integers. An integer can be 0, a positive number to infinity, or a negative number to negative infinity.

What are the 5 types of mathematical representations? ›

Lesh and colleagues (1987) proposed five different types of mathematical representations (i.e. visual, symbolic, verbal, contextual, and physical) which are relevant across mathematical content domains and the importance of making connections between them to deepen students' mathematical understanding.

What are the 5 logical symbols? ›

Logical connectives:
  • Negation: ¬, ~ : not.
  • Conjunction: ∧, &: and.
  • Disjunction: ∨, v: or.
  • Implication: →, –>: implies, if … , then … .
  • Biconditional: ↔, : if and only if.
  • Logical equivalence: ≡
Oct 11, 2014

What are the five types of symbols? ›

There are five types of cultural symbols:
  • Iconograms are illustrative representations. ...
  • Pictograms are pictorial representation, such as “ISOTYPE”.
  • Cartograms are topographical representatives with complete functions (statistics).
  • Diagrams are functional representations.
  • Phonograms are phonic representations.
Sep 27, 2021

What does 5 represent in maths? ›

We use the notation 5! to represent 5 factorial. To find 5 factorial, or 5!, simply use the formula; that is, multiply all the integers together from 5 down to 1. When we use the formula to find 5!, we get 120.

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