Math Symbols

Mathematical Symbols: Symbols, Numbers, and Formulas

For students, mathematics symbols have a great deal of value. Students need to learn them so that they can solve more complex math equations. There are some symbols like Roman numerals, fractions, pi, and division that they need to understand.

And, reading this article can be a great initiative for learners. Not even mathematics requires these symbols, but also they are useful in science subjects. You all must have noticed that the whole of mathematics is made up of symbols. Numbers are also part of it. In the field of mathematics, math symbols are very useful. Students can use them for different purposes in this subject. Mathematicians use these symbols to represent ideas, concepts, and numbers. They sometimes use it as a reference for different types of equations. The extraction of maximum values from calculations, equations, and formulae can be done with the help of math symbols. To create a logical sequence, the symbols are required for the physical events representation. A predefined value can also be denoted by symbols. Students use math symbols to simplify calculations. While solving any mathematical problem, students should feel confident. By using various symbols like greater than sign, parenthesis, brackets, equal signs and many more can help you to be comfortable when making calculations. They are the best way to describe a standard or an idea. Around the world, these symbols may be used in languages because every mathematician needs to understand them equally.

Some Ways to Remember Mathematical Symbols

Before studying math symbols, there are few thing you need to keep in the mind. We have listed here some points that you must remember when understanding symbols.

  • Various symbols are there in mathematics nearly above 10,000. But, some of them we rarely use. So you need to focus on the math symbols that have been frequently used.
  • In maths, it is important to understand mathematical expressions. You can make it easier by using symbols to represent certain information.
  • Further, you should use them constantly in the subject. You can also use them to refer to non-varying objects.
math symbols

math symbols for class 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, UPSC, SSC, LIC, JEE, JEE Advance, NEET, CLAT aspirants.

Math Symbols List

All symbols that are useful in mathematics are mentioned in this place. Mathematical symbols are required, especially for calculations and formulas. To understand the language of mathematics, candidates need to learn these symbols. If you are constantly in contact with maths then you can bookmark this page or you can save each table to refer to frequently.

Basic Math Symbol

On this page, we have mentioned basic math symbols which are the foundation of mathematics. Those who want to express mathematical ideas will do that with the help of basic mathematical symbols. Also, there is a relationship between the symbol and the value. Arithmetic is incomplete without these symbols if we say them in easy words. To explain a few concepts and ideas clearly, symbols are required. Below, the mathematical symbols with symbol names and its definition are given in the table. Once you take a look at that you will understand how to use math symbols.

Symbol

Symbol Name Meaning
= equals sign

equality

not equal sign

inequality

approximately equal

approximation

>

strict inequality greater than
< strict inequality

less than

inequality greater than or equal to
inequality

less than or equal to

( )

parentheses calculate expression inside first
[ ] brackets

calculate expression inside first

+

plus sign

addition

minus sign subtraction
± plus – minus

both plus and minus operations

±

minus – plus both minus and plus operations
* asterisk

multiplication

×

times sign multiplication
multiplication dot

multiplication

÷

division sign / obelus division
/ division slash

division

horizontal line division / fraction
mod modulo

remainder calculation

.

period decimal point, decimal separator
ab; power

exponent

a^b

caret exponent
√a square root

√⋅√a =a

3√a

cube root 3√a⋅3√a⋅3√a⋅& =a
4√a fourth root

4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a =a

n√a

n-th root (radical)
% percent

1%=1/100

per-mile 1‰=1/1000=0.1%
ppm per-million

1ppm=1/1000000

ppb

per-billion 1ppb=1/1000000000
ppt per-trillion

1ppt=10&minussup12;

Geometry Symbols

In mathematics, the geometry symbols are also there. It is compulsory for the students to know geometry symbols as they are helping to solve problems of mathematics. Here, you can view them to complete the studies of math subject.

Symbol

Symbol Name Meaning
formed by two rays

∠ABC=30°

measured angle

spherical angle

right angle =90°
° degree

1 turn=360°

deg

degree 1 turn=360deg
prime

arcminute, 1°=60′

double prime

arcsecond, 1′=60″
line

infinite line

AB

line segment line from point A to point B
ray

line that start from point A

perpendicular perpendicular lines (90° angle)
parallel

parallel lines

congruent to equivalence of geometric shapes and size
similarity

same shapes, not same size

Δ

triangle triangle shape
∣x−y∣ distance

distance between points x and y

π

pi constant π=3.141592654…

is the ratio between the circumference and diameter of a circle

rad radians

radians angle unit

grad

gradians ∕ gons grads angle unit
g gradians ∕ gons

grads angle unit

Algebra Symbols

A mathematical component of symbols and rules is none other than algebra. Like sentences are represented by the coordination of certain words. In the same way, mathematics is represented by the coordination of variables. This description of mathematics is present in algebra. The Non-fixed values representing symbols are also there in algebra. These symbols are known as variables.

Symbol

Symbol Name Meaning
χ x variable

unknown value to find

equivalence identical to
equal by definition

equal by definition

equal by definition equal by definition
approximately equal

weak approximation

approximately equal approximation
proportional to

proportional to

lemniscate infinity symbol
much less than

much less than

⁽ ⁾

much grataer than much grataer than
⁽ ⁾ parentheses

calculate expression inside first

[ ]

brackets calculate expression inside first
{ } braces

set

⌊ χ ⌋

floor brackets rounds number to lower integer
⌈ χ ⌉ ceiling brackets

rounds number to upper integer

χ!

exclamation mark factorial
|χ| vertical bars

absolute value

Af(χ)

function of x maps values of x to f(x)
(f°g) function composition

(f°g)(x)=f(g(x))

(a,b)

open interval (a,b)={ x | a < x < b }
[a,b] closed interval

[a,b]={x | a≤ x ≤b }

Δ

delta change / difference
Δ discriminant

Δ=b²-4ac

sigma summation – sum of all values in range of series
∑∑ sigma

double summation

capital pi product – product of all values in range of series
e e constant / Euler’s number

e = 2.718281828…

γ

Euler-Mascheroni constant γ= 0.5772156649…
φ golden ratio

golden ratio constant

π

pi constant

π = 3.141592654…

It is the ratio between the circumference and diameter of a circle

Linear Algebra Symbols

Linear algebra symbols are also included in the world of mathematics. In higher standards, the following symbols are most useful. All the linear algebra symbols are listed here for students. These symbols are very helpful for those having mathematics subjects in their studies.

Symbol

Symbol Name Meaning
· dot

scalar product

×

cross vector product
A⊗B tensor product

tensor product of A and B

inner product

[ ] brackets

matrix of numbers

| A |

determinant determinant of matrix A
det(A) determinant

determinant of matrix A

∥ x ∥

double vertical bars norm
AT transpose

matrix transpose

A

Hermitian matrix matrix conjugate transpose
A* Hermitian matrix

matrix conjugate transpose

A-1

inverse matrix AA-1=/
rank(A) matrix rank

rank of matrix A

dim(U)

dimension

dimension of matrix A

Probability and Statistics Symbols

In mathematics, a part of probability and statistics symbols are there. For now, we assume that some of you have already studied them. Still, you can use the below table to revise them. If you have not studied the probability statistics symbol, then check out the following list.

Symbol

Symbol Name Meaning
P(A) probability function

probability of event A

P(A ∩ B)

probability of events intersection probability that of events A and B
P(A ∪ B) probability of events union

probability that of events A or B

P(A | B)

conditional probability function probability of event A given event B occured
f( X ) probability density function (pdf)

P( a ≤ x ≤ b ) =∫f( X ) dx

F( X )

cumulative distribution function (cdf) F( X ) =P( X ≤ x)
μ population mean

mean of population values

E ( X )

expectation value expected value of random variable X
E ( X | Y ) conditional expectation

expected value of random variable X given Y

var( X )

variance variance of random variable X
σ2 variance

variance of population values

std( X )

standard deviation standard deviation of random variable X
σx standard deviation

standard deviation value of random variable X

median

middle value of random variable x

cov( X,Y )

covariance covariance of random variables X and Y
corr( X,Y ) correlation

correlation of random variables X and Y

cov( X,Y )

covariance covariance of random variables X and Y
corr( X,Y ) correlation

correlation of random variables X and Y

ρ x,y

correlation correlation of random variables X and Y
summation

summation – sum of all values in range of series

∑∑

double summation double summation
Mo mode

value that occurs most frequently in population

MR

mid-range MR =( xmax+xmin)/2
Md sample median

half the population is below this value

Q1

lower / first quartile 25 % of population are below this value
Q2 median / second quartile

50% of population are below this value = median of samples

Q3

upper / third quartile 75% of population are below this value
x sample mean

average / arithmetic mean

s2

sample variance population samples variance estimator
s sample standard deviation

population samples standard deviation estimator

Zx

standard score Zx=(x-x)/ Sx
X ~ distribution of X

distribution of random variable X

X ~

distribution of X distribution of random variable X
N(μσ2) normal distribution

gaussian distribution

U( a,b )

uniform distribution equal probability in range a,b
exp(λ) exponential distribution

f(x)=λe-λx x≥0

gamma(c, λ)

gamma distribution f(x)=λ c xc-1 e-λx / Γ ( c ) x≥0
χ2(k) chi-square distribution

f(x)=xk/2-1 e-x/2 / ( 2k/2Γ )(k/2) )

F (k1,k2)

F distribution
Bin( n,p ) binomial distribution

F(k) = nCk pk(1-p)n-k

Poisson( λ )

Poisson distribution F(k) = λke-λ / k !
Geom( p ) geometric distribution

F(k) = p( 1-p)k

HG( N ,K ,n )

hyper-geometric distribution
Bern( p )

Bernoulli distribution

Combinatorics Symbols

Combinatorics refers to accounting in mathematics. You can count the number of orders with the help of combinatorics. Here, we have provided combinatorics symbols in the table.

Set Theory Symbols

The study related to collections of objects, the relationship between them and their properties are introduced in the branch of mathematics called set theory. Students need to learn set theory symbols to know about sets and their properties. Sir Georg Ferdinand Ludwig Philipp Cantor is the one who developed set theory first. He was a German mathematician. In order to talk about collections of objects, it has been developed by the mathematician. In this part, a list of set theory symbols is mentioned.

Logic Symbols

To express rational thoughts and common patterns of reasoning, logic symbols are used in mathematics. Individuals use these symbols to show highly complex logical relationships between statements. We have provided symbol, symbol name, and their meaning for logic symbols here. We want aware all the students so that they will be able to use different symbols in the context. Below, you will have these symbols specifically arranged in the table.

Calculus & Analysis Symbols

A lot of symbols and equations are included in this unique branch of mathematics. If you are newly learning then it might be confusing for you. Some of the calculus and analysis symbols of mathematics are mentioned here. When studying math subject, these may be helpful for you.

Numeral Symbols

Western Arabic, Hebrew, and Roman numeral symbols are listed in this place.

Greek Alphabet Letters

In general, many people including mathematicians represent consistency, functions, flexibility, and others with the help of Greek letters. Here, we have listed the Greek symbols which are part of maths. You can use them in the work as well as in subject studies.

Upper Case Letter Lower Case Letter Greek Letter Name English Equivalent Letter Name Pronounce
Α α Alpha a al-fa
Β β Beta b be-ta
Γ γ Gamma g ga-ma
Δ δ Delta d del-ta
Ε ε Epsilon e ep-si-lon
Ζ ζ Zeta z Ze-ta
Η η Eta h eh-ta
Θ θ Theta th te-ta
Ι ι Iota i io-ta
Κ κ Kappa k ka-pa
Λ λ Lambda l lam-da
Μ μ Mu m m-yoo
Μ μ Mu m m-yoo
Ν ν Nu n noo
Ν ν Nu n noo
Ξ ξ Xi x x-ee
Ο ο Omicron o o-mee-c-ron
Π π Pi p pa-yee
Ρ ρ Rho r row
Σ σ Sigma s sig-ma
Τ τ Tau t ta-oo
Υ υ Upsilon u oo-psi-lon
Φ φ Phi ph f-ee
Χ χ Chi ch kh-ee
Ψ ψ Psi ps p-see
Ω ω Omega o o-me-ga

Roman Numerals

Romans are the people who use Roman numerals as numerical notation. Different combinations are created with the help of these numbers to denote Roman numerals. Like V is the Roman numeral for and IV is for 4. In many areas, we do use these numerals. For example, class I, Class II and Class X use Roman numerals and it has wide applications here.  Here, a chart of Roman numerals is provided for the students. The Roman numeral symbols for 1 to 10,00,000 are given below. This will help you to learn these numerals in detail.

Numeral

Roman Number
1

I

2

II
3

III

4

IV
5

V

6

VI
7

VII

8

VIII
9

IX

10

X
11

XI

12

XII
13

XIII

14

XIV
15

XV

16

XVI
17

XVII

18

XVIII
19

XIX

20

XX
21

XXI

22

XXII
23

XXIII

24

XXIV
25

XXV

26

XXVI
27

XXVII

28

XXVIII
29

XXIX

30

XXX
31

XXXI

32

XXXII
33

XXXIII

34

XXXIV
35

XXXV

36

XXXVI
37

XXXVII

38

XXXVIII
39

XXXIX

40

XL
41

XLI

42

XLII
43

XLIII

44

XLIV
45

XLV

46

XLVI
47

XLVII

48

XLVIII
49

XLIX

50

L

In Roman Numeral,

L means 50

C means 100

D means 500

M means 1000

Mathematical symbols: why are they important?

  • You can denote many quantities with the help of mathematical symbols.
  • It is possible to make the reference easy with the help of these symbols.
  • For every individuals the symbols can break the language barrier. It is applicable world-wide.
  • Also, it is easy to establish a relationship between two different quantities.
  • You can identify the type of operation with the help of symbols.

Mathematics on Respective Math Symbols

Symbol ‘=’

Example:

x + 5 = 8

Or, x = 8 – 5 = 3

y + 4 = 7

Or, x = 7 – 4 = 3

∴ x = y = 3

 

Symbol ‘≠’

Example:

x + 6 = 8

Or, x = 2

y + 8 = 20

Or, y = 12

∴ x ≠ y

 

Symbol ‘≈’

Example:

x + 6.50 = 8.75

Or, x = 8.75 – 6.50 = 2.25

∴ x ≈ 2

If decimal value greater than 0.5 then round up to the nearest whole number and vice verse.

 

Symbol ‘>’

Example:

x2 – 5x + 6 = 0

Or, x2 – 2x – 3x + 6 = 0

Or, x (x – 2) (x – 3) = 0

∴ Either, x – 2 = 0

Or, x = 2

Or, x – 3 = 0

Or, x = 3

y2 – 11y + 30 = 0

Or, y2 – 5xy – 6y + 30 = 0

Or, y (y – 5) – 6 (y – 5) = 0

Or, (y – 5) (y – 6) = 0

Either, y – 5 = 0 or, y – 6 = 0

Or, y = 5 or, y = 6

∴ x = 7.2, 3 and y = 5, 6

∴ y > x (y greater than x)

 

 

Symbol ‘<’

Example:

Similarly, above sum, represents.

x < y (x less than y)

 

Symbol ‘≥’

Example:

x2 – 5x + 6 = 0

Or, x2 – 2x – 3x + 6 = 0

Or, x (x – 2) – 3 (x – 2) = 0

Or, (x – 2) (x – 3) = 0

∴ Either, x = 2 or, x = 3

y2 – 7y + 12 = 0

Or, y2 – 4y – 3y – 12 = 0

Or, y (y – 4) – 3 (y – 4) = 0

Or, (y – 4) (y – 3) =

Either y = 4, or, y = 3

∴ x = 2, 3 & y = 4, 3

∴ y ≥ x (y is greater or equal to x).

 

Symbol ‘≤’

Example:

Similarly on the above sum,

x = 2, 3 & y = 4, 3

∴ x ≤ y (x is good less or equal to y)

 

Symbol ‘( )’

Example:

5 (6 ÷ 3) + 4 = x

∴ x = 5 of 2 + 4

Or, x = 10 + 4 = 14

Following BODMAS rule —- calculation is done first in the above equation.

 

 

Symbol ‘[  ]’

Example:

5 [4 + (6 ÷ 2)] + 10 = x

Or, x = 5 [4 + 3] + 10

Or, x = 5 of 7 + 10

Or, x = 35 + 10 = 45

Here, the less bracket calculation is done before the third brackets according to brackets rule.

 

Symbol ‘+’

Example:

2 + 3 = 5 [Addition Rule]

 

Symbol ‘-’

Example:

3 – 2 = 1 [substruction Rule]

 

Symbol ‘±’

Example:

√25 = ± 5

∵ + 5x + 5 = 25 also,

– 5x – 5 = 25

When two minus are multiplied the overall value is always positive.

∴ The ‘±’ sign is used for any sq root value.

 

Symbol ‘

Example:

Similar to ‘±’ rule.

 

Symbol ‘×’

Example:

5 × 2 = 10 [Multiplication rule]

Or, 5 + 5 = 10 [Here, 5 is added 2 times as it is multiplied by 2]

 

Symbol ‘.’

Example:

5.2 = 10

Or, 5×2 = 10 [Same as multiplication]

 

Symbol ‘÷’

Example:

10 ÷ 5 = 2

Division rule

 

 

Symbol ‘/’

Example: 

10/5 = [Same as division]

 

 

Symbol ‘mod’

Example: 

100 ÷ 11

Remainder

∴ 100 mod 11 is 1.

Mod represent the remainder of one number divided by another. 

 

Symbol ‘:’

Example: 

5.25 + 6.75 = 8 (5 + 6) : (25 + 75)

= 11 + 1.00

= 12.00

∵ represent decimal value.

 

Symbol ‘a5

Example:

52 = 25 means. 5 × 5 = 25

Here, 5 is multiplied 7 times.

Since exponent value is 2.

Similarly 53 = 5 × 5 × 5 = 125

 

Symbol ‘a^b’

Example: 

5^2 = 5×5 = 25

Also, represent exponent as the previous example.

 

Symbol ‘√a’

Example: 

√25 = ± 5, as ‘√’ represents — root

So, LCM of 25 is 5, 5

∴ The LCM common value is the sq root.

 

Symbol ‘∛a

Example: 

∛125 = 5 as ‘∛’ represents Cube root.

So, LCM of 125 is 5, 5, 5

3 common multiplies are cube root.

 

Symbol ‘

Example:

∜16 = 2

As 2×2×2×2 = 16

∴ LCM of 16 is 2, 2, 2, 2

∴ Similar to cube root

 

Symbol ‘n√

Example:

n√64 =? to find n th root.

We need LCM of the number

64

∴ 64 = 2×2×2×2×2×2

∴ 6 common multiple of 2 becomes 64

∴ 6√64 = 2

 

 

Symbol ‘%

Example:

% —- out of 100 part —- much is a number for eg.

x % of 100 = 25

Or, x/100 × 100 = 25

Or, x = 25

∴ 25% of 100 = 25

Similarly, x % of 200 = 40

Or, x/100 × 200 = 40

Or, 2x = 40

Or, x = 20

∴ 20% of 200 = 40

Similar to 1000th part e.g.

 

 

Symbol ‘%.

Example:

Similar to 1000th part e.g.

x %. of 5000 = 100

Or, x/1000 × 5000 = 100

Or, 5x = 100

Or, x = 20

∴ 20%. of 5000 = 100

 

Symbol ‘ppm

Example:

‘ppm’ means per million or per 10 laks

∴ x ppm of 5000000 = 1000

Or, x/1000000 × 5000000 = 1000

Or, 5x = 1000

Or, x = 200

∴ 200 ppm of 5000000 = 1000

 

 

Symbol ‘ppb

Example:

‘ppb’ means per billion or per 10 crore.

x ppb of 500000000 = 1000

Or, x/100000000 × 500000000 = 1000

Or, x = 20

∴ 200 ppb of 500000000 = 1000

 

 

Symbol ‘ppt

Example:

‘ppt’ represents per trillion or per lakh crore

∴ x ppt 5 × 10 = 1000

Or, x/10 × 5 × 10 = 1000

Or, x = 200

∴ 200 ppt of 5 × 10 = 1000

∴ 1012 represents the no. of zeroes after 5.

Frequently Asked questions on Math Symbols

What is meant by U in mathematics?

In math, U is represented in a situation where two sets have a union. The symbol U is the union of the values present in each set. You can learn more about the U by reading the above article.

How to improve children’s memory of symbols?

Understanding mathematical symbols is not possible with the direct instructional method. There are online learning platforms, video tools, and games that can help you with symbol learning.

What is the math symbol for the area of a circle?

To find the area of a circle, you can use Pi as a math symbol.

What are the basic math symbols and the total number of mathematical symbols?

Some of the basic math symbols are +, =, ±, *. And ˗. For the whole list of mathematical symbols, you check out the above article. In maths, more than 10,000 symbols are there.

What are the common arithmetic math symbols?

Here, students can view a list of common arithmetic and math symbols:

  • Plus Sign + (Useful in Addition)
  • Minus Sign – (Useful in Subtraction)
  • Multiplication * or × (Useful in Multiplication)
  • Division ÷ or Slash Sign / (Useful in Division)

Also See: