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 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 1000^th part e.g.

 

 

Symbol ‘%.’

Example:

Similar to 1000^th 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:

• List of Math Articles for Students
• Magical Maths