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 nonvarying 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 
a^{b;}  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 
nth root (radical)  
%  percent 
1%=1/100 
‰ 
permile  1‰=1/1000=0.1% 
ppm  permillion 
1ppm=1/1000000 
ppb 
perbillion  1ppb=1/1000000000 
ppt  pertrillion 
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 Nonfixed 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=b²4ac 
∑ 
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 
EulerMascheroni 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 
A^{T}  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 
σ^{2}  variance 
variance of population values 
std( X ) 
standard deviation  standard deviation of random variable X 
σ_{x}  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 
midrange  MR =( x_{max}+x_{min})/2 
Md  sample median 
half the population is below this value 
Q_{1} 
lower / first quartile  25 % of population are below this value 
Q_{2}  median / second quartile 
50% of population are below this value = median of samples 
Q_{3} 
upper / third quartile  75% of population are below this value 
x  sample mean 
average / arithmetic mean 
s^{2} 
sample variance  population samples variance estimator 
s  sample standard deviation 
population samples standard deviation estimator 
Z_{x} 
standard score  Z_{x}=(xx)/ S_{x} 
X ~  distribution of X 
distribution of random variable X 
X ~ 
distribution of X  distribution of random variable X 
N(μσ^{2})  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 x^{c1} e^{λx} / Γ ( c ) x≥0 
χ^{2}(k)  chisquare distribution 
f(x)=x^{k/21} e^{x/2} / ( 2^{k/2}Γ )(k/2) ) 
F (k_{1},k_{2}) 
F distribution  
Bin( n,p )  binomial distribution 
F(k) = _{n}C_{k} p^{k}(1p)^{nk} 
Poisson( λ ) 
Poisson distribution  F(k) = λ^{k}e^{λ / k !} 
Geom( p )  geometric distribution 
F(k) = p( 1p)^{k} 
HG( N ,K ,n ) 
hypergeometric 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  alfa 
Β  β  Beta  b  beta 
Γ  γ  Gamma  g  gama 
Δ  δ  Delta  d  delta 
Ε  ε  Epsilon  e  epsilon 
Ζ  ζ  Zeta  z  Zeta 
Η  η  Eta  h  ehta 
Θ  θ  Theta  th  teta 
Ι  ι  Iota  i  iota 
Κ  κ  Kappa  k  kapa 
Λ  λ  Lambda  l  lamda 
Μ  μ  Mu  m  myoo 
Μ  μ  Mu  m  myoo 
Ν  ν  Nu  n  noo 
Ν  ν  Nu  n  noo 
Ξ  ξ  Xi  x  xee 
Ο  ο  Omicron  o  omeecron 
Π  π  Pi  p  payee 
Ρ  ρ  Rho  r  row 
Σ  σ  Sigma  s  sigma 
Τ  τ  Tau  t  taoo 
Υ  υ  Upsilon  u  oopsilon 
Φ  φ  Phi  ph  fee 
Χ  χ  Chi  ch  khee 
Ψ  ψ  Psi  ps  psee 
Ω  ω  Omega  o  omega 
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 worldwide.
 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:
x^{2} – 5x + 6 = 0
Or, x^{2} – 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
y^{2} – 11y + 30 = 0
Or, y^{2} – 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:
x^{2} – 5x + 6 = 0
Or, x^{2} – 2x – 3x + 6 = 0
Or, x (x – 2) – 3 (x – 2) = 0
Or, (x – 2) (x – 3) = 0
∴ Either, x = 2 or, x = 3
y^{2} – 7y + 12 = 0
Or, y^{2} – 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 ‘a^{5}’
Example:
5^{2} = 25 means. 5 × 5 = 25
Here, 5 is multiplied 7 times.
Since exponent value is 2.
Similarly 5^{3} = 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
∴ 10^{12} 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: