Math is all about numbers, symbols and Maths formulas. These symbols are required for different operations. These symbols are used in different mathematical fields. From representing the equation to telling the relationship between the two numbers. All mathematical symbols are used in mathematical operations for various concepts.
There are so many mathematical symbols that are important for students. To make it easier for you we’ ve given here the mathematical symbols table with definitions and examples. From addition, subtraction to geometry to algebra, etc, there are various types of symbols. Find all the symbols in the tables given below:
In Mathematics, it's all about numbers, symbols and formulas. Here we're discussing the foundation of Mathematics. In simple words, without symbols, we cannot do arithmetic. Mathematical symbols and symbols are considered to represent a value.
Basic mathematical symbols are used to express mathematical ideas. The relationship between the symbol and the value refers to the basic mathematical requirement. With the help of symbols, certain concepts and ideas are clearly explained. Here is a list of commonly used mathematical symbols with words and meanings. Also, an example is given to understand the use of mathematical symbols.
Symbol | Symbol Name | Meaning / definition | Example |
= |
equals sign | equality |
10 = 2+8
10 is equal to 2+8 |
≠ | not equal sign | inequality |
2 ≠ 8
2 is not equal to 8 |
≈ | approximately equal | approximation |
sin (0.01) ≈ 0.01,
x ≈ y means is approximately equal to y |
> | strict inequality | greater than |
8 > 2
8 is greater than 2 |
< | strict inequality | less than |
2 < 8
2 is less than 8 |
≥ | inequality | greater than or equal to |
8 ≥ 2,
x ≥ y means x is greater than or equal to y |
≤ | inequality | less than or equal to |
2 ≤ 8,
x ≤ y means is less than or equal to y |
( ) | parentheses | calculate expression inside first | 2 × (4+8) = 24 |
[ ] | brackets | calculate expression inside first | [(2+3)×(4+6)] = 50 |
+ | plus sign | addition | 2 + 8 = 10 |
− | minus sign | subtraction | 8 - 2 = 6 |
± | plus - minus | both plus and minus operations | 2 ± 8 = 10 or -6 |
± | minus - plus | both minus and plus operations | 2∓8 = -6 or 10 |
* | asterisk | multiplication | 2*8 = 16 |
× | times sign | multiplication | 2 × 8 = 16 |
⋅ | multiplication dot | multiplication | 2 sdot; 8 = 16 |
÷ | division sign / obelus | division | 8 ÷ 2 = 4 |
/ | division slash | division | 8 / 2 = 4 |
— | horizontal line | division / fraction | 6—2=3 |
mod | modulo | remainder calculation | 7 mod 2 = 1 |
. | period | decimal point, decimal separator | 3.84 = 3+84/100 |
a^{b; } | power | exponent | 2^{3=8 } |
a^b | caret | exponent | 2^3=8 |
√a | square root | √⋅√a =a | √4=±2 |
3√a | cube root | 3√a⋅3√a⋅3√a⋅& =a | 3√8=2 |
4√a | fourth root | 4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a =a | 4√16=±2 |
n√a | n-th root (radical) | for n=3,n√8=2 | |
% | percent | 1%=1/100 | 10%× 80=8 |
‰ | per-mile | 1‰=1/1000=0.1% | 10‰ × 80=0.8 |
ppm | per-million | 1ppm=1/1000000 | 10ppm × 80=0.0008 |
ppb | per-billion | 1ppb=1/1000000000 | 10ppb × 80=8×10&minussup7; |
ppt | per-trillion | 1ppt=10&minussup12; | 10ppt × 80=8×10&minussup10; |
There are geometry symbols which are used in mathematics. Here we’re mentioning each and every geometry symbols which are necessary for students to know.
Symbol | Symbol Name | Meaning / definition | Example |
∠ | formed by two rays | ∠ABC=30° | |
measured angle | ABC=30° | ||
spherical angle | AOB=30° | ||
∟ | right angle | =90° | α=90° |
° | degree | 1 turn=360° | α=60° |
deg | degree | 1 turn=360deg | α=60deg |
′ | prime | arcminute, 1°=60′ | α=60°59′ |
″ | double prime | arcsecond, 1′=60″ | α=60°59′ 59″ |
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) | AC ⊥ BC |
∥ | parallel | parallel lines | AB ∥ CD |
≅ | congruent to | equivalence of geometric shapes and size | ∆ABC≅∆XYZ |
∼ | similarity | same shapes, not same size | ∆ABC∼∆XYZ |
Δ | triangle | triangle shape | ;ΔABC ≅ΔBCD |
∣x−y∣ | distance | distance between points x and y | ∣x−y∣=5 |
π | pi constant |
π=3.141592654...
is the ratio between the circumference and diameter of a circle |
c=π⋅d=2⋅π⋅r |
rad | radians | radians angle unit | 360°=2π rad |
grad | gradians ∕ gons | grads angle unit | 360°;=400 grad |
g | gradians ∕ gons | grads angle unit | 360°=400g |
Algebra is a mathematical component of symbols and rules to deceive those symbols. In algebra, those symbols represent non-fixed values, called variables. How sentences describe the relationship between certain words, in algebra, mathematics describes the relationship between variables.
A | Symbol Name | Meaning / definition | Example |
χ | x variable | unknown value to find | when 2χ=4, then χ=2 |
≡ | equivalence | identical to | |
≜ | equal by definition | equal by definition | |
≔ | equal by definition | equal by definition | |
∽ | approximately equal | weak approximation | 11∽10 |
≈ | approximately equal | approximation | sin(0.01) ≈ 0.01 |
∝ | proportional to | proportional to | y ∝ x when y=kx, k constant |
∞ | lemniscate | infinity symbol | |
≪ | much less than | much less than | 1≪1000000 |
⁽ ⁾ | much grataer than | much grataer than | 1000000 ≫1 |
⁽ ⁾ | parentheses | calculate expression inside first | 2 *(3+5) = 16 |
[ ] | brackets | calculate expression inside first | [ (1+2)*(1+5) ] = 18 |
{ } | braces | set | |
⌊ χ ⌋ | floor brackets | rounds number to lower integer | ⌊4.3⌋ = 4 |
⌈ χ ⌉ | ceiling brackets | rounds number to upper integer | ⌈4.3⌉ = 5 |
χ! | exclamation mark | factorial | 4! =1*2*3*4 = 24 |
|χ| | vertical bars | absolute value | | -5 | = 5 |
Af(χ) | function of x | maps values of x to f(x) | f(x)=3x+5 |
(f°g) | function composition | (f°g)(x)=f(g(x)) | f(x)=3x,g(x)=x-1⇒(f°g)(x)=3(x-1) |
(a,b) | open interval | (a,b)={ x | a < x < b } | x∈(2,6) |
[a,b] | closed interval | [a,b]={x | a≤ x ≤b } | x&isin[2,6] |
Δ | delta | change / difference | Δ=t_{1}-t_{0} |
Δ | discriminant | Δ=b²-4ac | |
∑ | sigma | summation - sum of all values in range of series | ∑x_{1}=x_{1}+x_{2}+...+x_{n} |
∑∑ | sigma | double summation | |
∏ | capital pi | product - product of all values in range of series | ∏x_{1}=x_{1}∙x_{2}∙...∙x_{n} |
e | e constant / Euler's number | e = 2.718281828... | e =lim (1+1/x)^{x},x→∞ |
γ | Euler-Mascheroni constant | γ= 0.5772156649... | |
φ | golden ratio | golden ratio constant | |
π | pi constant |
π = 3.141592654...
is the ratio between the circumference and diameter of a circle |
c=π⋅d=2⋅π⋅r |
These are the linear Algebraic Symbols. It's also a part of mathematics. These symbols are generally used in higher standard. Here's the list of all linear algebra symbols which are helpful for you guys.
Symbol | Symbol Name | Meaning / definition | Example |
· | dot | scalar product | a·b |
× | cross | vector product | a×b |
A⊗B | tensor product | tensor product of A and B | A ⊗ 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^{T} ) _{ij} = ( A ) _{ji} |
A^{†} | Hermitian matrix | matrix conjugate transpose | (A^{†} ) _{ij} = ( A ) _{ji} |
A^{*} | Hermitian matrix | matrix conjugate transpose | (A^{*} ) _{ij} = ( A ) _{ji} |
A^{-1} | inverse matrix | AA^{-1}=/ | |
rank(A) | matrix rank | rank of matrix A | rank(A)= 3 |
dim(U) | dimension | dimension of matrix A | dim(U)= 3 |
Probability and statistics are also a part of mathematics. As you’ve already studied probability and statistics from the junior classes. So here’s the list of the most important probability and statistics symbols.
Symbol | Symbol Name | Meaning / definition | Example |
P(A) | probability function | probability of event A | P(A)= 0.5 |
P(A ∩ B) | probability of events intersection | probability that of events A and B | P(A ∩ B)= 0.5 |
P(A ∪ B) | probability of events union | probability that of events A or B | P(A ∪ B)= 0.5 |
P(A | B) | conditional probability function | probability of event A given event B occured | P(A | B)= 0.3 |
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 | μ= 10 |
E( X ) | expectation value | expected value of random variable X | E( X ) = 10 |
E( X | Y ) | conditional expectation | expected value of random variable X given Y | E( X | Y = 2 ) = 5 |
var( X ) | variance | variance of random variable X | var( X )= 4 |
σ^{2} | variance | variance of population values | σ^{2}= 4 |
std( X ) | standard deviation | standard deviation of random variable X | std( X ) = 2 |
σ_{x} | standard deviation | standard deviation value of random variable X | σ_{x} = 2 |
median | middle value of random variable x | ||
cov( X,Y ) | covariance | covariance of random variables X and Y | cov( X,Y )= 4 |
corr( X,Y ) | correlation | correlation of random variables X and Y | corr( X,Y )= 0.6 |
cov( X,Y ) | covariance | covariance of random variables X and Y | cov( X,Y )= 4 |
corr( X,Y ) | correlation | correlation of random variables X and Y | corr( X,Y )= 0.6 |
ρ x,y | correlation | correlation of random variables X and Y | ρ x,y= 0.6 |
∑ | 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 =( 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 | x=(2+5+9) /3=5.333 |
s^{2} | sample variance | population samples variance estimator | s^{2}= 4 |
s | sample standard deviation | population samples standard deviation estimator | s= 2 |
Z_{x} | standard score | Z_{x}=(x-x)/ S_{x} | |
X ~ | distribution of X | distribution of random variable X | X ~ N (0,3) |
X ~ | distribution of X | distribution of random variable X | X ~ N (0,3) |
N(μσ^{2}) | normal distribution | gaussian distribution | X ~ N (0,3) |
U( a,b ) | uniform distribution | equal probability in range a,b | X ~ U (0,3) |
exp(λ) | exponential distribution | f(x)=λe^{-λx} x≥0 | |
gamma(c, λ) | gamma distribution | f(x)=λ c x^{c-1} e^{-λx} / Γ ( c ) x≥0 | |
χ^{2}(k) | chi-square distribution | f(x)=x^{k/2-1} 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}(1-p)^{n-k} | |
Poisson( λ ) | Poisson distribution | F(k) = λ^{k}e^{-λ / k ! } | |
Geom( p ) | geometric distribution | F(k) = p( 1-p)^{k} | |
HG( N ,K ,n ) | hyper-geometric distribution | ||
Bern( p ) | Bernoulli distribution |
Mathematicians often use Greek letters in their work to represent flexibility, consistency, functions and more. Some of the Greek symbols commonly used in Maths are listed below -
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 |
Q1. What do math symbols mean?
Ans. It means all the symbols which show the quantities or the relationship between two quantities.
Q2. What is the value of pi?
Ans. The value of pi is 22/7 and 3.14. It is a Greek alphabet. It is an irrational number. While solving NCERT Solutions you'll find many questions about where you've to use them.
Q3. What is the * symbol called?
Ans. In English, the * symbol generally means asterisk, but in Mathematics it is generally used to represent multiplication between two quantities.
Q4. How are symbols used in math?
Ans. The symbols make it easier to refer to Mathematical quantities. It is interesting to note that Mathematics is wholly based on numbers and symbols. The math symbols refer to different quantities and represent the relationship between two quantities.
Q5. What does => mean in math?
Ans. It stands for "implies that." For example, x=2⟹x2=4 - if x is 2, then it is evident that x squared is 4; the symbol essentially shows a function here.
Q6. What is the oldest math symbol?
Ans. The Humble plus sign is one of the oldest mathematical symbols agreed upon but came into use around 1360. The measuring mark was established in 1557 by Scottish mathematician Robert Recorde.