Mathematics is a science that particularly deals with shapes, numbers, and arrangements. It is used everywhere in our day-to-day life or we can say this is the building block whatever we do. Either it is smartphones, construction, buildings, artwork, money, sports, or engineering, etc., the application of mathematics can be seen everywhere.

What are the Topics in Math?

Topics include Numbers, Algebra, Probability & Statistics, Calculus & Analysis, Math Symbols, Math Calculators, and Number Converters.

What is a formula in math?

Here you can check the Math formula by class, topics, and theorem that is mention above in the body content.

Why do we need math formulas?

Math formulas help to resolve math problem, you can easily get better results as well as save time to solve the math problems.

Maths Formulas Made Simple: A Step-by-Step Guide

Table of Contents

Maths Formulas

Maths Formulas

Sometimes, Math is Fun and sometimes it could be a surprising fact too. In our routine life, you can check the best route to your school, you can check where more discounted products are available in the market, and you can check which bank can offer the superior interests. This is all about calculation and connecting dots that we are able to find the solution.

Mensuration Maths Formulas

Formula of Square

Area of Square = \( l^{2} \)
Perimeter of Square = \( 4 \times l \)

Where,
l : length of side

Formula of Rectangle

Area of Rectangle = \( l \times w \)
Perimeter of Rectangle = \( 2 (l+w) \)

Where,
L = Length, w = Width

Formula of Circle

Area of Circle = \( \pi r^{2} \)
Perimeter of Circle = \( 2 \pi r \)

Where,
𝒓 = Radius, d = Diameter, d = 2𝒓

Formula of Scalene Triangle

Area of Scalene Triangle = \( \sqrt{s(s-a)(s-b)(s-c)} \)
Perimeter of Scalene Triangle = \( a+b+c \)

Where,
a, b, c are Side of Scalene Triangle

Formula of Isoscele Triangle

Area of Isoscele Triangle = \(\frac{1}{2}bh\)
Altitude of an Isosceles Triangle = \(\sqrt{a^{2}-\frac{b^{2}}{4}}\)
Perimeter of Isosceles Triangle,P = \( 2a+b \)

Where,
b = Base, h = Height, a = length of the two equal sides

Formula of Right Triangle

Area of an Right Triangle = \( \frac{\sqrt{1}}{2}bh\)
Perimeter of an Right Triangle = \( a+b+c\)
semi Perimeter of an Right Triangle = \( \frac{a+b+c}{2}\)

where,
b = Base, h = Hypotenuse, a = Hight

Formula of Equilateral Triangle

Area of an Equilateral Triangle = \( \frac{\sqrt{3}}{4}a^{2}\)
Perimeter of an Equilateral Triangle = \( 3a\)
Semi Perimeter of an Equilateral Triangle = \( \frac{3a}{2}\)
Height of an Equilateral Triangle = \( \frac{\sqrt{3}}{2}a\)

Where,
a = side, h = altitude

Formula of Rhombus

Perimeter of a rhombus = \(4\times Side\)
Area of a Rhombus A = \( \frac{1}{2} \times d_{1} \times d_{2} \)

Where,
d1 and d2 are the diagonals

Formula of Parallelogram

Area of a Parallelogram = \( b\times h\)
Perimeter of Parallelogram = \( 2\left(b+h\right)\)

Where,
b: Base, h: Height.

Formula of Trapezoid

Perimeter of a Trapezoid = \(a+b+c+d\)
Area of a Trapezoid = \( \frac{1}{2} \times h \times (a + b)\)

Where:
h = height, a = the short base, b = the long base, c, d are the lengths of side.

Formula of Cube

Surface area of Cube = \(6a^{2}\)
Volume of a cube = \(a^{3}\)

Where,
a is the side length of the cube.

Formula of Cuboid

Surface area of Cuboid = \( 2(lb + bh + hl)\)
Volume of a Cuboid = \( h \times l \times w\)

Where,
l: Height, h: Legth, w: Depth

Formula of sphere

Diameter of a sphere = \(2r\)
Circumference of a sphere = \(2\pi r\)
Surface area of a sphere = \(4\pi r^{2}\)
Volume of a sphere = \(\frac{4}{3}\: \pi r^{3}\)

Where,
r: Radius

Formula of Hemisphere

Curved Surface area of a Hemisphere = \(4\pi r^{2}\)
Total Surface area of a Hemisphere = \(3\pi r^{2}\)
Volume of a Hemisphere = \(\frac{2}{3}\: \pi r^{3}\)

Where,
r: Radius

Formula of Cylinder

Curved Surface area of a Cylinder = \(2\pi rh\)
Total Surface area of a Cylinder = \(2\pi r(r+h)\)
Volume of a Cylinder = \( \pi r^{2} h\)

Where,
r: Radius, h: Height

Formula of cone

Total Surface Area of cone = \(\pi r \left (s+r \right )\)
Vomule of cone = \(\frac {1}{3}\pi r^{2}h\)
Curved Surface Area of cone = \(\pi rs\)

Where,
r = radius, h = height, s = slant height

Trigonometry Maths Formulas

\(\sin \theta = \frac{Opposite}{Hypotenuse}\)
\(\sec \theta = \frac{Hypotenuse}{Adjacent}\)
\(\cos\theta = \frac{Adjacent}{Hypotenuse}\)
\(\tan \theta =\frac{Opposite}{Adjacent}\)
\(csc \theta = \frac{Hypotenuse}{Opposite}\)
\(cot \theta = \frac{Adjacent}{Opposite}\)

The Reciprocal Identities are given as:

\(cosec\theta =\frac{1}{\sin\theta }\)
\(sec\theta =\frac{1}{\cos\theta }\)
\(cot\theta =\frac{1}{\tan\theta }\)
\(sin\theta =\frac{1}{csc\theta }\)
\(cos\theta =\frac{1}{\sec\theta }\)
\(tan\theta =\frac{1}{cot\theta }\)

Trigonometric Values of Special Angles

Degree	sin	cos	tan	cot	sec	cosec
0∘	0	1	0	Not Defined	1	Not Defined
30∘	\[\frac{1}{2}\]	\[\frac{√3}{2}\]	\[\frac{1}{√3}\]	√3	\[\frac{2}{√3}\]	2
45∘	\[\frac{1}{√2}\]	\[\frac{1}{√2}\]	1	1	√2	√2
60∘	\[\frac{√3}{2}\]	\[\frac{1}{2}\]	√3	\[\frac{1}{√3}\]	2	\[\frac{2}{√3}\]
90∘	1	0	Not Defined	0	Not Defined	1

Product:

\(\sin\: x\cdot \cos\:y=\frac{\sin(x+y)+\sin(x-y)}{2}\)
\(\cos\: x\cdot \cos\:y=\frac{\cos(x+y)+\cos(x-y)}{2}\)
\(\sin\: x\cdot \sin\:y=\frac{\cos(x+y)-\cos(x-y)}{2}\)

Sum to Product:

\(\sin\: x+\sin\: y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}\)
\(\sin\: x-\sin\: y=2\cos\frac{x+y}{2}\sin\frac{x-y}{2}\)
\(\cos\: x+\cos\: y=2\cos\frac{x+y}{2}\cos\frac{x-y}{2}\)
\(\cos\: x-\cos\: y=-2\sin\frac{x+y}{2}\sin\frac{x-y}{2}\)<

Pythagorean

Sin²x + Cos²x = 1
1 + tan²x = sec²x
1 + cot²x = cosec²x

Pythagorean in Radical Form

sinx = ∓√1–cos2x
tanx = ∓√sec2x-1
cosx = ∓√1–sin2x

Odd-Even

Sin(-x)=-sin x
cos(-x)=-cos x
tan(-x)=-tan x
cot(-x)=-cot x
sec(-x)=-sec x
cosec(-x)=-cosec x

Ratio or Quotient Identities are given as:

\( Sinθ = Cosθ \times Tanθ \)
\( Cosθ = Sinθ \times Cotθ \)
\( Tanθ = \frac{Sinθ}{Cosθ} \)
\( Cotθ = \frac{Cosθ}{Sinθ} \)

Periodicity

\(sin(x+2\pi )=sin\; x\)
\(cos(x+2\pi )=cos\; x\)
\(tan(x+\pi )=tan\; x\)
\(cot(x+\pi )=cot\; x\)

Co-function:

\(sin(90^{\circ}-x)=cos\; x\)
\(cos(90^{\circ}-x)=sin\; x\)
\(tan(90^{\circ}-x)=cot\; x\)
\(cot(90^{\circ}-x)=tan\; x\)

Sum/Difference:

\( \sin (x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)\)
\(\cos(x + y) = \cos(x) \cos(y) – \sin(x) \sin(y)\)
\(\tan(x+y)=\frac{\tan\: x+\tan\: y}{1-\tan\: x\cdot \tan\: y}\)
\(\sin(x – y) = \sin(x) \cos(y) – \cos(x) \sin(y)\)
\(\cos(x – y) = \cos(x) \cos(y) + \sin(x) \sin(y)\)
\(\tan(x-y)=\frac{\tan\: x – \tan\: y}{1+\tan\: x\cdot tan\: y}\)

Double Angle:

\(\sin(2x) = 2\sin(x).\cos(x)\)
\(\cos(2x) = \cos^{2}(x) – \sin^{2}(x)\)
\(\cos(2x) = 2 \cos^{2}(x) -1\)
\(\cos(2x) = 1 – 2 \sin^{2}(x)\)
\(\tan(2x) = \frac{[2\: \tan(x)]}{[1 -\tan^{2}(x)]}\)

Half Angle:

\(\sin\frac{x}{2}=\pm \sqrt{\frac{1-\cos\: x}{2}}\)
\(\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}\)
\(\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\)

Albegra Maths Formulas

(a + b)²=a² + 2ab + b²
(a−b)²=a²−2ab + b²
(a + b)(a – b)=a² – b²
(x + a)(x + b)=x² + (a + b)x + ab
(x + a)(x – b)=x² + (a – b)x – ab
(x – a)(x + b)=x² + (b – a)x – ab
(x – a)(x – b)=x² – (a + b)x + ab
(a + b)³=a³ + b³ + 3ab(a + b)
(a – b)³=a³ – b³ – 3ab(a – b)
(x + y + z)²=x² + y² + z² + 2xy + 2yz + 2xz
(x + y – z)²=x² + y² + z² + 2xy – 2yz – 2xz
(x – y + z)²=x² + y² + z² – 2xy – 2yz + 2xz
(x – y – z)²=x² + y² + z² – 2xy + 2yz – 2xz
x³ + y³ + z³ – 3xyz=(x + y + z)(x² + y² + z² – xy – yz−xz)
(x + a)(x + b)(x + c)=x³ + (a + b + c)x² + (ab + bc + ca)x + abc
x³ + y³=(x + y)(x² – xy + y²)
x³ – y³=(x – y)(x² + xy + y²)
(a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴)
(a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴)
a⁴ – b⁴ = (a – b)(a + b)(a² + b²)
a⁵ – b⁵ = (a – b)(a⁴ + a³b + a²b² + ab³ + b⁴)
If n is a natural number, aⁿ – bⁿ = (a – b)(a^n-1 + a^n-2b+…+ b^n-2a + b^n-1)
If n is even (n = 2k), aⁿ + bⁿ = (a + b)(a^n-1 – a^n-2b +…+ b^n-2a – b^n-1)
If n is odd (n = 2k + 1), aⁿ + bⁿ = (a + b)(a^n-1 – a^n-2b +…- b^n-2a + b^n-1)
(a + b + c + …)² = a² + b² + c² + … + 2(ab + ac + bc + ….
Laws of Exponents
(a^m)(aⁿ) = a^m+n(ab)^m = a^mb^m(a^m)ⁿ = a^mn
Fractional Exponents
a⁰ = 1
aman=am−naman=am−n
amam = 1a−m1a−ma−ma−m = 1am

\( x^{2} + y^{2} = \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]\)

\( x^{2} + y^{2} + z^{2} -xy – yz – zx = \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]\)

\(\mathbf{a_{1}x + b_{1}y + c_{1} = 0}\)

\(\mathbf{a_{2}x+ b_{2}y + c_{2}} = 0 \)

Distributive Property	a ( b+c) = (a × b) + (a × c)
Commutative Property of Addition	a + b = b+a
Commutative Property of Multiplication	a× b = b×a
Associative Property of Addition	a + (b + c ) = ( a+ b ) +c
Associative Property of Multiplication	a ( b × c ) = ( a× b ) × c
Additive Identity Property	a +0 = a
Multiplicative Identity Property	a×1 = a
Additive Inverse Property	a+ ( -a) = 0
Multiplicative Inverse Property	a × 1/a = 1
Zero Property of Multiplication	a × 0 = 0

If\(\vec{a}=x\hat{i}+y\hat{j}+z\hat{k}\) then magnitude or length or norm or absolute value of \(\vec{a} \) is \( \left | \overrightarrow{a} \right |=a=\sqrt{x^{2}+y^{2}+z^{2}}\)

A vector of unit magnitude is unit vector. If \(\vec{a}\) is a vector then unit vector of \(\vec{a}\) is denoted by \(\hat{a}\) and \(\hat{a}=\frac{\hat{a}}{\left | \hat{a} \right |}\) Therefore \( \hat{a}=\frac{\hat{a}}{\left | \hat{a} \right |}\hat{a}\)

Important unit vectors are \(\hat{i}, \hat{j}, \hat{k}\), where \(\hat{i} = [1,0,0],\: \hat{j} = [0,1,0],\: \hat{k} = [0,0,1]\)

If \( l=\cos \alpha, m=\cos \beta, n=\cos\gamma,\) then \( \alpha, \beta, \gamma,\) are called directional angles of the vectors\(\overrightarrow{a}\) and \(\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma = 1\)

\(\vec{a}+\vec{b}=\vec{b}+\vec{a}\)

\(\vec{a}+\left ( \vec{b}+ \vec{c} \right )=\left ( \vec{a}+ \vec{b} \right )+\vec{c}\)

\(k\left ( \vec{a}+\vec{b} \right )=k\vec{a}+k\vec{b}\)

\(\vec{a}+\vec{0}=\vec{0}+\vec{a}\), therefore \( \vec{0}\) is the additive identity in vector addition.

\(\vec{a}+\left ( -\vec{a} \right )=-\vec{a}+\vec{a}=\vec{0}\), therefore \(\vec{a}\) is the inverse in vector addition.

Probability and Set Theory Maths Formulas

Commutative= \( A\cup B = B\cup A \) and \( A\cap B = B\cap A \)
Associative= \( A\cup (B\cup C) = A\cup (B\cup C) \) and \( A\cap (B\cap C) = A\cap (B\cap C) \)
Neutral element= \( A\cup \theta = A \) and \( A\cap E = A \)
Absorbing element= \( A\cup E = E \) and \( A\cap \theta = \theta \)
Distributive= \( A\cup (B\cap C)=(A\cup B)\cap (A\cup C) \) and \( A\cap (B\cup C)=(A\cap B)\cup (A\cap C) \)
De Morgan’s laws= \( \bar(A\cap B) = \bar A \cup \bar B \) and \( \bar(A\cup B) = \bar A \cap \bar B \)
Independent Events= \( P(A | B)=P(A) \) and \( P(A\cap B)=P(A)×P(B)\)
Conditional Probability= \( P(A | B)=\frac{P(A\cap B)}{P(B)} \)
Laplace laws= \( P(A)=\frac{Number\;of\;ways\;it\;can\;happen}{Total\;Number\;of\;Outcomes} \)
Complement of an Event= \( P (\bar A)=1 – P(A)\)
Union of Events= \( P(A\cup B)=P(A)+P(B)−P(A\cap B)\)

Statistics Maths Formulas

\(Direct\; Method: x̅ = \frac{\sum_{i=1}^{n}f_i x_i}{\sum_{i=1}^{n}f_i}\)

where f_ix_i is the sum of observations from value i = 1 to n And f_iis the number of observations from value i = 1 to n

\(Assumed\; mean\; method : x̅ = a+\frac{\sum_{i=1}^{n}f_i d_i}{\sum_{i=1}^{n}f_i}\)

\(Step \;deviation \;method : x̅ = a+\frac{\sum_{i=1}^{n}f_i u_i}{\sum_{i=1}^{n}f_i}\times h\)

\(Mode = l+\frac{f_1 – f_0}{2f_1 – f_0 – f_2} \times h\)

\( Range = Largest\; Value – Smallest\; Value \)

\(Median = l+\frac{\frac{n}{2} – cf}{f} \times h\)

\( Variance = \sigma ^{2} = \frac{\sum (x- \bar{x})^{2}}{n}\)
Where, x = Items given, x¯ = Mean, n = Total number of items

\( Standard\;Deviation \; \sigma = \sqrt{\frac{\sum (x-\bar{x})^{2}}{n}}\)
Where, x = Items given, x¯ = Mean, n = Total number of items

Exponents and Powers Maths Formulas

Power zero = \( a^{ 0 } = 1\)
Power one = \( a^{ 1 } = a\)
Fraction formula = \( \sqrt{ a } = a^{ \frac{ 1 }{ 2 }}\)
Reverse formula = \( \sqrt{ n } { a } = a^{\frac{ 1 } { n }}\)
Negative power value = \( a^{ -n } = \frac{ 1 }{ a^{n} }\)
Fraction formula = \( a^{n} = \frac{1}{ a^{ -n } }\)
Product formula = \( a^{m}a^{n} = a^{ m + n }\)
Division Formula = \( \frac{ a^{ m }}{ a^{ n }} = a ^{ m-n }\)
Power of Power formula = \( (a^{ m })^{ p } = a^{ mp }\)
Power distribution Formula = \( (a^ { m }c^{ n })^{ x } = a ^ { mx } c ^{ nx }\)
The Power distribution Formula = \( \left ( \frac {a ^{ m }}{c^{ n }} \right )^{x} = \frac{a^{ mx }}{c^{ nx }}\)
Power Even Number = \( (-1)^{Even Number} = 1 \)
Power Odd Number = \( (-1)^{Odd Number} = -1 \)
Product of Power Formula = \( (ab)^m = a^m \times b^m \)

Complex Number Maths Formulas

Complex number = \( z=a+bi \)
Conjugate = \( \bar z =a−bi \)
Symmetry = \( −z=−a−bi \)
Equality = a+bi=c+di⇔a=c and b=d
Addition = \( (a+bi)+(c+di)=(a+c)+(b+d)i \)
Subtraction = \( (a+bi)−(c+di)=(a−c)+(b−d)i \)
Multiplication = \( (a+bi)\times(c+di)=(ac−bd)+(ad+bc)i \)
Division = \( \frac{(a+bi)}{(c+di)} = \frac{a+bi}{c+di} \times \frac{c-di}{c-di} = \frac{ac+bd}{c^{2}+d^{2}} + \frac{bc-ad}{c^{2}+d^{2}}\times i \)
Multiplication Conjugates = \( (a+bi)(a+bi)=a^{2}+b^{2} \)

Powers of Complex Numbers

iⁿ= i, if n = 4a+1, i.e. one more than the multiple of 4.

Example – i¹=i; i⁵=i; i⁹=i; i^4a+1;

iⁿ= -1, if n = 4a+2, i.e. two more than the multiple of 4.

Example – i²= -1; i⁶= -1; i¹⁰= -1; i^4a+2;

iⁿ= -i, if n = 4a+3, i.e. Three more than the multiple of 4.

Example – i³= -i; i⁷= -i; i¹¹= -i; i^4a+3;

iⁿ= -1, if n = 4a, i.e. the multiple of 4.

Example – i⁴= 1; i⁸= 1; i¹²= 1; i^4a;

Logic Maths Formulas

Conjunction			Disjunction			Implication
p	q	p∧ q	p	q	p∨q	p	q	p ⇒ q
V	V	V	V	V	V	V	V	V
V	F	F	V	F	V	V	F	F
F	V	F	F	V	V	F	V	V
F	F	F	F	F	F	F	F	V

Law of noncontradiction		p∧~p⇔F
Law of the excluded middle		p∨~p⇔V
Double Negation		~(~p)⇔p
Commutativity	Conjunction	p∧q⇔q∧p
Commutativity	Disjunction	p∨q⇔q∨p
Associativity	Conjunction	(p∧q)∧r⇔p∧(q∧r)
Associativity	Disjunction	(p∨q)∨r⇔p∨(q∨r)
Neutral Element	Conjunction	p∧V⇔p
Neutral Element	Disjunction	p∨F⇔p
Absorbing Element	Conjunction	p∧F⇔F
Absorbing Element	Disjunction	p∨V⇔V
Idempotence	Conjunction	p∧p⇔p
Idempotence	Disjunction	p∨p⇔p
Distributive Property	Conjunction over Disjunction	p∧(q∨r)⇔(p∧q)∨(p∧r)
Distributive Property	Disjunction over Conjunction	p∨(q∧r)⇔(p∨q)∧(p∨r)
Properties of Implication	Transitive	(p⇒q)∧(q⇒r)⇒(p⇒r)
	Implication and Disjunction	(p⇒q)⇔~p∨q
	Negation	~(p⇒q)⇔p∧~q
	Contrapositive of an Implication	(p⇒q)⇔(~q⇒~p)
Properties of Equivalence	Double implication	(p⇔q)⇔[(p⇒q)∧(q⇒p)]
	Transitive	[(p⇔q)∧(q⇔r)]⇒(p⇔r)
	Negation	~(p⇔q)⇔[(p∧~q)∨(q∧~p)]
De Morgan’s laws	Negation of a Conjunction	~(p∧q)⇔~p∨~q
De Morgan’s laws	Negation of a Disjunction	~(p∨q)⇔~p∧~q
De Morgan’s laws	Negation of Universal Quantifier	~(∀x,p(x))⇔∃x:~p(x)
De Morgan’s laws	Negation of Existential Quantifier	~(∃x:p(x))⇔∀x,~p(x)

Limits Maths Formulas

1) If \(\lim_{x \to a} f(x) = l\; and \; \lim_{x \to a} g(x) = m\), then

\( \lim_{x \to a} \left[ {f(x) \pm g(x)} \right] = l \pm m\)
\( \lim_{x \to a} f(x) \cdot g(x) = l \cdot m\)
\(\lim_{x \to a} \frac{{f(x)}}{{g(x)}} = \frac{l}{m}\), where \)m \ne 0\)
\(\lim_{x \to a} c{\text{ }}f(x) = c{\text{ }}l\)
\(\lim_{x \to a} \frac{1}{{f(x)}} = \frac{1}{l}\), where \)l \ne 0\)

2) \(\lim_{n \to \infty } {\left( {1 + \frac{1}{n}} \right)^n} = e\), where \)n\) is a real number.

3) \(\lim_{n \to 0} {\left( {1 + n} \right)^{\frac{1}{n}}} = e\), where \)n\) is a real number.

4) \(\lim_{x \to 0} \frac{{Sinx}}{x} = 1\), where \)x\) is measured in radians.

5) \(\lim_{x \to 0} \frac{{Tanx}}{x} = 1\)

6) \(\lim_{x \to 0} \frac{{Cosx – 1}}{x} = 0\)

7) \(\lim_{x \to a} \frac{{{x^n} – {a^n}}}{{x – a}} = n{a^{n – 1}}\)

8) \(\lim_{x \to 0} \frac{{{a^n} – 1}}{x} = \ln a\)

Logarithms Maths Formulas

Properties

\(\log_{b}1 = 0\) (∵ b^⁰ = 1)
\(\log_{b}b = 1\) (∵ b¹ = b)
\(y = \ln x \quad \Rightarrow e^y = x\)
\(x = e^y \quad \Rightarrow \ln x = y\)
\(x = \ln e^x = e^{\ln x}\)
\(b^{\log_{b}x} = x\)
\(\log_{b}{b^y} = y\)

Laws of Logarithms

1. \(\log_{b}{M \times N} = \log_b{{M}} + \log_b{{N}}\) (where b, M, N are positive real numbers and b ≠ 1)

2. \(\log_{b}\frac{M}{N} = \log_b{{M}} – \log_b{{N}}\)(where b, M, N are positive real numbers and b ≠ 1)

3. \(\log_{b}M^c = c \ \log_b{{M}}\) (where b and M are positive real numbers , b ≠ 1, c is any real number)

4. \(\log_{b}M = \frac{\log {M}}{\log b} = \frac{\ln {M}}{\ln b} = \frac{\log_{k} {M}}{\log_{k} b}\) (where b, k and M are positive real numbers, b ≠ 1, k ≠ 1)

5. \(\log_{b}a = \frac{1}{\log_{a}b}\) (where a and b are positive real numbers, a ≠ 1, b ≠ 1)

6. If \(\log_{b}{M}=\log_{b}{N}\), then M = N (where b, M and N are positive real numbers and b ≠ 1).

Direction Of A Vector Formula	Probability Distribution Formula
Quartile Formula	Circumference of a Circle Formula
Decay Formula	Margin of Error Formula
Population Mean Formula	Infinite Geometric Series Formula
Double Time Formula	Linear Approximation Formula
Cosine Formula	Spherical Segment Formula
Proportion Formula	Rectangular Prism Formula
R Squared Formula	Triangular Prism Formula
Statistical Significance Formula	Difference of Squares Formula
Vertex Formula	Perfect Square Formula
Vieta Formula	Right Angle Formula
U Substitution Formula	Percentage Change Formula
Regular Square Pyramid Formula	Gross Profit Formulas
Trajectory Formula	Exponential Formulas
Sample Mean Formula	Quotient Formulas
Real Number	Box Formulas
Simple Interest Formula	X& Y Intercept Formulas
Triangular Pyramid Formula	Coefficient Formulas
Distance Formula	Arithmetic Sequence Formulas
Weighted Mean Formula	Parallelogram Formulas
Multiplication Table	Pentagon Formulas
Volume Of Parallelepiped Formula	Octagon Formulas
Volume Of An Ellipsoid Formula	Binary Formulas
Volume Of A Square Pyramid Formula	Binomial Formulas
Charge Density Formula	Isosceles Triangle Formulas
Complex Number Power Formula	Equilateral Triangle Formulas
Diagonal Formula	Triangle Formulas
Division Formula	Area of Cube Formulas
Diameter Formula	Sphere Formulas
Coin Toss Probability Formula	Trapezoid Formulas
Circle Graph Formula	Hexagon Formulas
Chord Length Formula	Cube Formulas
Cofunction Formulas	Discount Formulas
Cofactor Formula	Rhombus Formulas
Cpk Cp Formula	Cone Formulas
Degree And Radian Measure Formula	Equation Formulas
Consecutive Integers Formula	Cylinder Formulas
Interpolation Formula	Pythagoras Formulas
Prime Number formula	Matrix Formulas
Euler Maclaurin formula	Area of Circle Formulas
Frequency Distribution formula	Circle Formulas
Hypergeometric Distribution formula	Compound Interest Formulas
Implicit Differentiation formula	Completing the Square Formulas
Inverse Function formula	Square Formulas
Inverse Hyperbolic Functions formula	Factorial Formulas
Pearson Correlation formula	Statistics Formulas
Confidence Interval formula	Linear Formulas
Lagrange Interpolation formula	Derivative Formulas
Hypothesis Testing formula	Differentiation Formulas
Kite formula	Pyramid Formulas
Degrees of Freedom formula	Rectangle Formulas
Interquartile Range formula	Probability Formulas
Function Notation formula	Mean Median Mode Formulas
Gaussian Distribution formula	Vector Formulas
Hyperbolic Function formula	Ellipse Formulas
What Is Numbers?	Permutation & Combination Formulas
Area under the Curve Formula	Complex Number Formulas
Axis of Symmetry Formula	Calculus Formulas
Arithmetic Progression Formula	Integration Formulas
Average Deviation Formula	Trigonometry Formulas
Equation of a Circle Formula	Polynomial Formulas
Chain Rule Formula	Geometry Formulas
Quadratic Interpolation Formula	Algebra Formulas
Change of Base Formula	LCM Formulas
Absolute Value Formula	Percentage Formulas
Discriminant Formula	Effect Size Formula

Learning Math is not easy and this is the reason why we have discovered unique ways to amplify your learning. We have given easy definitions and formulas of different mathematical concepts so that you can learn them at your fingertips quickly. Also, we have hosted a large sheet of formulas for your reference so that you can memorize them and apply them wherever needed.

Download 1300 Maths Formulas PDF

You just have to click on the topic and get all relevant details and formulas with simple navigation. Also, we have discussed the applications of the different mathematical concepts in real life and how it can help students in their careers. Well, formulas can be simpler or complex based on the topic you selected but there is a need for depth understanding of each of the formulas to solve a particular problem.

List of Math Theorems

MidPoint Theorem	Remainder Theorem
Stewart’s Theorem	Inscribed Angle Theorem
Cyclic Quadrilateral Theorem	Ceva’s Theorem
Apollonius Theorem	Angle Bisector Theorem
Quadrilateral Theorem	Bayes Theorem
Binomial Theorem	Pythagoras Theorem