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What is the Division Formula?

Basic Math Formulas

Last Updated : 29 May, 2025

Mathematics is divided into various branches according to the way of calculation involved and the topics covered by them. All the branches have various formulas that are used for solving various mathematical problems. The branches include geometry, algebra, arithmetic, percentage, exponential, etc.

This article will provide you with all the basic formulas for different branches of mathematics, including trigonometry, geometry, algebra, probability, coordinate geometry, etc.

List of Basic Algebra Formulas

a² – b² = (a – b)(a + b)
(a + b)² = a² + 2ab + b²
a²+ b² = (a + b)² – 2ab
(a – b)² = a² – 2ab + b²
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
(a – b – c)² = a² + b² + c² – 2ab + 2bc – 2ca
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a – b)³ = a³ – 3a²b + 3ab² – b³
a³ – b³ = (a – b)(a² + ab + b²)
a³ + b³ = (a + b)(a² – ab + b²)
(a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴
(a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴
a⁴– b⁴ = (a – b)(a + b)(a² + b²)
(a^m)(aⁿ) = a^{m + n}
(ab)^m = a^mb^m
(a^m)ⁿ = a^mn

Various algebraic formulas that are widely used are given in the image below.

Algebraic Formulas — Basic Algebraic Formulas

Basic Geometry Formulas

We study Geometry formulas under two headings, that is,

2-D Formulas
3-D Formulas

2D Formulas

Rectangle

Perimeter of Rectangle = 2(l + b)
Area of Rectangle = l × b
Where
‘l’ is Length
‘b’ is Breadth

Square

Area of Square = a²
Perimeter of Square = 4a
Where
‘a’ is the length of sides of a Square

Triangle

Area of Triangle= 1/2 × b × h
Where
‘b’ is the base of the triangle and
‘h’ is the height of the triangle

Trapezoid

Area of Trapezoid = 1/2 × (b₁ + b₂) × h
Where
b₁ and b₂are the bases of Trapezoid
h is height of Trapezoid

Circle

Area of Circle = π × r²
Circumference of Circle = 2πr
Where
‘r’ is radius of a Circle

Various formulas used for 2-D objects are,

Formulas for 2D Shapes — Basic Area Formula for 2d Shape

3D Formulas

Cube

Surface Area of Cube = 6a²
Volume of Cube = a³
Where
‘a’ is the length of sides of Cube

Cylinder

Curved Surface Area of Cylinder = 2πrh
Total Surface Area of Cylinder = 2πr(r + h)
Volume of Cylinder = V = πr²h
Where
‘r’ is the radius of base of Cylinder
‘h’ is the height of Cylinder

Cone

Curved Surface Area of Cone = πrl
Total Surface Area of Cone = πr(r + l) = πr[r + √(h² + r²)]
Volume of Cone = V = 1/3× πr²h
where,
‘r’ is the Radius of base of Cone
h is the Height of the Cone

Sphere

Surface Area of a Sphere = S = 4πr²
Volume of a Sphere = V = 4/3 × πr³
Where,
r is the Radius of Sphere

Various formulas used for 3-D objects are,

Formulas for 3D Shapes

Basic Probability Formulas

Probability can simply be defined as the possibility of the occurrence of an event. It is expressed on a linear scale from 0 to 1. There are three types of probability: theoretical probability, experimental probability, and subjective probability.

P(A) = n(A)/n(S)
Where,
P(A) is the Probability of an Event.
n(A) is the Number of Favourable Outcomes
n(S) is the Total Number of Events

Basic Fraction Formulas

A fraction is a number expressed with integers in which the numerator is divided by the denominator. A fraction is basically the quotient of a division.

Addition of a whole number and a fraction:
\left( a + \frac{b}{c} \right) = \frac{(a \times c) + b}{c}
Addition of fractions with the same denominator:
\frac{a}{b} + \frac{d}{b} = \frac{a + d}{b}
Addition of fractions with different denominators:
\frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d}
Multiplication of fractions:
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
Division of fractions:
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Basic Percentage Formula

A percentage is a numerical value or ratio expressed as a fraction of 100. It is generally symbolized by the sign %.

Percentage = (Given Value/Total Value) × 100

Distance Formula

If the coordinates of points A are (x₁, y₁) and B are (x₂, y₂), the formula used to calculate the distance between these two points is discussed in the image below.

Distance Formula

Trigonometry Formulas

The six basic functions of Trigonometry are,

Sin Function
Cos Function
Tan Function
Cosec function
Sec Function
Cot Function

The three basic trigonometric functions formulas are,

Trigonometry Formulas

Basic Math Formulas Chart

All the general formulas in Maths are discussed below.

Perimeter	Square Rectangle	P = 4a P = 2(l + b)
Circumference	Circle	C = 2 (π) r
Area	Square Rectangle Triangle Trapezoid Circle	A = a² A = l × b A = ½(b × h) A = ((b₁ +b₂ ) × h) / 2 A = π × r ²
Surface Area	Cube Cylinder Cone Sphere	S = 6l² CSA = 2 × π × r × h CSA = π × r × l S = 4 × π × r ²
Volume	Cylinder Cone Sphere	V = πr ²h V =1/3 πr ²h V = 4/3 × π × r³
Algebraic Formula	Pythagorean theorem The slope-intercept form of the equation of a line Distance formula Total cost Quadratic formula Laws of Exponents Fractional Exponents	a² + b² = c² y = mx + c d = st Total cost = (number of units) × (price per unit) x = [-b ± √(b² – 4ac)] /2a a^mx b ^m= (a x b)^m; a^mx a ⁿ= (a)^m+n a^1/2 = √a
Trigonometric Formulas	Sine Function Cosine Function Tangent Function	Sin x = Opposite Side/ Hypotenuse Cos x = Adjacent Side/ Hypotenuse Tan x = Opposite Side/ Adjacent Side
Interest Formulas	Simple Interest Compound Interest	S.I = P × R × T/100 C.I =P (1 + R/100 )ⁿ- P

Pythagoras Theorem	a² + b² = c²
Distance Formula	d = √[(x₂ – x₁)² +(y₂ – y₁)²]
The slope of a line	m = y₂– y₁ / x₂ – x₁
Mid-Point Formula	M = [(x₁ + x₂)/ 2 , (y₁ + y₂ )/ 2]

Math Formulas List

Here is the list of the most commonly used maths formulas :

2cosacosb Formula	Midpoint Formula
30-60-90 Formulas	Monthly Compound Interest Formula
Absolute Value Formula	Multiple Angle Formulas
Addition Formula	N Choose K Formula
Algebra Formulas	Natural Log Formula
Algebraic Expressions Formula	Newton’s Method Formula
Angle Formula	Normal Distribution Formula
Annulus Formula	Octagon Formula
Anova Formula	Orthocenter Formula
Antiderivative Formula	Parabola Formula
Arc Length Formula	Parallel Line Formula
Arccot Formula	Parallelogram Formula
Arctan Formula	Partial Differential Equations
Area Formula for Quadrilaterals	Pearson Correlation Formula
Area Formulas	Percent Composition Formula
Area of a Circle Formula	Percent Decrease Formula
Area of a Pentagon Formula	Percent Difference Formula
Area Of A Sector Of A Circle Formula	Percent Error Formula
Area of a Square Formula	Percentage Change Formula
Area of a Trapezoid Formula	Percentage Decrease Formula
Area Of An Octagon Formula	Percentage Formula
Area Of an Isosceles Triangle	Percentage Increase Formula
Area of a Regular Polygon Formula	Percentage Yield Formula
Area Under the Curve Formula	Percentile Formula
Arithmetic Mean Formula	Perfect Square Formula
Arithmetic Sequence Explicit Formula	Perfect Square Trinomial Formula
Arithmetic Sequence Formula	Perimeter Formulas
Arithmetic Sequence Recursive Formula	Perimeter of a Kite Formula
Associative Property Formula	Perimeter of a Parallelogram Formula
Asymptote Formula	Perimeter of a Square Formula
Average Deviation Formula	Perimeter of a Trapezoid Formula
Average Rate of Change Formula	Perimeter of a Triangle Formula
Axis of Symmetry Formula	Perimeter of a Hexagon Formula
Basic Math Formulas	Perimeter of a Rectangle
Bayes Theorem Formula	Perimeter of a Rhombus Formula
Binary Formula	Periodic Formulas
Binary to Decimal Formula	Permutation Formula
Binomial Distribution Formula	Permutations And Combinations Formulas
Binomial Expansion Formula	Perpendicular Line Formula
Binomial Probability Formula	Pi Formulas
Binomial Theorem Formula	Platonic Solids Formula
Calculus Formulas	Point Gradient Formula
Celsius Formula	Point of Intersection Formula
Central Angle of a Circle Formula	Point Slope Form Formula
Central Limit Theorem Formula	Poisson Distribution Formula
Centroid of a Trapezoid Formula	Polygon Formula
Chain Rule Formula	Polynomial Formula
Change of Base Formula	Population Mean Formula
Chi-Square Formula	Prime Number Formula
Circle Graph Formula	Prism Formula
Circumference Formula	Probability Distribution Formula
Coefficient of Determination Formula	Probability Formulas
Coefficient of Variation Formula	Product Rule Formula
Cofactor Formula	Product to Sum Formula
Cofunction Formulas	Profit Formula
Coin Toss Probability Formula	Profit Margin Formula
Combination Formula	Proportion Formula
Commutative Property Formula	Pyramid Formula
Completing the Square Formula	Pythagorean Theorem Formula
Complex Number Division Formula	Pythagorean Triples Formula
Complex Number Formula	Quadratic Function Formula
Complex Number Power Formula	Quadratic Interpolation Formula
Compound Interest Formula	Quadrilateral Formulas
Conditional Probability Formula	Quartile Formula
Confidence Interval Formula	Quotient Rule Formula
Consecutive Integers Formula	R Squared Formula
Correlation Coefficient Formula	Radians to Degrees Formula
Cos Double Angle Formula	Radical Formula
Cos Inverse Formula	Radius Formula
Cos Square theta Formula	Radius of Curvature Formula
Cos Theta Formula	Rate of Change Formula
Cosec Cot Formula	RATIO ANALYSIS FORMULA
Cosecant Formula	Ratio Formula
Cosine Formula	Rectangle Formula
Cot Half Angle Formula	Rectangular Parallelepiped Formula
Cotangent Formula	Recursive Formula
Cot-Tan formula	Reduction Formula
Covariance Formula	Regression Sum of Squares Formula
Covariance Matrix Formula	Regular Hexagon Formula
CP Formula	Regular Square Pyramid Formula
Cpk Formula	Regular Tetrahedron Formula
Cross Product Formula	RELATIVE FREQUENCY FORMULA
Cube Formula	Relative Standard Deviation Formula
Cube Root Formula	Resistors in Parallel Formula
Cubic Equation Formula	RESULTANT VECTOR FORMULA
Daily Compound Interest Formula	Retention Factor Formula
De Moivre Formula	Revenue Formula
Decay Formula	Rhombus Formula
Decimal to Binary Formula	Riemann Sum Formula
Decimal to Fraction Formula	Right Angle Formula
Definite Integral Formula	Right Triangle Formula
Degree and Radian Measure Formula	Root Mean Square Formula
Degrees of Freedom Formula	Rotation Formula
Derivative Formula	Sample Mean Formula
Determinant Formula	Sample Size Formula
Diagonal Formula	Sampling Error Formula
Diagonal of a Cube Formula	Scalene Triangle Formula
Diagonal Of A Polygon Formula	Scientific Notation Formula
Diagonal Of A Square Formula	Secant Formula
Diagonal of a Parallelogram Formula	Secant Square x Formula
Diameter Formula	Selling Price Formula
Difference of Cubes Formula	Sum of an Arithmetic Sequence Formula
Difference of Squares Formula	Sequences and Series Formulas
Difference Quotient Formula	Series Formula
Differential Equations formula	Set Formulas
Differentiation and Integration Formula	SIDE ANGLE SIDE FORMULA
Direct Variation Formula	Signal-to-Noise Ratio Formula
Direction of a Vector Formula	Simple Interest Formula
Discount Formula	Simpson’s Rule Formula
Discriminant Formula	Sin 30 Formula
Distributive Property Formula	Sin Cos Formulas
Division Formula	Sin squared x formula
Dot Product Formula	Sin Tan formula
Double Angle Formulas	Sin Theta Formula
Double Time Formula	Sin to Cos Formula
Effect Size Formula	Sin2x Formula
Ellipse Formula	Sine Cosine Tangent Formula
Empirical Probability Formula	Sine Formula
Equation Formula	Sine Half Angle Formula
Equation of a Circle Formula	Sine Rule Formula
Equation of a Line Formula	Skewness Formula
Equilateral Triangle Formula	Slant Asymptote Formula
Euler Maclaurin Formula	Slope Formula
Euler’s Formula	Slope Intercept Form Formula
Exponential Distribution Formula	Slope of the Secant Line Formula
Exponential Equation Formula	Sphere Formula
Exponential Formula	Spherical Cap Volume Formulas
Exponential Function Formula	Spherical Sector Formula
Exponential Growth Formula	Spherical Segment Formula
Exponents Formula	Spherical Wedge and Spherical Lune Formula
F Test Formula	Square Footage Formula
Factorial Formula	Square Formula
Factoring Formulas	Square Root Formula
Factoring Trinomials Formula	Square Root Property Formula
Fahrenheit to Celsius Formula	Standard Deviation Formula
Fibonacci Formula	Standard Error Formula
Foil Formula	Standard Form Formula
Fourier Series Formula	Statistical Significance Formula
Frequency Distribution Formula	Statistics Formulas
Frustum of a Regular Pyramid Formula	Stirling Formula
Frustum of a Right Circular Cone Formula	Subtraction Formulas
Function Formulas	Sum of an Arithmetic Sequence Formula
Function Notation Formula	Sum of Cubes Formula
Gaussian Distribution Formula	Sum of Squares Formula
Geometric Distribution Formula	SUMMATION FORMULA
Geometric Mean Formula	Surface Area Formulas
Geometric Sequence Formula	Surface Area of a Cone Formula
Geometric Series Formula	Surface Area of a Cube Formula
Geometry Formulas	Surface Area of a Cylinder Formula
Graph Formula	Surface Area of a Prism Formula
Graphs of Trigonometric Functions Formula	Surface Area of a Pyramid Formula
Great Circle Formula	Surface Area of a Rectangle Formula
Gross Profit Formula	Surface Area of a Rectangular Prism Formula
Half Angle Formula	Surface Area of a Sphere Formula
Half-LifeThe slope-intercept Formula	Surface Area of a Square Pyramid Formula
HARMONIC MEAN FORMULA	Surface Area of a Triangular Prism Formula
Height of a Parallelogram Formula	Surface Area of a Circle Formula
Hexagon Formula	Surface Area of a Hemisphere formula
Hexagonal Prism Formula	Tan Theta formula
HYPERBOLA FORMULA	Tan2x Formula
Hyperbolic Function Formula	Tangent 3 Theta Formula
Hypergeometric Distribution Formula	Tangent Addition Formula
Hypothesis Testing Formula	Tangent Circle Formula
Implicit Differentiation Formula	Tangent Formula
Infinite Geometric Series Formula	Tangent Line Formula
Infinite Series Formula	Tangential Quadrilateral Formula
Integral Calculus Formula	Taylor Series Formula
Integral Formulas	T-Distribution Formula
Integration By Parts Formula	Temperature Conversion Formula
Integration by Substitution Formula	The Distance Formula
Interest Rate Formula	Probability Class 10 Important Formulas
Interpolation Formula	Trajectory Formula
Interquartile Range Formula	Trapezoid formula
Inverse Function Formula	Trapezoidal Rule Formula
Inverse Hyperbolic Functions Formula	Triangle Formula
Inverse Matrix Formula	Triangular Pyramid Formula
Inverse Tangent Formula	Trigonometric Function Formulas
Inverse Trigonometric Formulas	T-Test Formula
Inverse Variation Formula	U Substitution Formula
Isosceles Trapezoid Formula	Uniform Distribution Formula
Isosceles Triangle Perimeter Formula	Unit Circle Formula
Lagrange Interpolation Formula	Unit Rate Formula
Lateral Area Formula	Unit Vector Formula
Law of Cosines Formula	Variance Formula
Law Of Sines And Cosines Formula	Vector Formulas
Law of Sines Formula	Vector Projection Formula
Law of tangent formula	Vertex of a Parabola Formula
LCM Formula	Vieta’s Formula
Limit Formula	Volume Charge Density Formula
Line of Best Fit Formula	Volume Formulas
Linear Approximation Formula	Volume of a Cone Formula
Linear Correlation Coefficient Formula	Volume of a Cube Formula
Linear Equations Formula	Volume Of A Cylinder Formula
Linear Function Formula	Volume of a Pyramid Formula
Linear Interpolation Formula	Volume of a Rectangular Prism Formula
Linear Regression Formula	Volume Of A Sphere Formula
Loan Balance Formula	Volume of a Square Pyramid Formula
Logarithm Formula	Volume of a Triangular Prism Formula
Maclaurin Series Formula	Volume of an Ellipsoid Formula
Magnitude of a Vector Formula	Volume of Parallelepiped Formula
Margin of Error Formula	Weighted Average Formula
Matrix Formula	Weighted Mean Formula
Mean Absolute Deviation Formula	X and Y Intercept Formula
Mean Deviation Formula	X Intercept Formula
Mean, Median, Mode Formula	Y Intercept Formula
Mean Value Theorem Formula	Z Score Formula

Solved Question on Basic Math Formulas

Question 1: Determine the probability of drawing an ace from a standard deck of cards.

Solution:

Given:
Total number of outcomes n(S) = 52
Number of favorable outcomes n(A) = 4 aces
Now,
P(A) = n(A)/n(S)
= 4/52
= 1/13
Hence, The probability of drawing an ace is 1/13

Question 2: Simplify 3/(x - 1) + 1/(x - 1) = 2/x

Solution:

3/(x-1) + 1/(x - 1) = 2/x
4/(x - 1) = 2/x
2x = x - 1
x = -1

Question 3: If x + 1/x = 3. Find the value of x²+ 1/x².

Solution:

Given,
x + 1/x = 3
Squaring both side
x + 1/x)²= (3)²
x²+ 2 × x × 1/x + (1/x)² = 9
x²+ 1/x²+ 2 = 9
x²+ 1/x² = 7

Question 4: If the radius of a circle is 21cm. Find the area of the given circle.

Solution:

Given:
Radius of Circle = 21cm
We have,
Area of the circle (A) = πr²
A = 22/7 × 21 × 21
A = 1386cm²
Hence, the area of the given circle is 1386cm²

Question 5: Find the area of a triangle having a base of 100cm and a height of 20cm.

Solution:

Given:
Base of the triangle = 100cm
Height of the triangle = 20cm
We have,
Area(A) = 1/2 × b × h
= 1/2 × 100 × 20
= 1000cm²

Question 6: Punam has 4/5 parts of the field, among which she uses 2/5 parts for farming. How many parts of the farm are left for other purposes?

Solution:

Given,
Total Fraction of Land = 4/5
Total Fraction used for Farming = 2/5.
Now,
Land Left = 4/5 - 2/5
= 2/5
Hence, 2/5 part of the field is left for other purposes.

Question 7: What will be 20% of 240 kg?

Solution:

Given,
= 20% of 240kg
= 20/100 × 240
= 48 kg
Hence, 20% of 240 kg will be 48 kg.

What is the Division Formula?

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Basic Math Formulas

Mathematics is divided into various branches according to the way of calculation involved and the topics covered by them. All the branches have various formulas that are used for solving various mathematical problems. The branches include geometry, algebra, arithmetic, percentage, exponential, etc.T