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Basic Math Formulas

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Mathematics is divided into various branches as per the way of calculation involved and the topics covered by them all the branches have various formulas that are used for solving various mathematics 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.

Basic Math Formulas

A formula is a mathematical expression or definite rule that is derived from the relation between two or more quantities and the derived final product is expressed in symbols. The formulas in math include numbers known as constants, letters that represent unknown values and are known as variables, mathematical symbols known as signs, and exponential powers in some cases.

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)
  • (am)(an) = am + n
  • (ab)m = ambm
  • (am)n = amn

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

Algebraic Formulas

 

Basic Geometry Formulas

We study Geometry formulas under two headings that are,

  • 2-D Formulas
  • 3-D Formulas

2 D 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 b2 are the bases of Trapezoid
h is height of Trapezoid

  • Circle
  • Area of Circle = Ï€ × r2
  • Circumference of Circle = 2Ï€r

Where 
‘r’ is radius of a Circle

Various formulas used for 2-D objects are,

Formulas for 2D Shapes

 

3 D 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 = 2Ï€rh
  • Total Surface Area of Cylinder = 2Ï€r(r + h)
  • Volume of Cylinder = V = Ï€r2h

Where 
‘r’ is the radius of base of Cylinder
‘h’ is the height of Cylinder

  • Cone
  • Curved Surface Area of Cone = Ï€rl
  • Total Surface Area of Cone = Ï€r(r + l) = Ï€r[r + √(h2 + r2)]
  • Volume of Cone = V = 1/3× Ï€r2h

where, 
‘r’ is the Radius of base of Cone
h is the Height of the Cone

  • Sphere
  1. Surface Area of a Sphere = S = 4Ï€r2
  2. 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 Formula

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

  • (a + b/c) = [(a × c) + b]/c
  • (a/b + d/b) = (a + d)/b
  • (a/b + c/d) = (a × d + b × c)/(b × d)
  • a/b × c/d = ac/bd
  • (a/b)/(c/d) = a/b × 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 coordinate of the points A is (x1, y1) and B is (x2, y2) the formula used to calculate the distance between these two points is discussed in the image below.

Distance Formula

Trigonometry Formulas

There are 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

Maths Formula Sheet

All the general formulas in Maths are discussed below.

Perimeter
  1. Square
  2. Rectangle
  1. P = 4a
  2. P = 2(l + b)
Circumference
  1. Circle
  1. C = 2 (Ï€) r
Area
  1. Square
  2. Rectangle
  3. Triangle
  4. Trapezoid
  5. Circle
  1. A = a2
  2. A = l × b
  3. A = ½(b × h)
  4. A = ((b1 +b2 ) × h) / 2
  5. A = π × r 2
Surface Area
  1. Cube
  2. Cylinder
  3. Cone
  4. Sphere
  1. S = 6l2
  2. CSA = 2 × π × r × h
  3. CSA = π × r × l
  4. S = 4 × π × r 2
Volume
  1. Cylinder
  2. Cone
  3. Sphere
  1. V = πr 2h
  2. V =1/3 πr 2h
  3. V = 4/3 × π × r3 
Pythagoras Theorem a2 + b2 = c2
Distance Formula d = √[(x2 – x1)2 +(y2 – y1)2]
Slope of a line m = y2 – y1 / x2 – x1
Mid-Point Formula M = [(x1 + x2 )/ 2 , (y1 + y2 )/ 2]
Algebraic Formula
  1. Pythagorean theorem
  2. Slope-intercept form of the equation of a line
  3. Distance formula
  4. Total cost
  5. Quadratic formula
  6. Laws of Exponents
  7. Fractional Exponents
  1. a2 + b2 = c2
  2. y = mx + c
  3. d = st
  4. Total cost = (number of units) × (price per unit)
  5. x = [-b ± √(b2 – 4ac)] /2a
  6. am x b m = (a x b)m; am x a n = (a)m+n
  7. a1/2 = √a
Trigonometric Formulas
  1. Sine Function
  2. Cosine Function
  3. Tangent Function
  1. Sin x = Opposite Side/ Hypotenuse
  2. Cos x = Adjacent Side/ Hypotenuse
  3. Tan x = Opposite Side/ Adjacent Side
Interest Formulas
  1. Simple Interest
  2. Compound Interest
  1. S.I = P × R × T/100
  2. C.I =P (1 + R/100 )n – P 

List of Math Formulas

Here is the list of most 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 Isosceles Triangle Percentage Increase Formula
Area of 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 Hexagon Formula
Basic Math Formulas Perimeter of Rectangle
Bayes Theorem Formula Perimeter of 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 Parallelogram Formula Secant Square x Formula
Diameter Formula Selling Price Formula
Difference of Cubes Formula 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 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 Circle Formula
Hexagon Formula Surface Area of 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 Formula The probability Distribution Function Formula
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 Examples on Math Formulas

Example 1: Determine the probability to get an ace from a card taken from a deck.

Solution:

Given:

Total number of favorable outcomes n(S) = 52

Number of face cards  in the deck = 12

Number of favorable outcomes n(A) = 12

Now,

P(A) = n(A)/n(S)

= 12/52

= 3/13

Hence, the probability to get a face card from a card deck is 3/13.

Example 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

Example 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

Example 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

Example 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 × 10 × 20

              = 1000cm2

Example 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.

Example 7: What will be the 20% of 240 kg?

Solution:

Given,

= 20% of 240kg

= 20/100 × 240

= 48 kg

Hence, 20% of 240 kg will be 48 kg.

FAQs on Math Formulas

What are some Basic Math Formulas?

Some basic Math formulas are :

  1. Perimeter of square = 4×a
  2. Perimeter of rectangle = 2 (l + b)
  3. Circumference of circle = 2 (pi) r
  4. Area of square = a2
  5. Area of rectangle = l × b 

What is the formula of a3 + b3?

a3 + b3 = (a + b) (a2 – ab + b2)

Where are Math formulas used?

These Math formulas can be used to solve the problems of various important topics such as algebra, mensuration, calculus, trigonometry, probability, etc.

Why are Math Formulas important?

Math formulas are important because they help us to solve complex problems based on conditional probability, algebra, mensuration, calculus, permutation and combination, geometry in less time. 



Last Updated : 17 Feb, 2024
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