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Basic Math Formulas

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Mathematics comes with an endless scope of research and study in the domain of numbers and their operations. Every branch of mathematics has something different to deal with. The branches explore new methods and standards of calculation for making daily trade even more convenient. 

Mathematics is divided into various branches as per the way of calculation involved and the topics covered by them. The branches include geometry, algebra, arithmetic, percentage, exponential, etc. Mathematics also provides standard-derived formulas to make the operations or calculations accurate. The given article provides all the basic formulas present in mathematics under its different branches or fields.

At GeeksforGeeks, the formulas have been created in such a manner that you can understand what the questions intend to ask and then implement the formula to solve the questions

Basic Math Formulae

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 of mathematics included 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.


Arithmetic is the oldest method of calculation known now. The word arithmetic is derived from the Greek word ‘Arithmos’ which literally means numbers. Brahmagupta the Indian mathematician is known as the ‘father of arithmetic‘. And, the Fundamental theory of number theory was proposed by Carl Friedrich Gauss in 1801.

The basic operations involved in arithmetic are addition, subtraction, multiplication, and division

Arithmetic formula

Arithmetic mean (average) = Sum of values/Number of values.


Algebra is an elementary subject of mathematics that deals with the study of the evaluation of numbers and symbols. The algebraic operations are carried out to determine the unknown values which are expressed by letters. Algebraic equations are the expressions formed by the combination of variables, constants, factors, and coefficients of variables.

Basic Algebra Formula

  • 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



Geometry is a part of mathematics that is concerned with the study of shapes, sizes, parameters, measurements, properties, and dimensions. There are generally three types of geometry. They are Euclidean geometry, Spherical geometry, and Hyperbolic geometry.

Basic Geometry Formula

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

l’ is Length
b’ is Breadth

  • Square
  • Area of Square = a2
  • Perimeter of Square = 4a

a’ is the length of sides of a Square

  • Triangle
  • Area of Triangle= 1/2 × b × h

b’ is the base of the triangle and 
h’ is the height of the triangle

  • Trapezoid
  • Area of Trapezoid = 1/2 × (b1 + b2) × h

b1 and b2 are the bases of Trapezoid
h is height of Trapezoid

  • Circle
  • Area of Circle = π × r2
  • Circumference of Circle = 2πr

r’ is radius of a Circle

Various formulas used for 2-D objects are,

2D Shapes


3-D Formulas

  • Cube
  • Surface Area of Cube = 6a2
  • Volume of Cube = a3

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

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

r’ is the Radius of base of Cone
h is the Height of the Cone

  • Sphere
  1. Surface Area of a Sphere = S = 4πr2
  2. Volume of a Sphere = V = 4/3 × πr3

r is the Radius of Sphere

Various formulas used for 3-D objects are,

3D Shapes



Probability is the mathematical term used to determine the chance of occurring a particular event. 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 theoretical probability, experimental probability, and subjective probability.

Basic Probability Formula

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

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


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. 

Basic Fractions Formula

  • (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


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

Basic Percentage Formula

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,



List of Math Formulas

The list of most used maths formulas is,

2cosacosb Formula Midpoint Formula
30-60-90 FormulasMonthly Compound Interest Formula
Absolute Value FormulaMultiple Angle Formulas
Addition FormulaN Choose K Formula
Algebra FormulasNatural Log Formula
Algebraic Expressions FormulaNewton’s Method Formula
Angle FormulaNormal Distribution Formula
Annulus FormulaOctagon Formula
Anova FormulaOrthocenter Formula
Antiderivative FormulaParabola Formula
Arc Length FormulaParallel Line Formula
Arccot FormulaParallelogram Formula
Arctan FormulaPartial Differential Equations
Area Formula for QuadrilateralsPearson Correlation Formula
Area FormulasPercent Composition Formula
Area of a Circle FormulaPercent Decrease Formula
Area of a Pentagon FormulaPercent Difference Formula
Area Of A Sector Of A Circle FormulaPercent Error Formula
Area of a Square FormulaPercentage Change Formula
Area of a Trapezoid FormulaPercentage Decrease Formula
Area Of An Octagon FormulaPercentage Formula
Area Of Isosceles TrianglePercentage Increase Formula
Area of Regular Polygon FormulaPercentage Yield Formula
Area Under the Curve FormulaPercentile Formula
Arithmetic Mean FormulaPerfect Square Formula
Arithmetic Sequence Explicit FormulaPerfect Square Trinomial Formula
Arithmetic Sequence FormulaPerimeter Formulas
Arithmetic Sequence Recursive FormulaPerimeter of a Kite Formula
Associative Property FormulaPerimeter of a Parallelogram Formula
Asymptote FormulaPerimeter of a Square Formula
Average Deviation FormulaPerimeter of a Trapezoid Formula
Average Rate of Change FormulaPerimeter of a Triangle Formula
Axis of Symmetry FormulaPerimeter of Hexagon Formula
Basic Math FormulasPerimeter of Rectangle
Bayes Theorem FormulaPerimeter of Rhombus Formula
Binary FormulaPeriodic Formulas
Binary to Decimal FormulaPermutation Formula
Binomial Distribution FormulaPermutations And Combinations Formulas
Binomial Expansion FormulaPerpendicular Line Formula
Binomial Probability FormulaPi Formulas
Binomial Theorem FormulaPlatonic Solids Formula
Calculus FormulasPoint Gradient Formula
Celsius FormulaPoint of Intersection Formula
Central Angle of a Circle FormulaPoint Slope Form Formula
Central Limit Theorem FormulaPoisson Distribution Formula
Centroid of a Trapezoid FormulaPolygon Formula
Chain Rule FormulaPolynomial Formula
Change of Base FormulaPopulation Mean Formula
Chi-Square FormulaPrime Number Formula
Circle Graph FormulaPrism Formula
Circumference FormulaProbability Distribution Formula
Coefficient of Determination FormulaProbability Formulas
Coefficient of Variation FormulaProduct Rule Formula
Cofactor FormulaProduct to Sum Formula
Cofunction FormulasProfit Formula
Coin Toss Probability FormulaProfit Margin Formula
Combination FormulaProportion Formula
Commutative Property FormulaPyramid Formula
Completing the Square FormulaPythagorean Theorem Formula
Complex Number Division FormulaPythagorean Triples Formula
Complex Number FormulaQuadratic Function Formula
Complex Number Power FormulaQuadratic Interpolation Formula
Compound Interest FormulaQuadrilateral Formulas
Conditional Probability FormulaQuartile Formula
Confidence Interval FormulaQuotient Rule Formula
Consecutive Integers FormulaR Squared Formula
Correlation Coefficient FormulaRadians to Degrees Formula
Cos Double Angle FormulaRadical Formula
Cos Inverse FormulaRadius Formula
Cos Square theta FormulaRadius of Curvature Formula
Cos Theta FormulaRate of Change Formula
Cosecant FormulaRatio Formula
Cosine FormulaRectangle Formula
Cot Half Angle FormulaRectangular Parallelepiped Formula
Cotangent FormulaRecursive Formula
Cot-Tan formulaReduction Formula
Covariance FormulaRegression Sum of Squares Formula
Covariance Matrix FormulaRegular Hexagon Formula
CP FormulaRegular Square Pyramid Formula
Cpk FormulaRegular Tetrahedron Formula
Cube FormulaRelative Standard Deviation Formula
Cube Root FormulaResistors in Parallel Formula
Daily Compound Interest FormulaRetention Factor Formula
De Moivre FormulaRevenue Formula
Decay FormulaRhombus Formula
Decimal to Binary FormulaRiemann Sum Formula
Decimal to fraction FormulaRight Angle Formula
Definite Integral FormulaRight Triangle Formula
Degree and Radian Measure FormulaRoot Mean Square Formula
Degrees of Freedom FormulaRotation Formula
Derivative FormulaSample Mean Formula
Determinant FormulaSample Size Formula
Diagonal FormulaSampling Error Formula
Diagonal of a Cube FormulaScalene Triangle Formula
Diagonal Of A Polygon FormulaScientific Notation Formula
Diagonal Of A Square FormulaSecant Formula
Diagonal of Parallelogram FormulaSecant Square x Formula
Diameter FormulaSelling Price Formula
Difference of Cubes FormulaSequence Formula
Difference of Squares FormulaSequences and Series Formulas
Difference Quotient FormulaSeries Formula
Differential Equations formulaSet Formulas
Differentiation and Integration FormulaSIDE ANGLE SIDE FORMULA
Direct Variation FormulaSignal-to-Noise Ratio Formula
Direction of a Vector FormulaSimple Interest Formula
Discount FormulaSimpson’s Rule Formula
Discriminant FormulaSin 30 Formula
Distributive Property FormulaSin Cos Formulas
Division FormulaSin squared x formula
Dot Product FormulaSin Tan formula
Double Angle FormulasSin Theta Formula
Double Time FormulaSin to Cos Formula
Effect Size FormulaSin2x Formula
Ellipse FormulaSine Cosine Tangent Formula
Empirical Probability FormulaSine Formula
Equation FormulaSine Half Angle Formula
Equation of a Circle FormulaSine Rule Formula
Equation of a Line FormulaSkewness Formula
Equilateral Triangle FormulaSlant Asymptote Formula
Euler Maclaurin FormulaSlope Formula
Euler’s FormulaSlope Intercept Form Formula
Exponential Distribution FormulaSlope of the Secant Line Formula
Exponential Equation FormulaSphere formula
Exponential FormulaSpherical Cap Volume Formulas
Exponential Function FormulaSpherical Sector Formula
Exponential Growth FormulaSpherical Segment Formula
Exponents FormulaSpherical Wedge and Spherical Lune Formula
F Test FormulaSquare Footage Formula
Factorial FormulaSquare Formula
Factoring FormulasSquare Root Formula
Factoring Trinomials FormulaSquare Root Property Formula
Fahrenheit to Celsius FormulaStandard Deviation Formula
Fibonacci FormulaStandard Error Formula
Foil FormulaStandard Form Formula
Fourier Series FormulaStatistical Significance Formula
Frequency Distribution FormulaStatistics Formulas
Frustum of a Regular Pyramid FormulaStirling Formula
Frustum of a Right Circular Cone FormulaSubtraction Formulas
Function FormulasSum of Arithmetic Sequence Formula
Function Notation FormulaSum of Cubes Formula
Gaussian Distribution FormulaSum of Squares Formula
Geometric Distribution FormulaSUMMATION FORMULA
Geometric Mean FormulaSurface Area Formulas
Geometric Sequence FormulaSurface Area of a Cone Formula
Geometric Series FormulaSurface Area of a Cube Formula
Geometry FormulasSurface Area of a Cylinder Formula
Graph FormulaSurface Area of a Prism Formula
Graphs of Trigonometric Functions FormulaSurface Area of a Pyramid Formula
Great Circle FormulaSurface Area of a Rectangle Formula
Gross Profit FormulaSurface Area of a Rectangular Prism Formula
Half Angle FormulaSurface Area of a Sphere Formula
Half-LifeThe slope-intercept FormulaSurface Area of a Square Pyramid Formula
HARMONIC MEAN FORMULASurface Area of a Triangular Prism Formula
Height of a Parallelogram FormulaSurface Area of Circle Formula
Hexagon FormulaSurface Area of Hemisphere formula
Hexagonal Prism FormulaTan Theta formula
Hyperbolic Function FormulaTangent 3 Theta Formula
Hypergeometric Distribution FormulaTangent Addition Formula
Hypothesis Testing FormulaTangent Circle Formula
Implicit Differentiation FormulaTangent Formula
Infinite Geometric Series FormulaTangent Line Formula
Infinite Series FormulaTangential Quadrilateral Formula
Integral Calculus FormulaTaylor Series Formula
Integral FormulasT-Distribution Formula
Integration By Parts FormulaTemperature Conversion Formula
Integration by Substitution FormulaThe Distance Formula
Interest FormulaThe probability Distribution Function Formula
Interpolation FormulaTrajectory Formula
Interquartile Range FormulaTrapezoid formula
Inverse Function FormulaTrapezoidal Rule Formula
Inverse Hyperbolic Functions FormulaTriangle Formula
Inverse Matrix FormulaTriangular Pyramid Formula
Inverse Tangent FormulaTrigonometric Function Formulas
Inverse Trigonometric FormulasT-Test Formula
Inverse Variation FormulaU Substitution Formula
Isosceles Trapezoid FormulaUniform Distribution Formula
Isosceles Triangle Perimeter FormulaUnit Circle Formula
Lagrange Interpolation FormulaUnit Rate Formula
Lateral Area FormulaUnit Vector Formula
Law of Cosines FormulaVariance Formula
Law Of Sines And Cosines FormulaVector Formulas
Law of Sines FormulaVector Projection Formula
Law of tangent formulaVertex of a Parabola Formula
LCM FormulaVieta’s Formula
Limit FormulaVolume Charge Density Formula
Line of Best Fit FormulaVolume Formulas
Linear Approximation FormulaVolume of a Cone Formula
Linear Correlation Coefficient FormulaVolume of a Cube Formula
Linear Equations FormulaVolume Of A Cylinder Formula
Linear Function FormulaVolume of a Pyramid Formula
Linear Interpolation FormulaVolume of a Rectangular Prism Formula
Linear Regression FormulaVolume Of A Sphere Formula
Loan Balance FormulaVolume of a Square Pyramid Formula
Logarithm FormulaVolume of a Triangular Prism Formula
Maclaurin Series FormulaVolume of an Ellipsoid Formula
Magnitude of a Vector FormulaVolume of Parallelepiped Formula
Margin of Error FormulaWeighted Average Formula
Matrix FormulaWeighted Mean Formula
Mean Absolute Deviation FormulaX and Y Intercept Formula
Mean Deviation FormulaX Intercept Formula
Mean Median Mode FormulaY Intercept Formula
Mean Value Theorem FormulaZ Score Formula

Maths Formula Sheet

All the general formulas used in Mathematics are discussed below.

  1. Square
  2. Rectangle
  1. P = 4a
  2. P = 2(l + b)
  1. Circle
  1. C = 2 (π) r
  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
  1. Cylinder
  2. Cone
  3. Sphere
  1. V = πr 2h
  2. V =1/3 πr 2h
  3. V = 4/3 × π × r
Pythagoras Theorema2 + b2 = c2
Distance Formulad = √[(x2 – x1)2 +(y2 – y1)2]
Slope of a linem = y2 – y1 / x2 – x1
Mid-Point FormulaM = [(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 

Solved Examples on Math Formulas

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



Total number of favorable outcomes n(S) = 52

Number of face cards  in the deck = 12

Number of favorable outcomes n(A) = 12


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


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.



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.



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.



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?



Total Fraction of Land = 4/5

Total Fraction used for Farming = 2/5.


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?



= 20% of 240kg

= 20/100 × 240

= 48 kg

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

FAQs on Math Formulas

Q1: 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 

Q2: What is the formula of a3 + b3?


a3 + b3 = (a + b) (a2 – ab + b2)

Q3: Where are these 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.

Q4: 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. 

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Last Updated : 03 May, 2023
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