Basic Math Formulas (original) (raw)

Last Updated : 25 Sep, 2025

Mathematics is built on formulas that simplify problem-solving and help in quick calculations. Each branch—algebra, geometry, mensuration, trigonometry, probability, etc.—has its own set of formulas that are used frequently in academics, competitive exams, and practical life.

**Algebra Formulas

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

Basic Algebraic Formulas

Some of the formulas are:

1. a2 – b2 = (a – b)(a + b)
2. (a + b)2 = a2 + 2ab + b2
3. a2 + b2 = (a + b)2 – 2ab
4. (a – b)2 = a2 – 2ab + b2
5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
6. (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
7. (a + b)3 = a3 + 3a2b + 3ab2 + b3
8. (a – b)3 = a3 – 3a2b + 3ab2 – b3
9. a3 – b3 = (a – b)(a2 + ab + b2)
10. a3 + b3 = (a + b)(a2 – ab + b2)
11. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
12. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
13. a4– b4 = (a – b)(a + b)(a2 + b2)
14. (am)(an) = am + n
15. (ab)m = ambm
16. (am)n = amn

**➢Also check: List of all Algebra formulas

**Mensuration Formulas

Mensuration is the study of areas and volumes of 2D and 3D shapes using mathematical formulas.

2D Shapes

Various formulas used for 2-D objects are,

Basic Area Formula for 2d Shape

**Rectangle

• Perimeter of Rectangle = 2(l + b)
• Area of Rectangle = l × b

**Square

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

**Triangle

• Area of Triangle= 1/2 × b × h

**Trapezoid

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

**Circle

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

3D Formulas

Various formulas used for 3-D objects are,

**Cube

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

**Cylinder

• Curved Surface Area of Cylinder = 2πrh
• Total Surface Area of Cylinder = 2πr(r + h)
• Volume of Cylinder = V = πr2h

**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

**Sphere

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

**➢Also check: List of Mensuration Formulas

**Probability Formula

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

Where:

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

**➢Also check: Important Probability formulas

**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}

**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

**➢Also check: Percentage formulas and tricks

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:

Trigonometry Formulas

The six basic functions of Trigonometry are:

**➢Also check: List of All Trigonometric Identities