Basic Math Formulas

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:

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. (a^m)(aⁿ) = a^{m + n}
15. (ab)^m = a^mb^m
16. (a^m)ⁿ = a^mn

➢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,

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