CBSE Class 6 to 12 Maths Formulas  Important Math Formulas
Math formulas are really helpful for students when dealing with tricky math problems. They make it easier and faster to find solutions. By using basic math formulas, students can tackle complex problems using different methods. Getting good marks in math is achievable with consistent hard work and smart study strategies. The key is to carefully read the problem, figure out what it's asking, and then find the right math formulas for the solution.
For those preparing for competitive exams, having all the important math formulas in one place can be useful for better understanding the subject. Our expert teachers have compiled formulas for different classes (6, 7, 8, 9, 10, 11, and 12) according to the CBSE syllabus. To solve math problems easily, students should learn and remember basic formulas based on fundamentals like algebra, arithmetic, and geometry.
While addition, subtraction, multiplication, and division are straightforward, more advanced topics like derivation, calculus, and geometry require specific formulas. At Physics Wallah, we offer a unique way of solving math problems, helping students understand how equations come into existence. This approach makes it easier to memorise and apply the formulas effectively. It's a better way to grasp and use math formulas for problemsolving.
CBSE Class 6 to 12 Maths Formulas
Math Formulas for Class 6

Divisibility Rule for Three: If the sum of the digits in a number is a multiple of three, then the number itself is divisible by three.

Divisibility Rule for Two: A number is divisible by two if it contains any of the digits 0, 2, 4, 6, or 8.

Variable in an Equation: In an equation, a variable represents a condition. The equation is divided into two sides, referred to as the LeftHand Side and the RightHand Side, separated by an equal (=) sign.

Polygon and Triangle: A polygon is a closed figure formed by connecting line segments. Specifically, a triangle is a polygon characterized by having three sides. Quadrilaterals are polygons with four sides.

The Perimeter of a Square: To find the perimeter of a square, multiply the length of one side by 4.

The Perimeter of a Rectangle: The perimeter of a rectangle is computed by adding twice its length to twice its breadth.

The Perimeter of an Equilateral Triangle: The perimeter of an equilateral triangle is determined by tripling the length of one of its sides.

Area of a Rectangle: The area of a rectangle is found by multiplying its length and breadth.
Math Formulas for Class 7

Profit Percentage: Profit Percentage is calculated as (Profit / Cost price) × 100.

Loss Percentage: Loss Percentage is calculated as (Loss / Cost price) × 100.

Simple Interest: Simple Interest is calculated as (Principal × Rate × Time) / 100.

Amount: The total Amount is the sum of Principal and Interest.

Percentage Change: Percentage Change is calculated as (Change / Original Amount) × 100.

Product of Rational Numbers: The product of rational numbers is calculated as (Product of Numerators) / (Product of Denominators).

Law of Product: am × an = am+n

Law of Quotient: am/an = amn

Law of Zero Exponent: a^0 = 1

Law of Negative Exponent: a^(m) = 1/a^m

Law of Power of a Quotient: (a/b)^m = a^m/b^m

Law of Power of a Power: (a^m)^n = a^(mn)

Law of Power of a Product: (ab)^m = a^m b^m

The perimeter of a Rectangle: The perimeter of a rectangle is calculated as 2 times the sum of its length and breadth.

Area of Rectangle: The area of a rectangle is calculated as the product of its length and breadth.

Area of a Square: The area of a square is calculated as the square of its side.

Area of Triangle: The area of a triangle is calculated as 1/2 times the product of its base and height.

The perimeter of a Square: The perimeter of a square is calculated as 4 times its side.

Area of a Parallelogram: The area of a parallelogram is calculated as the product of its base and height.

Area of a Circle: The area of a circle is calculated as πr^2.

Circumference of a Circle: The circumference of a circle is calculated as πd, where 'd' is the diameter of the circle and π ≈ 3.14.
Math Formulas for Class 8

Additive Inverse of Rational Number: a/b = b/a

Multiplicative Inverse: Multiplicative Inverse of a/b = c/d, if a/b × c/d = 1

Distributive Property: a(b – c) = ab – ac

Simple Interest: Simple Interest is calculated as (Principal × Rate × Time) / 100.

Amount: The total Amount is the sum of Principal and Interest.

Compound Interest Formula: Compound Interest is calculated as Amount – Principal. Amount in case the interest is calculated annually = Principal(1 + Rate/100)^n, where 'n' is the period.

Probability: Probability of the occurrence of an event = Number of outcomes that comprise an event / Total number of outcomes.\

2D Geometry Shapes
Shape 
Formula 
Rectangle 
Area of Rectangle (A) = Length × Width 
Perimeter of Rectangle (P) = 2 × (Length + Width) 

Triangle 
Area of Triangle (A) = ½ × Base × Height 
Perimeter of Triangle (P) = Sum of all three sides of the triangle 

Circle 
Area of Circle (A) = πr² 
Perimeter of Circle (P) = 2πr 

3D Geometry Shapes
3 Dimensional Shapes 
Total Surface Area 
Lateral/Curved Surface Area 
Volume 
Sphere 
4πr² 
4πr² 
4/3(πr³) 
Right Circular Cone 
πr(l + r) 
πrl 
⅓(πr²h) 
Cylinder 
2πr(r + h) 
2(π × r × h) 
πr²h 
Right Pyramid 
Lateral Surface Area + Area of Base 
½(Perimeter of Base × Slant Height) 
⅓(Area of Base) × Height 
Hemisphere 
3πr² 
2πr² 
⅔(πr³) 
Cuboid 
2(lb + bh + hl) 
2h(l + b) 
l × b × h 
Cube 
6a² 
4a² 
a³ 
Right Prism 
Lateral Surface Area + 2(Area of End) 
Perimeter of Base × Height 
Area of Base × Height 
Maths Formula for Class 9
Candidates can go through the list of Maths Formula for Class 9 from the below table:
Topics 
Formulas 
Real Numbers 
√ab = √a √b 
√(a/b) = √a / √b 

(√a + √b) (√a – √b) = a – b 

(√a + √b)² = a + 2√ab + b 

(a + √b) (a – √b) = a² – b 

(a + b) (a – b) = a² – b² 

Geometry Formulas 

Rectangle 
Area of Rectangle A = Length x Width 
Perimeter of Rectangle P = 2(Length + Width) 

Triangle 
Area of Triangle, A = ½ x Breadth x Height 
Perimeter of Triangle, P = Sum of all the three sides of a triangle 

Circle 
Area of Circle, A = πr² 
Perimeter of Circle, P = 2 πr 

Parallelogram 
Area of Parallelogram, A = Breadth x Height 
Perimeter of Parallelogram, P = 2( a+ b) (Here. a = side, b = base ) 

Trapezoid 
Area of Trapezoid A = ½ x Height x (b₁ x b₂) 
Perimeter of Trapezoid, P = Sum of all the sides of a trapezoid 

Cuboid 
Surface Area (A) = (lb + bh + hl), (l = length, b = Breadth, h = height) 
Volume V = Length x Breadth x Height 

Cylinder 
Surface area of Cylinder A = 2πr( h + r) [r = radius of the circular cylinder, H = height of a cylinder] 
Volume of Cylinder V = πr²H 

Cube 
The surface area of Cube. A = 6 side² 
Volume of a Cube V = Side³ 

Surface Area of a Sphere A = 4πr² 

The volume of a Cube V = 4/3πr³ 

Cone 
Surface area of a Cone (A) = πr( L + r) [l = slant height , r = Radius of base] 
Volume of a Cone (V) = ½ πr² 

Heron’s Formula 
Area of Triangle with 3 sides = √s(sa)(sb)(sc) 
Semi Perimeter, S = ( a + b + c)/2 

Polynomial Formula 
P (x) = anxn + an 1xn 1 – an 2xn 1 + …… ax + a0 
Algebra Identities 
(x + θ) (x – θ) = x² – θ² 
(x + β)² = x² + β² + 2 x β 

(x – β)² = x² + β² – 2 x β 

(x – α)(x + θ) = x² + (θ – α)x – xθ 

(x – α)(x – θ) = x² – (α + θ)x + αq 

(x + α)(x + θ) = x² + (α + θ)x + αθ 

(x + α)(x – θ) = x² + (α – θ)x – αθ 

(α + β + θ)² = α² + β² + θ² + 2αβ + 2βθ + 2αθ 

(α + β – θ)² = α² + β² + θ² + 2αβ – 2βθ – 2αθ 

(α – β + θ)² = α² + β² + θ² 2αβ – 2βθ + 2αθ 

(α – β – θ)² = α² + β² + θ² – 2αβ + 2βθ – 2αθ 

(α + θ)³ = α³ + θ³ + 3αθ(α + θ) 

(x)³ + (β)³ = ( x + β) (x² – xβ + β) 

(x)³ – (β)³ = ( x + β) (x² – xβ + β) 
Maths Formula for Class 10
Candidates can go through the list of Maths Formula for Class 10 from the below table:
Topics 
Math Formulas 
Arithmetic Formulas 
an = a + (n – 1) d, where an is the nth term. 
Sn= n/2 [2a + (n – 1)d] 

Trigonometry Formulas 
sin(90° – A) = cos A 
cos(90° – A) = sin A 

tan(90° – A) = cot A 

cot(90° – A) = tan A 

sec(90° – A) = cosec A 

cosec(90° – A) = sec A 

sin θ cosec θ = 1 

cos θ sec θ = 1 

tan θ cot θ = 1 

sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ 

cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1 

sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1 

Area and Volume Formulas 
The volume of Sphere = 4/3 ×π r3 
Lateral Surface Area of Sphere (LSA) = 4π r2 

Total Surface Area of Sphere (TSA) = 4πr2 

The volume of the Right Circular Cylinder = πr2h 

Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh) 

Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h) 

The volume of Hemisphere = ⅔ x (πr3) 

Lateral Surface Area of Hemisphere (LSA) = 2πr2 

Total Surface Area of Hemisphere (TSA) = 3πr2 

The volume of Prism = B × h 

Lateral Surface Area of Prism (LSA) = p × h 

Circle Formula 
The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √ [1+ m2]. 
The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2. 
Maths Formula for Class 11
Candidates can go through the list of Maths Formula for Class 11
from the below table:
Topics 
Math Formulas 
Algebra Formulas 
a × (b + c) = a × b + a × c (Distributive property) 
a + b = b + a (Commutative Property of Addition) 

a × b = b × a (Commutative Property of Multiplication) 

a + (b + c) = (a + b) + c (Associative Property of Addition) 

a × (b × c) = (a × b) × c (Associative Property of Multiplication) 

a + 0 = a (Additive Identity Property) 

a × 1 = a(Multiplicative Identity Property) 

a + (a) = 0 (Additive Inverse Property) 

a⋅(1/a) = 1 (Multiplicative Inverse Property) 

a × (0) =0 (Zero Property of Multiplication) 

Calculus Formulas 
d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)] 
d/dx [f(x) – g (x)] = d/dx [f(x)] – d/dx [g(x)] 

d/dx [f(x) × g (x)] = d/dx [f(x)] × [g(x)] + [f(x)] × d/dx [g(x)] 

d/dx [f(x) / g (x)] = {d/dx [f(x)] × [g(x)] – [f(x)] × d/dx [g(x)]} / g(x)² 

Geometry and Lines Formulas 
Slope m = rise/run = Δy/Δx = y₂−y₁/x₂−x₁ 
PointSlope Form y−y₁ = m (x−x₁) 

Trigonometry Formulas 
sin(90° – A) = cos A 
cos(90° – A) = sin A 

tan(90° – A) = cot A 

cot(90° – A) = tan A 

sec(90° – A) = cosec A 

cosec(90° – A) = sec A 

sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos² θ ⇒ cos² θ = 1 – sin² θ 

cosec² θ – cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ – 1 

sec² θ – tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec² θ – 1 

sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1 
Maths Formula for Class 12
Candidates can go through the list of Maths Formula for Class 12 from the below table:
Topics 
Math Formulas 
Trigonometry Formulas 
sin⁻¹(x) =  sin⁻¹x 
tan⁻¹x + cot⁻¹x = π / 2 

sin⁻¹x + cos⁻¹ x = π / 2 

cos⁻¹(x) = π – cos⁻¹x 

cot⁻¹(x) = π – cot⁻¹x 

Calculus Formulas 
∫ f(x) dx = F(x) + C 
Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ 1) 

Exponential Rules: ∫ ex dx = ex + C 

∫ ax dx = ax / ln(a) + C 

∫ ln(x) dx = x ln(x) – x + C 

Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant. 

Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C 

Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx 

Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx 

∫k f(x) dx = k ∫f(x) dx, , where k is any real number. 

Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx 

∫cos x dx = sin x + C 

∫ sin x dx = cos x + C 

∫ sec² x dx = tan x + C 

∫ cosec² x dx = cot x + C 

∫ sec x tan x dx = sec x + C 

∫ cosec x cot x dx = – cosec x + C 

Vector Formulas 
A + B = B + A (Commutative Law) 
A + (B + C) = (A + B) + C (Associative Law) 

(A • B )= 

(A × B )= 

k (A + B )= kA + kB 

A + 0 = 0 + A (Additive Identity) 

Geometry Formulas 
Cartesian equation of a plane: lx + my + nz = d 
Distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂): PQ = √ ((x₁ – x₂)² + (y₁ – y₂)² + (z₁ – z₂)²) 
Strategy for Maths

Know the entire CBSE syllabus for mathematics thoroughly.

Allocate time for each topic according to its weightage in the exam.

Focus on understanding the concepts rather than rote memorization.

Candidates should solve a variety of problems regularly to strengthen their understanding and problemsolving skills.

Refer to NCERT textbooks as they cover the CBSE syllabus comprehensively.

Candidates should solve CBSE sample papers and previous years' question papers to get familiar with the exam pattern and types of questions asked.

Taking mock tests helps candidates assess their preparation level and identify areas of improvement.

Memorize important formulas and theorems as they are essential for solving problems quickly.

Regularly revise the topics candidates have studied to reinforce their learning and retain information.

Don't hesitate to ask teachers or peers for help if candidates have doubts or difficulties with any concept.
CBSE Class 6 to 12 Maths Formulas FAQs
Q1. How can I effectively use these formulas for exam preparation?
Ans. Understand the underlying concepts, practice regularly, create a formula sheet for quick reference, solve sample papers, take mock tests, and seek help when needed.
Q2. Can I rely solely on these formulas for exam preparation?
Ans. While these formulas are valuable, it's crucial to complement them with a deep understanding of concepts, regular practice, and problemsolving skills to handle different types of problems.
Q3. Where can I find additional study materials for CBSE mathematics?
Ans. Additional study materials can be found in CBSEapproved textbooks, reference books, online educational platforms like Physics Wallah, and resources provided by your school. However, NCERT textbooks are highly recommended.