Class 6, 7, 8 Maths Formulas - Complete List Organised by Class and Topic
Every important maths formula for Class 6, 7, and 8 in one place. Area, perimeter, fractions, algebra, percentages, integers - with examples for each.
In short: This is your complete reference sheet for every important Maths formula across Class 6, 7, and 8. Organised by class and topic, each formula includes a one-line example so you can see it in action. Bookmark this page and use it for quick revision before exams, homework help, and building your personal formula notebook.
How to Use This Formula List
This page covers formulas from the new NCERT Ganita Prakash textbooks for Class 6, 7, and 8 under the 2026-27 curriculum. Each formula is listed with:
The formula itself
A one-line example showing how to use it
Which class it appears in
Study tip: Do not just read this list. Copy each formula into your own notebook, solve the example, and then create one more example of your own. Active writing beats passive reading for formula retention. Use spaced repetition to revise formulas regularly.
Class 6 Formulas
Number Properties and Operations
Formula / Rule
Example
Divisibility by 2: Last digit is 0, 2, 4, 6, or 8
246 is divisible by 2 (last digit 6)
Divisibility by 3: Sum of digits is divisible by 3
123 → 1+2+3 = 6, divisible by 3 ✓
Divisibility by 5: Last digit is 0 or 5
435 ends in 5, divisible by 5 ✓
Divisibility by 9: Sum of digits is divisible by 9
729 → 7+2+9 = 18, divisible by 9 ✓
Divisibility by 10: Last digit is 0
580 ends in 0, divisible by 10 ✓
Divisibility by 4: Last two digits divisible by 4
316 → 16 ÷ 4 = 4, divisible by 4 ✓
Divisibility by 6: Divisible by both 2 and 3
54 → even + (5+4=9, divisible by 3) ✓
Prime Numbers and Factors
Formula / Rule
Example
Prime number: A number with exactly 2 factors (1 and itself)
7 is prime (factors: 1, 7 only)
Composite number: A number with more than 2 factors
12 is composite (factors: 1, 2, 3, 4, 6, 12)
1 is neither prime nor composite
1 has only one factor
HCF (Highest Common Factor): Largest factor common to given numbers
HCF of 12 and 18 = 6
LCM (Least Common Multiple): Smallest multiple common to given numbers
LCM of 4 and 6 = 12
HCF × LCM = Product of two numbers
HCF(12,18) × LCM(12,18) = 6 × 36 = 216 = 12 × 18
Fractions
Formula / Rule
Example
Equivalent fractions: Multiply or divide numerator and denominator by the same number
Like terms: Terms with the same variable and power
3x and 5x are like terms; 3x and 3x² are not
Adding like terms: Add coefficients
3x + 5x = 8x
Subtracting like terms: Subtract coefficients
7y - 2y = 5y
Value of expression: Substitute variable value
If x = 3, then 2x + 5 = 2(3) + 5 = 11
Geometry
Formula / Rule
Example
Angle sum of triangle = 180°
If two angles are 60° and 70°, third = 180° - 130° = 50°
Exterior angle = Sum of two opposite interior angles
Exterior angle = 60° + 70° = 130°
Sum of angles of quadrilateral = 360°
If three angles are 90°, 90°, 80°, fourth = 100°
Pythagoras Theorem (right triangle): a² + b² = c²
3² + 4² = 9 + 16 = 25 = 5²
Area of parallelogram = base × height
A = 12 × 5 = 60 cm²
Area of circle = π × r²
A = π × 7² = 154 cm² (π ≈ 22/7)
Circumference of circle = 2 × π × r
C = 2 × 22/7 × 7 = 44 cm
Data Handling
Formula
Example
Mean = Sum of observations / Number of observations
Mean of 4, 6, 8 = 18/3 = 6
Mode = Most frequently occurring value
In 2, 3, 3, 5, 7 → Mode = 3
Median (odd set) = Middle value when arranged in order
In 3, 5, 7, 8, 9 → Median = 7
Median (even set) = Average of two middle values
In 3, 5, 7, 8 → Median = (5+7)/2 = 6
Probability = Favourable outcomes / Total outcomes
P(head on coin toss) = 1/2
Class 8 Formulas
Algebraic Identities (Most Important)
Identity
Expansion
Example
(a + b)² = a² + 2ab + b²
Square of a sum
(3 + 2)² = 9 + 12 + 4 = 25
(a - b)² = a² - 2ab + b²
Square of a difference
(5 - 3)² = 25 - 30 + 9 = 4
(a + b)(a - b) = a² - b²
Difference of squares
(7 + 3)(7 - 3) = 49 - 9 = 40
(x + a)(x + b) = x² + (a+b)x + ab
Product of binomials
(x+3)(x+4) = x² + 7x + 12
These four identities are the most important formulas in all of Class 8. Master them. For the chapter-wise strategy, see our Class 8 Maths guide.
Linear Equations
Rule
Example
Transposition: Move term to other side, change sign
2x + 5 = 11 → 2x = 11 - 5 = 6 → x = 3
Cross multiplication: a/b = c/d → ad = bc
x/3 = 4/6 → 6x = 12 → x = 2
Variables on both sides: Collect variables on one side
3x + 2 = x + 8 → 2x = 6 → x = 3
Squares and Square Roots
Formula / Rule
Example
Perfect square ends in: 0, 1, 4, 5, 6, or 9
144 ends in 4 → could be perfect square (12² = 144 ✓)
Square of even number is even
8² = 64 (even)
Square of odd number is odd
7² = 49 (odd)
Pythagorean triplet formula: 2m, m²-1, m²+1
m=3: 6, 8, 10 (6²+8²=100=10²)
√(a × b) = √a × √b
√(4 × 9) = √4 × √9 = 2 × 3 = 6
√(a/b) = √a / √b
√(16/25) = √16 / √25 = 4/5
Cubes and Cube Roots
Formula / Rule
Example
Cube of negative number is negative
(-3)³ = -27
∛(a × b) = ∛a × ∛b
∛(8 × 27) = ∛8 × ∛27 = 2 × 3 = 6
Geometry - Quadrilaterals
Property
Details
Angle sum of quadrilateral = 360°
Always true for any quadrilateral
Parallelogram: Opposite sides equal and parallel, opposite angles equal
Diagonals bisect each other
Rectangle: All angles 90°, opposite sides equal
Diagonals equal and bisect each other
Square: All sides equal, all angles 90°
Diagonals equal, bisect at 90°
Rhombus: All sides equal, opposite angles equal
Diagonals bisect at 90° (not equal)
Trapezium: One pair of opposite sides parallel
No equal diagonal property in general
Mensuration (Area and Volume Formulas)
Formula
Example
Area of trapezium = ½ × (a + b) × h (a, b are parallel sides)
A = ½ × (5+7) × 4 = 24 cm²
Area of rhombus = ½ × d₁ × d₂ (diagonals)
A = ½ × 8 × 6 = 24 cm²
Surface area of cube = 6 × side²
SA = 6 × 5² = 150 cm²
Volume of cube = side³
V = 5³ = 125 cm³
Surface area of cuboid = 2(lb + bh + hl)
SA = 2(4×3 + 3×2 + 2×4) = 2(12+6+8) = 52 cm²
Volume of cuboid = length × breadth × height
V = 4 × 3 × 2 = 24 cm³
Surface area of cylinder = 2πr(r + h)
SA = 2 × 22/7 × 7 × (7+10) = 748 cm²
Volume of cylinder = πr²h
V = 22/7 × 7² × 10 = 1540 cm³
Data Handling and Probability
Formula
Example
Probability of event = Favourable outcomes / Total outcomes
P(rolling 6 on a die) = 1/6
P(event) is always between 0 and 1
0 ≤ P(E) ≤ 1
P(sure event) = 1
P(getting 1-6 on a die) = 6/6 = 1
P(impossible event) = 0
P(rolling 7 on a die) = 0/6 = 0
P(not E) = 1 - P(E)
P(not getting 6) = 1 - 1/6 = 5/6
Exponents and Powers
Rule
Example
aᵐ × aⁿ = aᵐ⁺ⁿ
2³ × 2⁴ = 2⁷ = 128
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
3⁵ ÷ 3² = 3³ = 27
(aᵐ)ⁿ = aᵐⁿ
(2³)² = 2⁶ = 64
a⁰ = 1 (where a ≠ 0)
5⁰ = 1, 100⁰ = 1
a⁻ⁿ = 1/aⁿ
2⁻³ = 1/2³ = 1/8
(a × b)ⁿ = aⁿ × bⁿ
(2 × 3)² = 2² × 3² = 4 × 9 = 36
(a/b)ⁿ = aⁿ/bⁿ
(3/4)² = 9/16
Comparing Quantities
Formula
Example
Compound Interest: A = P(1 + R/100)ⁿ
A = 1000(1 + 10/100)² = 1000 × 1.21 = 1210
CI = A - P
CI = 1210 - 1000 = 210
Discount = Marked Price - Selling Price
Discount = 500 - 400 = 100
Discount % = (Discount / MP) × 100
Discount% = (100/500) × 100 = 20%
Sales Tax / VAT: Total = SP + Tax
Tax = 10% of 500 = 50, Total = 550
Quick Revision Tips
Make physical flashcards
Write the formula on one side and an example on the other. Test yourself daily. Physical flashcards work better than digital ones for maths because writing formulas by hand improves memory.
Group formulas by type
When revising, do not go class by class. Instead, group all area formulas together, all percentage formulas together, all algebra rules together. This builds connections between related concepts.
Test yourself without looking
Cover the formula column and try to recall each formula from the example. Then cover the example and try to create your own. If you can do both, the formula is truly learned.
Connect formulas to problems
A formula is useless if you cannot recognise when to use it. For each formula, solve at least 3 different types of problems. Our guide on solving maths word problems helps with this skill.
How These Formulas Connect to Class 9-10
The formulas on this page are not just for Class 6-8 exams. They carry forward:
Class 6-8 Formula Area
Class 9-10 Extension
Perimeter and Area
Heron's formula, surface area, volume of 3D shapes
Memorise the ones you use frequently (area, perimeter, identities, percentage). For others, focus on understanding — if you understand how a formula works, you can derive it during exams. The algebraic identities must be memorised perfectly since they are used in almost every algebra problem.
How do I remember formulas long-term?
Use spaced repetition: revise formulas on Day 1, Day 3, Day 7, Day 14, and Day 30. Each time you revise, the memory gets stronger. Writing formulas by hand (not typing) activates muscle memory. Check our spaced repetition guide for the complete method.
My child confuses similar formulas. What should I do?
Create comparison pairs: area of rectangle (l × b) vs perimeter of rectangle (2(l+b)). Practice them side by side. Also, always include units — area is in cm² (square units) and perimeter is in cm (linear units). The unit tells you which formula to use.
Are these all the formulas for Class 6-8?
These are the key formulas that appear most frequently in exams and homework. Some chapters have additional rules (like properties of specific triangle types or additional divisibility rules) that are covered in the chapter-wise guides for Class 6, Class 7, and Class 8.
Can I use this page during exams?
No — you need to have these formulas in your head before the exam. Use this page for learning and revision, then test yourself without looking. The goal is to recall any formula within 3 seconds during the exam.
Which formulas are most important for each class?
Class 6: Fractions operations, integer rules, area and perimeter. Class 7: Percentage, algebraic expression rules, angle properties. Class 8: Algebraic identities (all four), exponent rules, compound interest. If you master these core formulas, you can handle most exam problems.
Practice Maths Formulas with Padhaao
Knowing formulas is step one. Applying them to solve problems is what earns marks. Padhaao's AI tutor gives you unlimited practice problems for every formula on this page, explains solutions step by step, and follows the exact Ganita Prakash textbook syllabus for Class 6, 7, and 8.
