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 | 1/2 = 2/4 = 3/6 |
| Adding fractions (same denominator): a/c + b/c = (a+b)/c | 2/7 + 3/7 = 5/7 |
| Adding fractions (different denominators): Find LCM, convert, then add | 1/3 + 1/4 = 4/12 + 3/12 = 7/12 |
| Subtracting fractions: Same process as addition, subtract numerators | 3/4 - 1/3 = 9/12 - 4/12 = 5/12 |
| Mixed to improper: whole × denominator + numerator, over denominator | 2⅓ = (2×3+1)/3 = 7/3 |
| Improper to mixed: Divide numerator by denominator | 7/3 = 2 remainder 1 = 2⅓ |
Integers
| Formula / Rule | Example |
|---|---|
| Adding two positive integers: Result is positive | (+5) + (+3) = +8 |
| Adding two negative integers: Result is negative, add absolute values | (-5) + (-3) = -8 |
| Adding integers with different signs: Subtract smaller from larger, take sign of larger | (-7) + (+4) = -3 |
| Subtracting an integer = Adding its opposite | (-3) - (-5) = (-3) + (+5) = +2 |
| Positive × Positive = Positive | (+4) × (+3) = +12 |
| Negative × Negative = Positive | (-4) × (-3) = +12 |
| Positive × Negative = Negative | (+4) × (-3) = -12 |
Perimeter and Area
| Formula | Example |
|---|---|
| Perimeter of rectangle = 2 × (length + breadth) | P = 2 × (8 + 5) = 26 cm |
| Area of rectangle = length × breadth | A = 8 × 5 = 40 cm² |
| Perimeter of square = 4 × side | P = 4 × 6 = 24 cm |
| Area of square = side × side = side² | A = 6² = 36 cm² |
| Area of triangle = ½ × base × height | A = ½ × 10 × 6 = 30 cm² |
| Perimeter of triangle = sum of all three sides | P = 5 + 6 + 7 = 18 cm |
Lines and Angles
| Rule | Example |
|---|---|
| Complementary angles add to 90° | 35° and 55° are complementary |
| Supplementary angles add to 180° | 120° and 60° are supplementary |
| Vertically opposite angles are equal | If one angle is 70°, the opposite is also 70° |
| Angles on a straight line add to 180° | If one angle is 110°, the adjacent is 70° |
Practice any chapter on Padhaao
AI tutor for CBSE, ICSE & 15 state boards · 10 learning modes · 3 free chapters daily
Class 7 Formulas
Rational Numbers
| Formula / Rule | Example |
|---|---|
| Every integer is a rational number: n = n/1 | 5 = 5/1, -3 = -3/1 |
| Additive identity for rationals: a/b + 0 = a/b | 3/4 + 0 = 3/4 |
| Additive inverse: a/b + (-a/b) = 0 | 3/4 + (-3/4) = 0 |
| Multiplicative identity: a/b × 1 = a/b | 5/7 × 1 = 5/7 |
| Multiplicative inverse (reciprocal): a/b × b/a = 1 | 3/4 × 4/3 = 1 |
| Multiplying fractions: a/b × c/d = ac/bd | 2/3 × 4/5 = 8/15 |
| Dividing fractions: a/b ÷ c/d = a/b × d/c | 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6 |
Percentage, Ratio, and Proportion
| Formula | Example |
|---|---|
| Percentage = (Part / Whole) × 100 | 15 out of 60 = (15/60) × 100 = 25% |
| Part = (Percentage / 100) × Whole | 30% of 200 = (30/100) × 200 = 60 |
| Fraction to percentage: Multiply by 100 | 3/5 × 100 = 60% |
| Percentage to fraction: Divide by 100 | 75% = 75/100 = 3/4 |
| Profit = Selling Price - Cost Price | SP = 150, CP = 120, Profit = 30 |
| Loss = Cost Price - Selling Price | CP = 200, SP = 180, Loss = 20 |
| Profit % = (Profit / CP) × 100 | Profit% = (30/120) × 100 = 25% |
| Loss % = (Loss / CP) × 100 | Loss% = (20/200) × 100 = 10% |
| Simple Interest = (P × R × T) / 100 | SI = (1000 × 5 × 2)/100 = 100 |
| Ratio a:b means a/b | 3:4 means 3/4 |
| Proportion: a:b = c:d means a×d = b×c | 2:3 = 4:6 → 2×6 = 3×4 = 12 ✓ |
Algebraic Expressions
| Formula / Rule | Example |
|---|---|
| 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 |
| Algebraic identities | Polynomials, factorisation, quadratic equations |
| Percentage, Profit/Loss | Statistics, commercial mathematics |
| Probability (basic) | Formal probability, P(A or B), P(A and B) |
| Exponent rules | Real numbers, logarithms (Class 11) |
| Linear equations | Systems of equations, coordinate geometry |
For Class 9 Maths formulas, see our Class 9 Maths formulas complete list. For the complete study approach for building foundations, read our Class 6-7-8 foundation building guide.
Frequently Asked Questions
Should I memorise all these formulas?
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.
₹21/mo (annual plan)
Padhaao covers 17,000+ chapters across 17 boards
Your exact syllabus. 10 learning modes. 3 free daily. Pro for unlimited - ₹21/month (annual plan).
Want the full chapter with solved examples?
10 learning modes. Board-specific content. 3 free chapters every day.
Try it free