All formulas from NCERT Class 8 Maths — 13 chapters, 100+ formulas. Algebra identities, mensuration, exponents, compound interest & more. Free PDF download.
📥 Free PDF DownloadNCERT / CBSE13 Chapters100+ FormulasAll Identities
💡Exam tip: Chapters 7 (Compound Interest), 8 (Algebraic Identities), and 9 (Mensuration) carry the most marks in Class 8 exams. Start with those! Click any formula to copy it.
1
Rational Numbers
Properties, number line, between two rationals
Properties▼
Syllabus Topics
1.1 Introduction1.2 Properties of Rational Numbers1.3 Representation on Number Line1.4 Rational between Two Rationals1.5 Word Problems
Additive Inverse
-(p/q) = -p/q
p/q + (−p/q) = 0
Multiplicative Inverse
Reciprocal of p/q = q/p
p/q × q/p = 1
Rational Between a & b
n = (a + b) / 2
Mean of two rationals
Distributive Property
a × (b + c) = ab + ac
Works for all rational numbers
Commutative (Addition)
a + b = b + a
Associative (Addition)
(a+b)+c = a+(b+c)
2
Linear Equations in One Variable
Solving, applications, reducible forms
Algebra▼
Syllabus Topics
2.1 Introduction2.2 Linear on One Side2.3 Applications2.4 Variable on Both Sides2.5 More Applications2.6 Reducing to Simpler Form2.7 Reducible to Linear Form
5.1 Introduction5.2 Properties of Square Numbers5.3 Interesting Patterns5.4 Finding Square of a Number5.5 Square Roots5.6 Square Roots of Decimals5.7 Estimating Square Root
Square Formula
n² = n × n
1,4,9,16,25,36,49,64,81,100…
Pythagorean Triplet (m>1)
2m, m²−1, m²+1
e.g. m=2 → 4,3,5
Product Rule (√)
√(ab) = √a × √b
Quotient Rule (√)
√(a/b) = √a / √b
(a+b)²
= a² + 2ab + b²
(a−b)²
= a² − 2ab + b²
Number
Square
Number
Square
Number
Square
1
1
6
36
11
121
2
4
7
49
12
144
3
9
8
64
13
169
4
16
9
81
14
196
5
25
10
100
15
225
6
Cubes and Cube Roots
Perfect cubes, cube identities, prime factorisation method
▼
Syllabus Topics
6.1 Introduction6.2 Cubes6.3 Cube Roots
Cube
n³ = n × n × n
1,8,27,64,125,216,343…
(a+b)³
= a³+3a²b+3ab²+b³
(a−b)³
= a³−3a²b+3ab²−b³
Sum of Cubes
a³+b³ = (a+b)(a²−ab+b²)
Difference of Cubes
a³−b³ = (a−b)(a²+ab+b²)
Cube Root Product
∛(ab) = ∛a × ∛b
7
Comparing Quantities ⭐
Profit/loss, discount, SI, Compound Interest, GST
High Marks▼
Syllabus Topics
7.1 Ratios & Percentages7.2 Increase/Decrease %7.3 Discounts7.4 Profit & Loss7.5 Sales Tax / VAT / GST7.6 Compound Interest7.7 CI Formula Derivation7.8 Half-Yearly Compounding7.9 Applications of CI
Profit, Loss & Percentage
Percentage
% = (Part/Whole) × 100
Increase %
= (Increase/Original) × 100
Profit %
= (Profit / CP) × 100
CP = Cost Price
Loss %
= (Loss / CP) × 100
SP (with Profit)
SP = CP × (100+P%) / 100
SP (with Loss)
SP = CP × (100−L%) / 100
Discount
= Marked Price − Selling Price
Discount %
= (Discount / MP) × 100
SP after Discount
SP = MP × (100 − d%) / 100
GST Amount
GST = (GST% / 100) × Price
Simple & Compound Interest
⭐ Most Important Formulas — Chapter 7
Simple Interest
SI = (P × R × T) / 100
Amount (SI)
A = P + SI
Compound Interest
A = P(1 + R/100)ⁿ
Half-Yearly CI
A = P(1 + R/200)²ⁿ
CI = A − P
Compound Interest earned
Quarterly CI
A = P(1 + R/400)⁴ⁿ
8
Algebraic Expressions & Identities ⭐
All standard identities — most important for exams
High Marks▼
Syllabus Topics
9.1 What are Expressions?9.2 Terms, Factors & Coefficients9.3 Monomials, Binomials, Polynomials9.4 Like & Unlike Terms9.7 Multiplying Monomial × Monomial9.9 Polynomial × Polynomial9.10 What is an Identity?9.11 Standard Identities9.12 Applying Identities
⭐ 4 Standard Algebraic Identities (NCERT Class 8)
Identity I
(a+b)² = a²+2ab+b²
Identity II
(a−b)² = a²−2ab+b²
Identity III
a²−b² = (a+b)(a−b)
Identity IV
(x+a)(x+b) = x²+(a+b)x+ab
Additional Important Identities
(a+b+c)²
= a²+b²+c²+2ab+2bc+2ca
Monomial × Monomial
aˣ × aʸ = aˣ⁺ʸ
Multiply coefficients, add powers
a² + b²
= (a+b)² − 2ab
Derived from Identity I
2ab
= (a+b)² − (a²+b²)
9
Mensuration ⭐
Surface area & volume of cube, cuboid, cylinder
High Marks▼
Syllabus Topics
9.1 Introduction9.2 Let us Recall (2D)9.3 Area of Trapezium9.4 Area of General Quadrilateral9.5 Area of Polygons9.6 Solid Shapes9.7 SA of Cube, Cuboid, Cylinder9.8 Volume of Cube, Cuboid, Cylinder9.9 Volume and Capacity
2D Areas
Trapezium
A = ½(a+b) × h
a, b = parallel sides, h = height
General Quadrilateral
A = ½ × d × (h₁+h₂)
d = diagonal, h₁,h₂ = perpendiculars
Rhombus
A = (d₁ × d₂) / 2
Circle
A = πr² C = 2πr
3D Shapes — Surface Area & Volume
⭐ Cube, Cuboid, Cylinder — All Formulas
Cube: Volume
V = a³
Cube: TSA
TSA = 6a²
Cube: LSA
LSA = 4a²
Cube: Diagonal
d = a√3
Cuboid: Volume
V = l × b × h
Cuboid: TSA
2(lb+bh+lh)
Cuboid: LSA
2h(l+b)
Cylinder: Volume
V = πr²h
Cylinder: CSA
2πrh
Cylinder: TSA
2πr(r+h)
Capacity
1 L = 1000 cm³
Conversion
1 mL = 1 cm³
10
Exponents and Powers
Laws of exponents, negative powers, standard form
▼
Syllabus Topics
10.1 Introduction10.2 Negative Exponents10.3 Laws of Exponents10.4 Standard Form
Product Rule
aᵐ × aⁿ = aᵐ⁺ⁿ
Quotient Rule
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Power of Power
(aᵐ)ⁿ = aᵐⁿ
Zero Exponent
a⁰ = 1 (a ≠ 0)
Negative Exponent
a⁻ⁿ = 1 / aⁿ
Product to Power
(ab)ⁿ = aⁿ × bⁿ
Fraction to Power
(a/b)ⁿ = aⁿ / bⁿ
Standard Form
m × 10ⁿ (1 ≤ m < 10)
11
Direct and Inverse Proportions
Direct variation, inverse variation, unitary method
▼
Syllabus Topics
11.1 Introduction11.2 Direct Proportion11.3 Inverse Proportion
Direct Proportion
x/y = k (constant)
x ↑ → y ↑
Direct Proportion (cross)
x₁/y₁ = x₂/y₂
Inverse Proportion
x × y = k (constant)
x ↑ → y ↓
Inverse Proportion (cross)
x₁ × y₁ = x₂ × y₂
Speed — Distance — Time
D = S × T
Direct proportion example
Unitary Method
Find value for 1, then scale
12
Factorisation
HCF, regrouping, using identities, division
▼
Syllabus Topics
12.1 Introduction12.2 What is Factorisation?12.3 Division of Algebraic Expressions12.4 Division (Polynomial ÷ Polynomial)12.5 Can you Find the Error?
Common Factor
ab + ac = a(b+c)
Take out HCF
Regrouping
ab+ac+db+dc = a(b+c)+d(b+c) = (a+d)(b+c)
Using Identity I (reverse)
a²+2ab+b² = (a+b)²
Using Identity II (reverse)
a²−2ab+b² = (a−b)²
Using Identity III (reverse)
a²−b² = (a+b)(a−b)
Using Identity IV (reverse)
x²+(a+b)x+ab = (x+a)(x+b)
13
Introduction to Graphs
Coordinates, axes, linear graphs, applications
▼
Syllabus Topics
13.1 Introduction13.2 Linear Graphs13.3 Applications
Coordinate
(x, y) = (abscissa, ordinate)
Origin
O = (0, 0)
Linear Graph
y = mx + c
m = slope, c = y-intercept
Direct Variation Graph
y = kx
Passes through origin
Quadrants
Q1:(+,+) Q2:(−,+) Q3:(−,−) Q4:(+,−)
❓ FAQs — Class 8 Maths Formulas
What are the 4 standard identities in Class 8 Maths? ▼
The 4 standard algebraic identities in Class 8 NCERT are: (1) (a+b)² = a²+2ab+b², (2) (a−b)² = a²−2ab+b², (3) a²−b² = (a+b)(a−b), (4) (x+a)(x+b) = x²+(a+b)x+ab. These must be memorized as they are used extensively in Class 9 and 10 too.
What is the compound interest formula in Class 8? ▼
The Compound Interest formula is: A = P(1 + R/100)ⁿ where P = Principal, R = Rate of interest per annum, n = number of years. CI = A − P. For half-yearly compounding: A = P(1 + R/200)²ⁿ. This is one of the highest-marks-carrying formulas in Class 8.
What is the formula for the volume and surface area of a cylinder? ▼
For a cylinder with radius r and height h: Volume = πr²h, Curved Surface Area (CSA) = 2πrh, Total Surface Area (TSA) = 2πr(r+h). Use π = 22/7 or 3.14 as instructed in the problem.
What are the laws of exponents in Class 8? ▼
The laws of exponents for Class 8 are: (1) aᵐ × aⁿ = aᵐ⁺ⁿ, (2) aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (3) (aᵐ)ⁿ = aᵐⁿ, (4) a⁰ = 1, (5) a⁻ⁿ = 1/aⁿ, (6) (ab)ⁿ = aⁿbⁿ, (7) (a/b)ⁿ = aⁿ/bⁿ. Negative exponents and standard form are new topics in Class 8.
Which chapters are most important in Class 8 Maths for exams? ▼
The highest-weightage chapters in Class 8 Maths are: Chapter 7 (Comparing Quantities — profit/loss, CI), Chapter 8 (Algebraic Identities), Chapter 9 (Mensuration — SA and Volume), and Chapter 2 (Linear Equations). Master these 4 chapters and you're well-prepared for most exams.
Class 8 Maths Formula Sheet — Complete Guide
This page is a comprehensive Class 8 Maths formula sheet covering all 13 chapters of the NCERT Class 8 Mathematics textbook, aligned with the CBSE curriculum. Whether you're preparing for unit tests, half-yearly exams, or annual board exams, these formulas are your go-to reference.
Chapter-wise Class 8 Maths Formulas
Each chapter is broken down into individual formula cards. The most important chapters — Algebraic Identities, Comparing Quantities (Compound Interest), and Mensuration — are highlighted with ⭐ as they carry the highest marks. All 4 standard identities from Chapter 8 are displayed prominently.
Download Class 8 Maths Formula PDF
Use the PDF download button at the top to get a print-ready formula sheet with all chapters. It's perfect for last-minute revision before exams, sticking on your study wall, or studying offline.
How to Use This Formula Sheet
Click on any chapter header to expand its formulas. Click any formula card to copy it instantly. All formulas are based on the NCERT Class 8 Maths textbook and are valid for CBSE students across India.