📚 India's Best Free Maths Formula Sheet — Class 8 to 12 NCERT — Bookmark this page!
Complete Formula Sheet for Indian Students

All Maths Formulas in One Place

Complete formula sheet for Class 8, 9, 10, 11, 12 — NCERT based. Algebra, Trigonometry, Geometry, Statistics & more. Free. No login needed.

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🧮 Online Maths Tools for Students

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Scientific Calculator

Trigonometric, log, power functions

%

Percentage Calculator

Find %, increase, decrease, marks

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Heron's Formula

Area of triangle with 3 sides

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Distance Formula

Distance between two points

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Algebra Formulas
Identities, polynomials, quadratic & sequences — Class 8 to 12
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Basic Algebraic Identities Class 8Class 9

Square of Sum
(a + b)² = a² + 2ab + b²
Expand any binomial squared
Square of Difference
(a − b)² = a² − 2ab + b²
Useful in factorisation
Difference of Squares
a² − b² = (a+b)(a−b)
Factorisation shortcut
Cube of Sum
(a+b)³ = a³+3a²b+3ab²+b³
Also: a³+3ab(a+b)+b³
Cube of Difference
(a−b)³ = a³−3a²b+3ab²−b³
Also: a³−3ab(a−b)−b³
Sum of Cubes
a³+b³ = (a+b)(a²−ab+b²)
Key factorisation identity
Difference of Cubes
a³−b³ = (a−b)(a²+ab+b²)
(a+b+c)²
= a²+b²+c²+2ab+2bc+2ca

Quadratic Formula Class 10

Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
For ax² + bx + c = 0. Discriminant D = b²−4ac
Sum of Roots
α + β = −b/a
For quadratic ax²+bx+c=0
Product of Roots
α × β = c/a
For quadratic ax²+bx+c=0
Nature of Roots
D>0: real & distinct
D=0: equal
D<0: no real roots

Arithmetic & Geometric Progression Class 10Class 11

AP: nth Term
aₙ = a + (n−1)d
a = first term, d = common difference
AP: Sum of n Terms
Sₙ = n/2 [2a + (n−1)d]
Also Sₙ = n/2 (a + l)
GP: nth Term
aₙ = a · rⁿ⁻¹
a = first term, r = common ratio
GP: Sum of n Terms
Sₙ = a(rⁿ−1)/(r−1), r≠1
Sum of Natural Numbers
1+2+…+n = n(n+1)/2
Sum of Squares
Σn² = n(n+1)(2n+1)/6
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Trigonometry Formulas
Ratios, identities, compound angles — Class 10 to 12
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Basic Ratios Class 10

sin θ
sin θ = Opposite / Hypotenuse
cos θ
cos θ = Adjacent / Hypotenuse
tan θ
tan θ = sin θ / cos θ = Opp/Adj
Pythagorean Identity
sin²θ + cos²θ = 1
Sec Identity
1 + tan²θ = sec²θ
Cosec Identity
1 + cot²θ = cosec²θ

Standard Angle Values

θ 0°30°45°60°90°
sin 01/21/√2√3/21
cos 1√3/21/√21/20
tan 01/√31√3∞

Compound Angles Class 11

sin(A+B)
= sinA cosB + cosA sinB
sin(A−B)
= sinA cosB − cosA sinB
cos(A+B)
= cosA cosB − sinA sinB
cos(A−B)
= cosA cosB + sinA sinB
tan(A+B)
= (tanA+tanB) / (1−tanA tanB)
Double Angle: sin
sin 2A = 2 sinA cosA
Double Angle: cos
cos 2A = cos²A − sin²A
= 1−2sin²A = 2cos²A−1
Double Angle: tan
tan 2A = 2tanA / (1−tan²A)
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Geometry Formulas
Heron's formula, circles, triangles, similarity — Class 9, 10
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Triangle Formulas Class 9

Heron's Formula
Area = √(s(s−a)(s−b)(s−c))
s = (a+b+c)/2
s = semi-perimeter; a, b, c = sides
Area of Triangle (basic)
Area = ½ × base × height
Pythagorean Theorem
c² = a² + b²
c = hypotenuse, a & b = other sides
Equilateral Triangle Area
Area = (√3/4) × a²
a = side length
Isosceles Triangle Area
Area = (b/4)√(4a²−b²)
a = equal sides, b = base

Circle Formulas Class 10

Area of Circle
A = πr²
r = radius
Circumference
C = 2πr = πd
Arc Length
l = (θ/360) × 2πr
θ in degrees
Sector Area
A = (θ/360) × πr²
Tangent from External Pt.
PA² = PO² − r²
PO = distance from point to center

Quadrilaterals & Polygons Class 8

Rhombus Area
A = (d₁ × d₂) / 2
d₁, d₂ = diagonals
Trapezium Area
A = ½ × (a+b) × h
a, b = parallel sides, h = height
Sum of Interior Angles
(n−2) × 180°
n = number of sides
Each Interior Angle (regular)
[(n−2) × 180°] / n
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Coordinate Geometry Formulas
Distance, midpoint, section, slope — Class 10, 11
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Distance Formula
d = √((x₂−x₁)² + (y₂−y₁)²)
Between points (x₁,y₁) and (x₂,y₂)
Midpoint Formula
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Section Formula (Internal)
P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
Divides in ratio m:n internally
Area of Triangle (coords)
= ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|
Slope (m)
m = (y₂−y₁)/(x₂−x₁) = tan θ
Slope-Intercept Form
y = mx + c
Point-Slope Form
y − y₁ = m(x − x₁)
Centroid of Triangle
G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)
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Mensuration Formulas
2D shapes & 3D solids — Surface area & volume — Class 8, 9, 10
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3D Shapes

Cube
Vol = a³ | TSA = 6a²
Diagonal = a√3
Cuboid
Vol = l×b×h
TSA = 2(lb+bh+lh)
Cylinder
Vol = πr²h
CSA = 2πrh | TSA = 2πr(r+h)
Cone
Vol = ⅓πr²h
CSA = πrl | TSA = πr(r+l)
l = slant height = √(r²+h²)
Sphere
Vol = (4/3)πr³
SA = 4πr²
Hemisphere
Vol = (2/3)πr³
CSA = 2πr² | TSA = 3πr²
Frustum of Cone
Vol = πh/3(r₁²+r₂²+r₁r₂)
CSA = π(r₁+r₂)l
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Statistics Formulas
Mean, median, mode, empirical formula — Class 9, 10
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Mean (Direct Method)
x̄ = Σfᵢxᵢ / Σfᵢ
Mean (Assumed Mean)
x̄ = a + (Σfᵢdᵢ / Σfᵢ)
dᵢ = xᵢ − a
Median (Grouped)
M = l + [(n/2 − cf)/f] × h
l=lower boundary, cf=cumul. freq., f=freq., h=width
Mode (Grouped)
Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h
Empirical Formula ⭐
Mode = 3 Median − 2 Mean
Very important for Class 10 exams!
Standard Deviation
σ = √(Σ(xᵢ−x̄)²/n)
Variance
σ² = Σ(xᵢ−x̄)²/n
Median (Ungrouped, odd n)
M = ((n+1)/2)th value
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Commercial Maths Formulas
Profit, loss, percentage, SI, CI, discount — Class 8, 9, 10
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Profit %
Profit% = (Profit/CP) × 100
Loss %
Loss% = (Loss/CP) × 100
Percentage Formula
% = (Part/Whole) × 100
Simple Interest
SI = (P × R × T) / 100
P=Principal, R=Rate%, T=Time(years)
Compound Interest
A = P(1 + R/100)ⁿ
CI = A − P
Discount Formula
Discount = MP − SP
Discount% = (Discount/MP)×100
SP (with Profit%)
SP = CP × (100+P%) / 100
Time & Work
If A does in 'a' days, B in 'b' days:
Together = ab/(a+b) days
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Probability Formulas
Basic to conditional probability — Class 10, 11, 12
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Basic Probability
P(E) = Favourable Outcomes / Total Outcomes
Complement Rule
P(E') = 1 − P(E)
Addition Rule
P(A∪B) = P(A)+P(B)−P(A∩B)
Conditional Probability
P(A|B) = P(A∩B) / P(B)
Independent Events
P(A∩B) = P(A) × P(B)
Bayes' Theorem
P(A|B) = P(B|A)P(A) / P(B)
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Calculus Formulas (Class 11–12)
Limits, derivatives, integrals — NCERT Class 11, 12
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Differentiation

Power Rule
d/dx(xⁿ) = nxⁿ⁻¹
d/dx(sin x)
= cos x
d/dx(cos x)
= −sin x
d/dx(tan x)
= sec²x
d/dx(eˣ)
= eˣ
d/dx(ln x)
= 1/x
Product Rule
d/dx(uv) = u'v + uv'
Chain Rule
d/dx[f(g(x))] = f'(g(x))·g'(x)

Integration

Power Rule
∫xⁿ dx = xⁿ⁺¹/(n+1) + C
∫sin x dx
= −cos x + C
∫cos x dx
= sin x + C
∫eˣ dx
= eˣ + C
∫1/x dx
= ln|x| + C
∫sec²x dx
= tan x + C

❓ Frequently Asked Questions — Maths Formulas

What is Heron's formula and how do you use it? ▼
Heron's formula is used to find the area of a triangle when all three sides are known. Formula: Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2 is the semi-perimeter. For a triangle with sides 5, 6, 7: s = 9, Area = √(9×4×3×2) = √216 ≈ 14.7 cm².
What is the empirical formula in maths statistics? ▼
The empirical formula in statistics relates Mean, Median, and Mode: Mode = 3 Median − 2 Mean. It is used to estimate one measure of central tendency when the other two are known. This is an important Class 10 maths formula.
What is the distance formula in coordinate geometry? ▼
The distance formula gives distance between two points A(x₁,y₁) and B(x₂,y₂): d = √((x₂−x₁)² + (y₂−y₁)²). It is derived from the Pythagorean theorem and is a core Class 10 maths formula.
What are all the important Class 10 maths formulas? ▼
Key Class 10 maths formulas include: Quadratic formula, AP/GP formulas, Heron's formula, Distance formula, Section formula, Midpoint formula, Trigonometric ratios & identities, Areas of circles, Empirical formula in statistics, Probability formula, and Mensuration (surface area and volume) formulas for all 3D shapes.
What is the section formula in maths? ▼
The section formula finds a point P that divides the line joining A(x₁,y₁) and B(x₂,y₂) in ratio m:n internally: P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). The midpoint formula is a special case when m=n=1.
What are the Class 12 maths formula sheet topics? ▼
Class 12 maths formulas cover: Matrices & Determinants, Inverse trigonometric functions, Continuity & Differentiability, Derivatives (including higher-order), Integrals (definite and indefinite), Differential equations, Vectors & 3D geometry, and Probability (conditional, Bayes' theorem).

About This Maths Formula Sheet

This free maths formula sheet is designed specifically for Indian students following the NCERT curriculum — covering Class 8, 9, 10, 11, and 12. Whether you're preparing for your CBSE board exams, JEE, or just need a quick reference, all the important maths formulas are available here in one place.

Class 10 Maths Formula Sheet

The most searched section — Class 10 maths formulas include algebra identities, the quadratic formula, AP/GP, trigonometric ratios, Heron's formula, coordinate geometry (distance formula, section formula, midpoint formula), mensuration (surface area and volume), statistics (mean, median, mode, empirical formula), and probability. These form the foundation of your board exam preparation.

Maths Formula in Hindi (मैथ फार्मूला)

Many students search for maths ke formula or maths ka formula in Hindi medium. All formulas on this page use standard mathematical notation that is identical across Hindi and English NCERT textbooks. The formulas are the same — only language of explanation changes. Use the search bar to find any formula instantly.

Class 12 Maths Formula Sheet

For Class 11 and 12 students, this page covers trigonometry formula sheets, calculus (derivatives and integrals), vectors, matrices, and probability. These are essential for CBSE Class 12 board exams and competitive exams like JEE Main and Advanced.

How to Use This Formula Sheet

Use the class filter buttons at the top to show only formulas relevant to your class. Use the search bar to find any specific formula instantly. Click any formula card to copy it. Use the built-in online calculators (Heron's formula calculator, percentage calculator, distance formula calculator, scientific calculator) for quick calculations. Bookmark this page for easy access before exams!