CBSE · Class 9
Maths Formulas for Class 9
All important Maths formulas chapter-wise for CBSE Class 9 (2026-27) — quick-revision tables for Number Systems, Algebra, Geometry, Mensuration and Statistics.
For reference only. Always verify formulas and information against your official NCERT textbooks or board-prescribed materials before use in exams. Learnizo does not guarantee absolute accuracy.
Ch 1.Number Systems
| Formula / Relation | Expression |
|---|---|
| Rational number | p/q where p, q are integers and q ≠ 0 |
| Irrational number | Cannot be expressed as p/q (e.g. √2, π) |
| Laws of exponents (same base) | aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ/aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ |
| Rationalising factor | For a+√b, multiply by a−√b |
| a^(1/n) | = ⁿ√a |
Ch 2.Polynomials
| Formula / Relation | Expression |
|---|---|
| Remainder Theorem | p(x) ÷ (x−a) → remainder = p(a) |
| Factor Theorem | (x−a) is a factor of p(x) iff p(a) = 0 |
| (a+b)² | = a² + 2ab + b² |
| (a−b)² | = a² − 2ab + b² |
| a²−b² | = (a+b)(a−b) |
| (a+b+c)² | = a²+b²+c²+2ab+2bc+2ca |
| (a+b)³ | = a³+3a²b+3ab²+b³ |
| (a−b)³ | = a³−3a²b+3ab²−b³ |
| a³+b³ | = (a+b)(a²−ab+b²) |
| a³−b³ | = (a−b)(a²+ab+b²) |
| a³+b³+c³−3abc | = (a+b+c)(a²+b²+c²−ab−bc−ca) |
Ch 3.Coordinate Geometry
| Formula / Relation | Expression |
|---|---|
| Cartesian plane quadrants | I:(+,+), II:(−,+), III:(−,−), IV:(+,−) |
| Distance from origin | d = √(x²+y²) |
| Abscissa | x-coordinate of a point |
| Ordinate | y-coordinate of a point |
Ch 4.Lines and Angles
| Formula / Relation | Expression |
|---|---|
| Vertically opposite angles | Equal when two lines intersect |
| Linear pair | ∠a + ∠b = 180° (angles on a straight line) |
| Angle sum (triangle) | ∠A + ∠B + ∠C = 180° |
| Exterior angle | = sum of two non-adjacent interior angles |
| Parallel lines: co-interior angles | Sum = 180° |
Ch 5.Triangles (Congruence)
| Formula / Relation | Expression |
|---|---|
| Congruence criteria | SSS, SAS, ASA, AAS, RHS |
| Isosceles triangle | If AB=AC, then ∠B=∠C |
| Pythagoras Theorem | c² = a² + b² (right angle at C) |
Ch 6.Quadrilaterals
| Formula / Relation | Expression |
|---|---|
| Angle sum (quadrilateral) | ∠A+∠B+∠C+∠D = 360° |
| Parallelogram properties | Opposite sides equal; opposite angles equal; diagonals bisect each other |
| Midpoint Theorem | Line joining midpoints of two sides ∥ third side and = half its length |
Ch 7.Circles
| Formula / Relation | Expression |
|---|---|
| Equal chords | Equidistant from centre |
| Angle in semicircle | = 90° |
| Angles in same segment | Equal |
| Cyclic quadrilateral | Opposite angles sum = 180° |
Ch 8.Heron's Formula
| Formula / Relation | Expression |
|---|---|
| Semi-perimeter (s) | s = (a+b+c)/2 |
| Area of triangle | A = √[s(s−a)(s−b)(s−c)] |
Ch 9.Surface Areas and Volumes
| Formula / Relation | Expression |
|---|---|
| Cuboid: TSA | 2(lb + bh + hl) |
| Cuboid: Volume | l × b × h |
| Cube: TSA | 6a² |
| Cube: Volume | a³ |
| Cylinder: CSA | 2πrh |
| Cylinder: TSA | 2πr(h+r) |
| Cylinder: Volume | πr²h |
| Cone: Slant height | l = √(r²+h²) |
| Cone: CSA | πrl |
| Cone: TSA | πr(l+r) |
| Cone: Volume | (1/3)πr²h |
| Sphere: SA | 4πr² |
| Sphere: Volume | (4/3)πr³ |
| Hemisphere: CSA | 2πr² |
| Hemisphere: TSA | 3πr² |
Ch 10.Statistics
| Formula / Relation | Expression |
|---|---|
| Mean | x̄ = (sum of all observations) / n |
| Median (odd n) | Middle value when data is sorted |
| Median (even n) | Average of two middle values |
| Mode | Most frequently occurring value |
| Range | Maximum − Minimum |
Ch 11.Probability
| Formula / Relation | Expression |
|---|---|
| P(E) | = number of favourable outcomes / total outcomes |
| P(E) range | 0 ≤ P(E) ≤ 1 |
| P(E) + P(Ē) | = 1 |
Frequently Asked Questions
Which are the most important formulas in Class 9 Maths?
Algebraic identities (all 8 standard ones), Heron's formula, surface area and volume formulas, and the angle-sum properties form the core of Class 9 Maths. The algebraic identities (a+b)², (a−b)², a²−b² etc. are used in factorisation problems throughout Class 9 and 10.
What is Heron's formula and when is it used?
Heron's formula calculates the area of a triangle when all three sides are known: A = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter. It is used when the height of the triangle is not given. For composite figures (like a quadrilateral split into two triangles), apply Heron's formula to each triangle.
What is the Remainder Theorem?
The Remainder Theorem states that when a polynomial p(x) is divided by (x−a), the remainder equals p(a). So to find the remainder of p(x) ÷ (x−2), simply calculate p(2). The Factor Theorem extends this: if p(a) = 0, then (x−a) is a factor of p(x).
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