Formula Sheets – Maths, Physics & Chemistry

104 key formulas for Classes 9–12 maths, physics and chemistry — searchable and printable.

Last updated: 7 October 2026

Maths Algebraic identities

Square of a sum: (a + b)² = a² + 2ab + b²
Square of a difference: (a − b)² = a² − 2ab + b²
Difference of squares: a² − b² = (a + b)(a − b)
Cube of a sum: (a + b)³ = a³ + b³ + 3ab(a + b)
Cube of a difference: (a − b)³ = a³ − b³ − 3ab(a − b)
Sum of cubes: a³ + b³ = (a + b)(a² − ab + b²)
Difference of cubes: a³ − b³ = (a − b)(a² + ab + b²)
Three-term square: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Maths Quadratic equations

Standard form: ax² + bx + c = 0, a ≠ 0
Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a
Discriminant: D = b² − 4ac (D > 0: two real roots, D = 0: equal roots, D < 0: no real roots)
Sum and product of roots: α + β = −b/a, αβ = c/a

Maths Arithmetic progression

nth term: aₙ = a + (n − 1)d
Sum of n terms: Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l)
Sum of first n natural numbers: 1 + 2 + … + n = n(n + 1)/2

Maths Geometric progression

nth term: aₙ = a·rⁿ⁻¹
Sum of n terms: Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1
Sum to infinity: S∞ = a/(1 − r), |r| < 1

Maths Trigonometry

Basic ratios: sin θ = P/H, cos θ = B/H, tan θ = P/B
Pythagorean identity: sin²θ + cos²θ = 1
Secant identity: 1 + tan²θ = sec²θ
Cosecant identity: 1 + cot²θ = cosec²θ
Sum formulas: sin(A + B) = sin A cos B + cos A sin B; cos(A + B) = cos A cos B − sin A sin B
Double angle: sin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ − sin²θ = 1 − 2 sin²θ
Standard values: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, tan 45° = 1

Maths Coordinate geometry

Distance formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Section formula (m : n): P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))
Mid-point: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Slope: m = (y₂ − y₁)/(x₂ − x₁)
Area of a triangle: ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

Maths Mensuration

Circle: Area = πr², circumference = 2πr
Triangle (Heron): Area = √[s(s − a)(s − b)(s − c)], s = (a + b + c)/2
Cylinder: Volume = πr²h, CSA = 2πrh, TSA = 2πr(r + h)
Cone: Volume = ⅓πr²h, CSA = πrl, l = √(r² + h²)
Sphere: Volume = ⁴⁄₃πr³, surface area = 4πr²
Hemisphere: Volume = ⅔πr³, TSA = 3πr²
Frustum of a cone: Volume = ⅓πh(R² + r² + Rr)

Maths Statistics & probability

Mean: x̄ = Σx / n
Mean of grouped data: x̄ = Σfx / Σf
Empirical relation: Mode = 3 Median − 2 Mean
Probability: P(E) = favourable outcomes / total outcomes; P(E) + P(not E) = 1
Combinations: ⁿCᵣ = n! / [r!(n − r)!]
Permutations: ⁿPᵣ = n! / (n − r)!

Maths Calculus (Class 12)

Power rule: d/dx (xⁿ) = n xⁿ⁻¹
Trig derivatives: d/dx sin x = cos x; d/dx cos x = −sin x
Exponential & log: d/dx eˣ = eˣ; d/dx ln x = 1/x
Product rule: (uv)′ = u′v + uv′
Quotient rule: (u/v)′ = (u′v − uv′)/v²
Integral of xⁿ: ∫xⁿ dx = xⁿ⁺¹/(n + 1) + C, n ≠ −1
Integration by parts: ∫u dv = uv − ∫v du

Physics Motion

First equation: v = u + at
Second equation: s = ut + ½at²
Third equation: v² = u² + 2as
Average speed: total distance / total time
Projectile range: R = u² sin 2θ / g
Uniform circular motion: a = v²/r, T = 2πr/v

Physics Force, work & energy

Newton’s second law: F = ma
Momentum: p = mv; impulse = FΔt = Δp
Weight: W = mg (g ≈ 9.8 m/s²)
Work: W = Fs cos θ
Kinetic energy: KE = ½mv²
Potential energy: PE = mgh
Power: P = W/t
Gravitation: F = Gm₁m₂/r²
Pressure: P = F/A
Density: ρ = m/V

Physics Electricity

Ohm’s law: V = IR
Charge: Q = It
Resistance: R = ρL/A
Series resistors: R = R₁ + R₂ + R₃ …
Parallel resistors: 1/R = 1/R₁ + 1/R₂ + 1/R₃ …
Electric power: P = VI = I²R = V²/R
Electrical energy: E = Pt (1 kWh = 3.6 × 10⁶ J)
Coulomb’s law: F = kq₁q₂/r², k ≈ 9 × 10⁹ N m²/C²

Physics Light & waves

Mirror formula: 1/f = 1/v + 1/u
Lens formula: 1/f = 1/v − 1/u
Magnification: m = h′/h (mirror: −v/u, lens: v/u)
Power of a lens: P = 1/f (f in metres, P in dioptres)
Refractive index: n = c/v = sin i / sin r
Wave speed: v = fλ

Physics Heat & modern physics

Heat: Q = mcΔT
Latent heat: Q = mL
Photon energy: E = hf = hc/λ
Mass–energy: E = mc²
Half-life: N = N₀ (½)^(t/T½)

Chemistry Mole concept

Number of moles: n = mass / molar mass
Particles: N = n × Nₐ (Nₐ = 6.022 × 10²³ mol⁻¹)
Molar volume of a gas at STP: 22.4 L mol⁻¹ (at 0 °C, 1 atm)
Percentage composition: % = (mass of element / molar mass) × 100

Chemistry Solutions

Molarity: M = moles of solute / litres of solution
Molality: m = moles of solute / kg of solvent
Dilution: M₁V₁ = M₂V₂
Mole fraction: x_A = n_A / (n_A + n_B)
Mass percentage: (mass of solute / mass of solution) × 100

Chemistry Gases

Boyle’s law: P₁V₁ = P₂V₂ (constant T)
Charles’s law: V₁/T₁ = V₂/T₂ (constant P)
Ideal gas equation: PV = nRT (R = 8.314 J mol⁻¹ K⁻¹ = 0.0821 L atm mol⁻¹ K⁻¹)
Kelvin: T(K) = T(°C) + 273.15

Chemistry Acids, bases & electrochemistry

pH: pH = −log[H⁺]
pOH relation: pH + pOH = 14 (at 25 °C)
Water ion product: K_w = [H⁺][OH⁻] = 1 × 10⁻¹⁴ (at 25 °C)
Nernst equation: E = E° − (0.0591/n) log Q (at 298 K)
Gibbs energy: ΔG = ΔH − TΔS; ΔG° = −nFE°
First-order reaction: k = (2.303/t) log([A]₀/[A]); t½ = 0.693/k

Formula sheets for quick revision

Before a test, you need the formulas in one place, not scattered across three textbooks. These formula sheets collect the most important maths, physics and chemistry formulas for Classes 9 to 12 — algebraic identities, the quadratic formula, trigonometry, mensuration, equations of motion, Ohm's law, lens and mirror formulas, the mole concept, gas laws, pH and more. Filter by subject, search for any formula, and print a compact revision sheet.

How to use it

Pick a subject, or search for a topic or formula name.
Revise the formulas, then test yourself without looking.
Print the sheet for last-minute revision.

Example

A car speeds up from rest (u = 0) at 2 m/s² for 5 seconds. From v = u + at its speed becomes 10 m/s, and from s = ut + ½at² it covers 25 m. Solve equations instantly with thequadratic equation solver andscientific calculator, and look up elements on theperiodic table.

Frequently asked questions

Which classes are these formulas for?

They cover the core formulas of Classes 9 to 12 (CBSE/NCERT level) — the ones that come up again and again in board exams, JEE and NEET foundations. Calculus formulas are from Class 12.

Can I print the formula sheet?

Yes. Choose a subject (or All) and tap Print — only the formulas are printed, in a compact layout that fits a few pages. On a phone, use Print → Save as PDF.

What is the best way to memorise formulas?

Understand where each formula comes from, then practise using it in problems. Write the ones you forget on flashcards and review them every day — recall practice beats re-reading.

Are SI units used?

Yes. Physics and chemistry formulas assume SI units (metres, kilograms, seconds, kelvin) unless a different unit is mentioned, as with litres in the gas constant.