CBSE · Class 11

Physics Formulas for Class 11

Q: Which chapters are most important for Class 11 Physics numericals?

Kinematics, Laws of Motion, Work-Energy-Power, and Rotational Motion are the numerical-heavy chapters. Gravitation and Oscillations also have important formulas. Together these chapters account for around 50% of Class 11 Physics marks.

Q: What are the three equations of motion?

v = u + at; s = ut + ½at²; v² = u² + 2as. Here u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time. These apply only when acceleration is uniform (constant).

Q: What is the difference between escape velocity and orbital velocity?

Orbital velocity (v₀ = √(GM/r)) is the speed needed to maintain a circular orbit at radius r. Escape velocity (v_e = √(2GM/R)) is the minimum speed to escape Earth's gravity entirely. Note v_e = √2 × v₀ for an orbit at Earth's surface.

Q: How do you calculate the efficiency of a Carnot engine?

η = 1 − T₂/T₁, where T₁ is the temperature of the hot source and T₂ is the temperature of the cold sink (both in Kelvin). A Carnot engine is the most efficient theoretically possible heat engine. At T₂=0 K, efficiency would be 100% but this is unachievable.

All important Physics formulas chapter-wise for CBSE Class 11 (2026-27) — Kinematics, Laws of Motion, Work & Energy, Rotational Motion, Gravitation, Thermodynamics and Waves.

11 chapters86+ formulasCBSE 2026–27

Ch 1 Ch 2 Ch 3 Ch 4 Ch 5 Ch 6 Ch 7 Ch 8 Ch 9 Ch 10 Ch 11

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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.Physical World and Measurement

Formula / Relation	Expression	Note
Significant figures (multiplication)	Result has same number of sig figs as least precise factor
Absolute error	Δa = \|aᵢ − ā\|
Relative error	δa = Δā / ā
Percentage error	= (Δā / ā) × 100%

Ch 2.Kinematics

Formula / Relation	Expression	Note
Velocity	v = Δx/Δt	Average velocity
Acceleration	a = Δv/Δt
v = u + at	(1st equation of motion)
s = ut + ½at²	(2nd equation of motion)
v² = u² + 2as	(3rd equation of motion)
sₙ = u + a(2n−1)/2	Distance in nth second
Projectile: Range	R = u²sin2θ/g	Maximum at θ=45°
Projectile: Max Height	H = u²sin²θ/(2g)
Projectile: Time of Flight	T = 2u sinθ/g
Relative velocity	v_AB = v_A − v_B

Ch 3.Laws of Motion

Formula / Relation	Expression	Note
Newton's 2nd Law	F⃗ = ma⃗	Net force = mass × acceleration
Impulse	J = FΔt = Δp	Change in momentum
Momentum	p⃗ = mv⃗
Friction force	f = μN	μ = coefficient, N = normal force
μₛ vs μₖ	μₛ ≥ μₖ (static ≥ kinetic)
Tension in Atwood machine	T = 2m₁m₂g/(m₁+m₂)
Acceleration (Atwood)	a = (m₁−m₂)g/(m₁+m₂)

Ch 4.Work, Energy and Power

Formula / Relation	Expression	Note
Work done	W = F·d·cosθ = F⃗·d⃗
Kinetic Energy	KE = ½mv²
Potential Energy (gravity)	PE = mgh
Elastic PE (spring)	PE = ½kx²	k = spring constant
Work-Energy Theorem	W_net = ΔKE
Power	P = W/t = Fv cosθ	Unit: Watt
Efficiency	η = (useful output / total input) × 100%
Elastic collision: velocities	v₁ = (m₁−m₂)u₁/(m₁+m₂) + 2m₂u₂/(m₁+m₂)

Ch 5.Rotational Motion

Formula / Relation	Expression	Note
Angular velocity	ω = dθ/dt; v = rω
Angular acceleration	α = dω/dt; a = rα
Rotational KE	KE = ½Iω²	I = moment of inertia
Torque	τ = r × F = Iα
Angular momentum	L = Iω = r × p
Conservation of L	If τ_net = 0, L = constant (I₁ω₁ = I₂ω₂)
MI: Solid cylinder (axis)	I = ½MR²
MI: Hollow cylinder (axis)	I = MR²
MI: Solid sphere	I = (2/5)MR²
MI: Thin rod (centre)	I = ML²/12
Parallel axis theorem	I = I_cm + Md²	d = distance from cm to new axis
Rolling without slipping	v = Rω; Total KE = ½mv²(1 + I/mR²)

Ch 6.Gravitation

Formula / Relation	Expression	Note
Newton's Law of Gravitation	F = Gm₁m₂/r²	G = 6.674 × 10⁻¹¹ N·m²·kg⁻²
Acceleration due to gravity	g = GM/R²	At surface
g at height h	g_h = g(1 − 2h/R) for h << R
g at depth d	g_d = g(1 − d/R)
Orbital velocity	v₀ = √(GM/r) = √(gR²/r)
Escape velocity	v_e = √(2GM/R) = √(2gR)	≈ 11.2 km/s for Earth
Orbital period	T = 2π√(r³/GM)	Kepler's 3rd: T² ∝ r³
Gravitational PE	U = −GMm/r	Negative (bound system)

Ch 7.Properties of Solids and Fluids

Formula / Relation	Expression	Note
Stress	= Force/Area	Unit: Pa = N/m²
Strain	= ΔL/L (longitudinal)	Dimensionless
Young's Modulus (Y)	Y = Stress/Strain = FL/(AΔL)
Bulk Modulus (B)	B = −ΔP/(ΔV/V)	For fluids
Pressure in fluid	P = P₀ + ρgh
Archimedes' Principle	Buoyant force = weight of displaced fluid = ρ_fluid · V_sub · g
Bernoulli's equation	P + ½ρv² + ρgh = constant
Stokes' Law	F = 6πηrv	η = viscosity, r = radius, v = velocity
Terminal velocity	v_t = 2r²(ρ−σ)g/(9η)	ρ = density of sphere, σ = density of fluid

Ch 8.Thermodynamics

Formula / Relation	Expression	Note
First Law	ΔU = Q − W	Q = heat absorbed, W = work done by gas
Work by gas (isothermal)	W = nRT ln(V₂/V₁)
Work by gas (isobaric)	W = PΔV = nRΔT
Work (adiabatic)	W = (P₁V₁ − P₂V₂)/(γ−1)
Efficiency of Carnot engine	η = 1 − T₂/T₁	T₁ = hot reservoir, T₂ = cold reservoir
COP of refrigerator	β = T₂/(T₁−T₂)
Adiabatic relation	PVᵞ = constant; TVᵞ⁻¹ = constant	γ = Cp/Cv

Ch 9.Kinetic Theory of Gases

Formula / Relation	Expression	Note
Ideal gas: PV = nRT	P = ρRT/M	ρ = density, M = molar mass
KE per molecule	= (3/2)kT	k = 1.38 × 10⁻²³ J/K
u_rms	= √(3RT/M)
Degrees of freedom	Monoatomic: 3; Diatomic: 5; Polyatomic: 6
Cp − Cv	= R
γ = Cp/Cv	Monoatomic: 5/3; Diatomic: 7/5

Ch 10.Oscillations (SHM)

Formula / Relation	Expression	Note
SHM displacement	x = A sin(ωt + φ)	A = amplitude, ω = angular frequency
Angular frequency	ω = 2π/T = 2πf
Velocity in SHM	v = ω√(A²−x²); v_max = Aω at x=0
Acceleration in SHM	a = −ω²x; a_max = Aω² at x=±A
Energy (SHM)	E = ½mω²A² = ½kA²	Constant
Spring-mass period	T = 2π√(m/k)
Simple pendulum period	T = 2π√(L/g)	For small angles

Ch 11.Waves

Formula / Relation	Expression	Note
Wave speed	v = fλ = λ/T
Speed of sound (Newton-Laplace)	v = √(γP/ρ)	γ = 1.4 for air; v ≈ 331+0.61T m/s (T in °C)
Speed on string	v = √(T/μ)	T = tension, μ = linear mass density
Standing wave (string, both ends fixed)	λₙ = 2L/n; fₙ = nv/(2L)	n = 1,2,3,…
Open pipe harmonics	fₙ = nv/(2L)	All harmonics
Closed pipe harmonics	fₙ = (2n−1)v/(4L)	Odd harmonics only
Doppler effect (source moving)	f' = f(v ± v_o)/(v ∓ v_s)	+ observer approaching; − source approaching
Beats	f_beat = \|f₁ − f₂\|

Frequently Asked Questions

Which chapters are most important for Class 11 Physics numericals?

Kinematics, Laws of Motion, Work-Energy-Power, and Rotational Motion are the numerical-heavy chapters. Gravitation and Oscillations also have important formulas. Together these chapters account for around 50% of Class 11 Physics marks.

What are the three equations of motion?

v = u + at; s = ut + ½at²; v² = u² + 2as. Here u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time. These apply only when acceleration is uniform (constant).

What is the difference between escape velocity and orbital velocity?

Orbital velocity (v₀ = √(GM/r)) is the speed needed to maintain a circular orbit at radius r. Escape velocity (v_e = √(2GM/R)) is the minimum speed to escape Earth's gravity entirely. Note v_e = √2 × v₀ for an orbit at Earth's surface.

How do you calculate the efficiency of a Carnot engine?

η = 1 − T₂/T₁, where T₁ is the temperature of the hot source and T₂ is the temperature of the cold sink (both in Kelvin). A Carnot engine is the most efficient theoretically possible heat engine. At T₂=0 K, efficiency would be 100% but this is unachievable.

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