Class 11 Physics Formula Sheet (PDF) — All Important Formulas Free

Free class 11 physics formula sheet — all 69 key formulas on one page, downloadable as PDF for fast revision before CBSE board exams. No signup.

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TL;DR: Free class 11 physics formula sheet — all 69 key formulas on one page, downloadable as PDF for fast revision before CBSE board exams. No signup.

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Complete formula sheet for CBSE Class 11 Physics. Covers mechanics, thermodynamics, waves, and properties of matter. SI units throughout.

Units & Measurement

Formula	Expression
Dimensional Analysis	[M^a L^b T^c I^d K^e] — M = mass, L = length, T = time, I = current, K = temperature, N = amount of substance
Standard Units	Length (m), Mass (kg), Time (s), Current (A), Temperature (K) — SI base units. Derived units combine these: velocity (m/s), force (N=kg⋅m/s²)
Uncertainty & Errors	Δx/x = ±(Δa/a + Δb/b) for products/quotients — Percentage error = (Δx/x)×100%. Random errors reduce with multiple measurements.

Kinematics

Formula	Expression
Position & Displacement	s = x₂ - x₁ (vector), distance = \|s\| (scalar) — Displacement can be negative (change in position)
Velocity & Acceleration	v = ds/dt, a = dv/dt = d²s/dt² — Average: v_avg = Δs/Δt, a_avg = Δv/Δt
Equation of Motion 1	v = u + at — Linear motion, constant acceleration
Equation of Motion 2	s = ut + ½at² — Displacement formula
Equation of Motion 3	v² = u² + 2as — Connects velocity, acceleration, displacement
Projectile Motion	x = v₀ₓt, y = v₀ᵧt - ½gt², tan θ = v₀ᵧ/v₀ₓ — x-axis: uniform, y-axis: uniformly accelerated (g = 10 m/s²)
Range & Max Height	R = v₀² sin 2θ / g, H = v₀² sin² θ / (2g) — R maximum at θ = 45°. H for vertical component only.

Laws of Motion

Formula	Expression
Newton's First Law	F_net = 0 → a = 0 (equilibrium) — Object at rest/uniform motion stays so unless net force acts
Newton's Second Law	F_net = ma → a = F_net/m — F in newtons (N), m in kg, a in m/s²
Newton's Third Law	F_AB = -F_BA — Action-reaction forces are equal, opposite, on different objects
Friction	f_s ≤ μ_s N, f_k = μ_k N — μ_s = static friction coefficient, μ_k = kinetic, N = normal force
Weight & Normal Force	W = mg, N = mg cos θ (on incline) — Weight always downward, normal force perpendicular to surface
Tension in String	T = ma + mg (for acceleration upward) — Free body diagram essential. For pulley systems, use F_net on each mass.

Work, Energy & Power

Formula	Expression
Work Done	W = F⃗ · s⃗ = Fs cos θ — W in joules (J). Positive: force in direction of motion, Negative: against motion
Kinetic Energy	Ek = ½mv² — Energy due to motion. KE always ≥ 0
Potential Energy (Gravity)	Ep = mgh — Relative to reference level. Change in PE = mg(h₂ - h₁)
Work-Energy Theorem	W_net = ΔEk = ½m(v₂² - v₁²) — Net work equals change in kinetic energy
Conservation of Energy	E_total = Ek + Ep = constant (no friction) — Mechanical energy conserved in isolated systems
Power	P = W/t = Fv cos θ — P in watts (W). Average vs instantaneous power
Elastic Potential Energy	Ep = ½kx² — k = spring constant (N/m), x = extension (m)

Rotational Motion

Formula	Expression
Angular Displacement	θ = s/r (in radians) — s = arc length, r = radius. 1 radian = 57.3°, 2π rad = 360°
Angular Velocity	ω = dθ/dt, v = rω — ω in rad/s. Linear velocity v at circumference
Angular Acceleration	α = dω/dt, a_t = rα — α in rad/s². a_t = tangential acceleration
Centripetal Acceleration	a_c = v²/r = ω²r — Directed toward center. Always perpendicular to velocity
Moment of Inertia	I = Σmᵢrᵢ² = ∫r²dm — Rotational mass. Depends on axis of rotation
Torque	τ = r⃗ × F⃗ = rF sin θ — τ in N⋅m. Perpendicular distance × force
Rotational Equation of Motion	τ_net = Iα — Torque analogous to force, I to mass, α to acceleration
Rotational Kinetic Energy	Ek,rot = ½Iω² — Analogous to ½mv² for translation
Angular Momentum	L = Iω, τ_net = dL/dt — Conservation: L = constant if τ_net = 0

Gravitation

Formula	Expression
Newton's Law of Gravitation	F = GMm/r² — G = 6.67×10⁻¹¹ N⋅m²/kg². F attractive, always
Gravitational Field	g = F/m = GM/r² — g at Earth's surface ≈ 9.8 m/s² or 10 m/s²
Gravitational Potential	V = -GM/r — V in J/kg. Potential energy Ep = mV = -GMm/r
Escape Velocity	v_esc = √(2GM/R) = √(2gR) — R = planet radius. For Earth ≈ 11.2 km/s
Orbital Velocity	v_orb = √(GM/r) = √(gR²/r) — For circular orbit, v_esc = √2 × v_orb
Kepler's Third Law	T² ∝ r³ or T² = (4π²/GM)r³ — T = orbital period. Constant for all planets orbiting same star

Thermodynamics & Kinetic Theory

Formula	Expression
Internal Energy	U = nCvT (ideal gas) — Cv = molar heat capacity at constant volume. U depends only on T
First Law of Thermodynamics	ΔU = Q - W — Q = heat added, W = work done by gas. ΔU = change in internal energy
Work Done by Gas	W = PΔV (constant pressure), W = nRT ln(Vf/Vi) (isothermal) — W positive if gas expands, negative if compressed
Heat Capacity	Q = nCvΔT (const V), Q = nCpΔT (const P) — Cp = Cv + R. For monatomic Cv = (3/2)R, diatomic Cv = (5/2)R
Ideal Gas Law	PV = nRT = NkT — R = 8.314 J/(mol⋅K), k = 1.38×10⁻²³ J/K (Boltzmann), N = number of particles
Mean Kinetic Energy	⟨Ek⟩ = (3/2)kT (monatomic) — Average KE of gas molecules. Temperature measure of molecular motion
RMS Velocity	v_rms = √(3kT/m) = √(3RT/M) — m = molecular mass, M = molar mass (kg/mol)
Entropy Change	ΔS = Q/T (reversible), ΔS = nR ln(Vf/Vi) (isothermal) — S = disorder measure. Second law: ΔS_universe ≥ 0

Oscillations & SHM

Formula	Expression
Simple Harmonic Motion	x = A sin(ωt + φ) — A = amplitude, ω = angular frequency, φ = phase. Acceleration a = -ω²x
Period & Frequency	T = 2π/ω, f = ω/(2π) = 1/T — T in seconds, f in hertz (Hz)
Velocity in SHM	v = ±ω√(A² - x²), v_max = ωA — Velocity maximum at equilibrium, zero at amplitude
Energy in SHM	E = ½kA² = ½mω²A² — Total energy constant. E = Ek + Ep at any instant
Simple Pendulum	T = 2π√(L/g) — L = length, g = 9.8 m/s². Independent of mass
Spring-Mass System	T = 2π√(m/k), ω = √(k/m) — k = spring constant. Period independent of amplitude
Damped Oscillations	x = A₀ e^(-t/τ) sin(ωt + φ) — Amplitude decreases exponentially. τ = damping time constant

Waves

Formula	Expression
Wave Equation	y = A sin(kx - ωt + φ) — k = 2π/λ (wave number), ω = 2πf (angular frequency)
Wave Velocity	v = λf = ω/k — λ = wavelength, f = frequency. v = λ × f always
Intensity of Wave	I = (1/2)ρvω²A² — I = power per unit area. I ∝ A² (intensity proportional to amplitude squared)
Doppler Effect	f' = f(v + v_obs)/(v - v_source) — v = wave velocity. +v when source/observer move closer, -v moving apart
Interference Condition	Constructive: Δx = nλ, Destructive: Δx = (n + ½)λ — Δx = path difference, n = 0, 1, 2, ... Two coherent sources required
Young's Double Slit	λ = ax/D — a = slit separation, x = fringe width, D = distance to screen
Diffraction Minima	b sin θ = nλ (single slit) — b = slit width, θ = diffraction angle, n = 1, 2, 3, ...

Properties of Matter

Formula	Expression
Density & Relative Density	ρ = m/V, R.D. = ρ_substance / ρ_water — ρ in kg/m³. R.D. dimensionless
Stress	Stress = F/A — F = force, A = cross-sectional area. Tensile, compressive, shear stress
Strain	Strain = ΔL/L (linear), Strain = ΔV/V (volumetric) — Dimensionless. Change relative to original length/volume
Young's Modulus	Y = (F/A)/(ΔL/L) = (stress)/(strain) — Y in Pa (N/m²). Elasticity measure for tension/compression
Bulk Modulus	B = -V(ΔP/ΔV) — Resistance to volume change. B in Pa
Shear Modulus	η = (F/A)/(Δx/L) = (shear stress)/(shear strain) — η in Pa. Resistance to shape change
Surface Tension	T = F/L — F = force, L = length. T in N/m (dyn/cm). Creates surface energy
Viscosity	F = ηA(dv/dz) — η = coefficient of viscosity (Pa⋅s). Resistance to flow
Stokes' Law	F = 6πηrv — Drag on sphere, radius r, velocity v in viscous medium

FAQs

What's the difference between average and instantaneous velocity?

Average velocity = total displacement / total time. Instantaneous velocity = velocity at a specific moment (dv/dt). For constant acceleration, average velocity = (initial + final)/2.

How do I solve pulley and incline problems?

Draw free body diagram for each mass separately. Apply Newton's 2nd law (F = ma) to each. For pulleys: if rope doesn't slip, both masses have same acceleration magnitude. For inclines: resolve weight into parallel (mg sin θ) and perpendicular (mg cos θ) components.

When should I use conservation of energy vs work-energy theorem?

Use conservation when no friction/non-conservative forces (Ek₁ + Ep₁ = Ek₂ + Ep₂). Use work-energy when forces act (W_net = ΔEk). For friction problems, W_friction = -μmg×distance, then use work-energy.

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