JEE Main physics formula sheet, unit by unit

In this guide

Units, measurement and experimental skills
Kinematics
Laws of motion and friction
Work, energy, power and collisions
Centre of mass and rotation
Gravitation
Properties of solids and liquids, and heat
Thermodynamics and kinetic theory
Oscillations and waves
Electrostatics and capacitors
Current electricity
Magnetism, EMI and AC
Optics
Modern physics and electronic devices
How to use this sheet

A formula sheet is only useful if it tells you when a formula works. Most wrong answers in JEE Main physics come from a correct formula used in the wrong situation, so each table below has a column for the condition. Use it for quick revision, not as a first introduction; every chapter has its own guide with derivations and worked problems.

The sheet follows the units of the official 2026 syllabus. Symbols are standard: k = 1/4πε₀ ≈ 9 × 10⁹ N m² C⁻², hc ≈ 1240 eV nm, 1 u ≈ 931.5 MeV.

Units, measurement and experimental skills

Formula	Note
Relative error of z = aᵖbᵐ/cⁿ: Δz/z = pΔa/a + mΔb/b + nΔc/c	Errors always add, even for division
Δ(a ± b) = Δa + Δb	Absolute errors add for sums and differences
Vernier least count = 1 MSD − 1 VSD	Subtract the zero error with its sign
Screw gauge least count = pitch/number of circular divisions	Same zero-error rule

Kinematics

Formula	Note
v = u + at, s = ut + ½at², v² = u² + 2as	Constant acceleration only
Distance in the nth second = u + a(2n − 1)/2	Constant acceleration
T = 2u sin θ/g, H = u² sin²θ/2g, R = u² sin 2θ/g	Level ground, no air resistance
R_max = u²/g at θ = 45°	Angles θ and 90° − θ give the same range
y = x tan θ − gx²/(2u² cos²θ)	Trajectory equation
Relative velocity v_AB = v_A − v_B	Vector subtraction
a_c = v²/r = ω²r	Uniform circular motion

Laws of motion and friction

Formula	Note
F = dp/dt; impulse J = FΔt = Δp	Newton's second law in general form
f_s ≤ μ_s N, f_k = μ_k N	Static friction adjusts up to its limit
Angle of repose: tan θ = μ_s	Block about to slide
Level road: v_max = √(μrg)	Friction provides the centripetal force
Banked road, no friction: tan θ = v²/rg	With friction, v_max = √[rg(μ + tan θ)/(1 − μ tan θ)]
Atwood: a = (m₁ − m₂)g/(m₁ + m₂), T = 2m₁m₂g/(m₁ + m₂)	Light string, frictionless pulley

Work, energy, power and collisions

Formula	Note
W = F·s = Fs cos θ; W = ∫F dx	Variable force: integrate
W_net = ΔK (work–energy theorem)	Includes work by all forces
P = dW/dt = F·v	Instantaneous power
Spring: U = ½kx²	x from natural length
Vertical circle (string): v_top ≥ √(gr), v_bottom ≥ √(5gr)	Tension difference T_bottom − T_top = 6mg
e = (velocity of separation)/(velocity of approach)	e = 1 elastic, e = 0 perfectly inelastic
1-D elastic, m₂ at rest: v₁ = (m₁ − m₂)u₁/(m₁ + m₂), v₂ = 2m₁u₁/(m₁ + m₂)	Equal masses exchange velocities
KE lost in perfectly inelastic collision = m₁m₂(u₁ − u₂)²/[2(m₁ + m₂)]	Momentum is still conserved

Centre of mass and rotation

Formula	Note
x_cm = Σmᵢxᵢ/Σmᵢ	For a cut-out, treat the hole as negative mass
τ = r × F = Iα	About a fixed axis or the centre of mass
L = Iω; if τ_ext = 0, I₁ω₁ = I₂ω₂	KE is not conserved in general
KE_rot = ½Iω²; I = Mk²	k is the radius of gyration
Parallel axis: I = I_cm + Md²	Axes must be parallel, one through the CM
Perpendicular axis: I_z = I_x + I_y	Planar bodies only
Ring MR², disc ½MR², solid sphere ⅖MR², hollow sphere ⅔MR²	About a central axis (diameter for spheres)
Rod: ML²/12 about the centre, ML²/3 about one end	Axis perpendicular to the rod

Gravitation

Formula	Note
F = Gm₁m₂/r², g = GM/R²	Point masses or spheres
g_h = gR²/(R + h)² ≈ g(1 − 2h/R)	Approximation for h much smaller than R
g_d = g(1 − d/R)	Uniform Earth; g = 0 at the centre
U = −GMm/r, V = −GM/r	Zero at infinity
v_e = √(2GM/R) = √(2gR)	Independent of the launch direction
v_o = √(GM/r), T² = 4π²r³/GM	Circular orbit of radius r
Satellite energy E = −GMm/2r; KE = GMm/2r	E = −KE

Properties of solids and liquids, and heat

Formula	Note
Y = (F/A)/(ΔL/L); B = −ΔP/(ΔV/V)	Within the elastic limit
Elastic energy per volume = ½ × stress × strain	Energy stored = ½F ΔL
P = P₀ + ρgh	Static fluid
Stokes: F = 6πηrv; terminal velocity v_t = 2r²(ρ − σ)g/9η	Small sphere, streamline flow
A₁v₁ = A₂v₂; P + ½ρv² + ρgh = constant	Incompressible, non-viscous, streamline flow
Efflux speed v = √(2gh)	h below the free surface
Reynolds number Re = ρvD/η	Low Re: streamline; high Re: turbulent
Excess pressure: drop 2T/r, soap bubble 4T/r	A bubble has two surfaces
Capillary rise h = 2T cos θ/(rρg)	θ is the angle of contact
ΔL = LαΔT, β = 2α, γ = 3α	Isotropic solid
Q = mcΔT; Q = mL	Calorimetry: heat lost = heat gained
Conduction: H = KAΔT/L; thermal resistance L/KA	Steady state

Thermodynamics and kinetic theory

Formula	Note
ΔU = Q − W	Physics convention: W is work done by the gas
W = ∫P dV; isothermal W = nRT ln(V₂/V₁)	Reversible processes
Adiabatic: PVᵞ = constant, W = (P₁V₁ − P₂V₂)/(γ − 1)	Q = 0
ΔU = nC_vΔT	Any process, ideal gas
C_p − C_v = R, γ = C_p/C_v = 1 + 2/f	Per mole
Heat engine efficiency η = W/Q₁ = 1 − Q₂/Q₁	Q₂ is heat rejected
P = ⅓ρv_rms², v_rms = √(3RT/M)	M in kg/mol
Average KE per molecule = (3/2)k_BT; U = (f/2)nRT	Equipartition: ½k_BT per degree of freedom
Mean free path λ = 1/(√2 πd²n)	n = number density

Oscillations and waves

Formula	Note
x = A sin(ωt + φ), v = ω√(A² − x²), a = −ω²x	SHM
Spring: T = 2π√(m/k); pendulum: T = 2π√(l/g)	Pendulum: small angles
Springs in series 1/k = 1/k₁ + 1/k₂; parallel k = k₁ + k₂	Same extension in parallel, same force in series
Energy E = ½kA² = ½mω²A²	Constant in SHM
y = A sin(kx − ωt), v = ω/k = fλ	Wave travelling in +x
String: v = √(T/μ); gas: v = √(γP/ρ)	μ = mass per unit length
String fixed at both ends or open pipe: fₙ = nv/2L	All harmonics
Closed pipe: f = (2n − 1)v/4L	Odd harmonics only
Resonance tube: λ/2 = L₂ − L₁	End correction cancels
Beat frequency = f₁ − f₂	Audible only for a small difference

Electrostatics and capacitors

Formula	Note
F = kq₁q₂/r², E = kq/r², V = kq/r	Point charges
Dipole: E_axial = 2kp/r³, E_equatorial = kp/r³	r much larger than the dipole length
τ = p × E, U = −p·E	Uniform field
Gauss: Φ = q_enclosed/ε₀	Any closed surface
Line charge E = λ/2πε₀r; sheet E = σ/2ε₀	Infinite wire and plane sheet
Thin shell: E = kQ/r² outside, 0 inside	V = kQ/R everywhere inside
E = −dV/dr; U = kq₁q₂/r	Field points towards falling potential
C = ε₀A/d; with dielectric filling the gap, C = Kε₀A/d	Parallel plates
Series 1/C = 1/C₁ + 1/C₂; parallel C = C₁ + C₂	Series: same charge; parallel: same voltage
U = ½CV² = Q²/2C = ½QV; energy density ½ε₀E²	Q fixed if the battery is removed
Common potential V = (C₁V₁ + C₂V₂)/(C₁ + C₂)	Charge is shared; some energy is lost

Current electricity

Formula	Note
I = neAv_d, μ = v_d/E	Drift velocity and mobility
R = ρL/A; R_T = R₀(1 + αΔT)	Stretched wire: R ∝ L²
I = E/(R + r); V = E − Ir	Discharging cell
P = VI = I²R = V²/R; P_max at R = r	Maximum power transfer
Wheatstone balance: P/Q = R/S	No current in the galvanometer
Metre bridge: R/S = l/(100 − l)	l in cm

Magnetism, EMI and AC

Formula	Note
Long wire B = μ₀I/2πr; loop centre B = μ₀I/2R	N turns: multiply by N
Loop axis B = μ₀IR²/[2(R² + x²)√(R² + x²)]	Distance x from the centre
Solenoid B = μ₀nI	n = turns per metre
F = q(E + v × B); r = mv/qB; T = 2πm/qB	T is independent of speed
F = IL × B; parallel wires F/L = μ₀I₁I₂/2πd	Like currents attract
τ = NIAB sin θ = m × B	m = NIA
Ammeter shunt S = I_gG/(I − I_g); voltmeter series R = V/I_g − G	G = galvanometer resistance
Bar magnet: B_axial = μ₀2m/4πr³, B_equatorial = μ₀m/4πr³	Far from the magnet
ε = −dΦ/dt; rod ε = Blv; rotating rod ε = ½Bωl²	Lenz's law gives the direction
ε = −L dI/dt; U = ½LI²; solenoid L = μ₀n²Al	Al is the solenoid's volume
AC generator ε = NBAω sin ωt	Peak emf NBAω
I_rms = I₀/√2; X_L = ωL; X_C = 1/ωC	Sinusoidal AC
Z = √[R² + (X_L − X_C)²], tan φ = (X_L − X_C)/R	Series LCR
Resonance ω₀ = 1/√(LC); P = V_rms I_rms cos φ	cos φ is the power factor
Ideal transformer: V_s/V_p = N_s/N_p = I_p/I_s	No losses; power in = power out
c = 1/√(μ₀ε₀); E₀ = cB₀; I_d = ε₀ dΦ_E/dt	EM waves; displacement current

Optics

Formula	Note
Mirror 1/v + 1/u = 1/f, f = R/2, m = −v/u	Cartesian signs
Lens 1/v − 1/u = 1/f, m = v/u, P = 1/f (f in m)	Power in dioptres
Lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂)	In air
Lenses in contact: 1/f = 1/f₁ + 1/f₂	Powers add
sin C = 1/n	Denser to rarer medium
Prism: A = r₁ + r₂, δ = i + e − A; n = sin[(A + δ_m)/2]/sin(A/2)	Thin prism: δ = (n − 1)A
Microscope m ≈ (L/f_o)(D/f_e); telescope m = f_o/f_e	Final image at infinity
Fringe width β = λD/d	Young's double slit
I = I₁ + I₂ + 2√(I₁I₂) cos φ	Equal intensities: 4I₀ cos²(φ/2)
Single slit minima a sin θ = nλ; central maximum width 2λD/a	Central maximum is twice the width of the others
Brewster: tan i_B = n; Polaroid: I = I₀ cos²θ	Unpolarised light is halved by the first Polaroid

Modern physics and electronic devices

Formula	Note
E = hν = hc/λ; E (eV) = 1240/λ (nm)	Photon energy
KE_max = hν − φ = eV₀	Photocurrent depends on intensity, KE_max does not
λ = h/p = h/√(2mK); electron λ = 1.227/√V nm	V in volts
Bohr: r = 0.529 n²/Z Å, E = −13.6 Z²/n² eV	Hydrogen-like species
1/λ = RZ²(1/n₁² − 1/n₂²); lines from level n = n(n − 1)/2	R ≈ 1.097 × 10⁷ m⁻¹
Nuclear radius R = R₀∛A, R₀ ≈ 1.2 fm	Density is nearly constant
BE = Δm c², Δm = Zm_p + (A − Z)m_n − M	1 u = 931.5 MeV
Half-wave output frequency f; full-wave 2f	Rectifiers
NAND = NOT(A AND B); NOR = NOT(A OR B)	Universal gates

How to use this sheet

Cover the right-hand column and say each condition aloud; the conditions are what the exam tests.
Rewrite one unit's table from memory each day; compare and correct.
For any formula you cannot derive in two lines, go back to its chapter guide, for example current electricity or modern physics.
Read common physics mistakes alongside this sheet; most of them are about conditions.

A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the National Testing Agency website .

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