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JEE Physics Formulas
Complete Formula Sheet

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📐 Units & Dimensions 🏃 Kinematics ⚡ Electrostatics 🌡️ Thermodynamics 🔭 Modern Physics 💡 Optics 🧲 Magnetism 🌊 Waves
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Table of Contents

1
Units & Dimensions
2
Kinematics
3
Laws of Motion & Friction
4
Work, Power & Energy
5
Circular Motion
6
Centre of Mass & Momentum
7
Rotational Dynamics
8
Gravitation
9
Simple Harmonic Motion
10
Fluid Mechanics
11
Thermodynamics
12
Waves & Sound
13
Electrostatics
14
Current Electricity
15
Magnetism
16
EMI & AC Circuits
17
Optics
18
Modern Physics
📏

1. Units & Dimensions

8 Formulas
Fundamental SI Units
Physical QuantitySI UnitSymbol
LengthMetrem
MassKilogramkg
TimeSeconds
Electric CurrentAmpereA
TemperatureKelvinK
Luminous IntensityCandelacd
Amount of SubstanceMolemol
Metric Prefixes
PrefixSymbolFactor
Picop\(10^{-12}\)
Nanon\(10^{-9}\)
Microμ\(10^{-6}\)
Millim\(10^{-3}\)
Centic\(10^{-2}\)
Kilok\(10^{3}\)
MegaM\(10^{6}\)
GigaG\(10^{9}\)
Important
Dimensional Formula – Force
\[ [F] = [MLT^{-2}] \]
M=Mass, L=Length, T=Time
Dimensional Formula – Energy
\[ [E] = [ML^2T^{-2}] \]
Dimensional Formula – Power
\[ [P] = [ML^2T^{-3}] \]
Dimensional Formula – Pressure
\[ [P] = [ML^{-1}T^{-2}] \]
🏃

2. Kinematics

14 Formulas
Key
Average Velocity
\[ v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
Average Speed
\[ \text{Speed}_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Important
1st Equation of Motion
\[ v = u + at \]
u=initial velocity, a=acceleration, t=time
Important
2nd Equation of Motion
\[ s = ut + \frac{1}{2}at^2 \]
s=displacement
Important
3rd Equation of Motion
\[ v^2 = u^2 + 2as \]
Displacement in n-th Second
\[ s_n = u + a\!\left(n - \frac{1}{2}\right) \]
Key
Projectile – Time of Flight
\[ T = \frac{2u\sin\theta}{g} \]
Key
Projectile – Maximum Range
\[ R = \frac{u^2\sin 2\theta}{g} \]
Max range when θ = 45°
Key
Projectile – Maximum Height
\[ H = \frac{u^2\sin^2\theta}{2g} \]
Relative Velocity
\[ \vec{v}_{AB} = \vec{v}_A - \vec{v}_B \]
Velocity of A relative to B
Velocity of Projectile at any Instant
\[ v_x = u\cos\theta,\quad v_y = u\sin\theta - gt \]
Resultant Velocity
\[ v = \sqrt{v_x^2 + v_y^2} \]
⚖️

3. Laws of Motion & Friction

12 Formulas
Newton's 1st Law
Every object remains at rest or in uniform motion unless acted upon by an external force.
Newton's 2nd Law
\[ \vec{F} = m\vec{a} \]
Net force = mass × acceleration
Newton's 3rd Law
\[ \vec{F}_{12} = -\vec{F}_{21} \]
Every action has equal & opposite reaction
Key
Spring Force (Hooke's Law)
\[ F = -kx \]
k=spring constant, x=extension
Series Spring Constant
\[ \frac{1}{k_{eq}} = \frac{1}{k_1} + \frac{1}{k_2} \]
Parallel Spring Constant
\[ k_{eq} = k_1 + k_2 \]
Key
Kinetic Friction
\[ f_k = \mu_k N \]
μₖ=coefficient of kinetic friction, N=normal force
Key
Static Friction (Maximum)
\[ f_{s,\max} = \mu_s N \]
Acceleration on Inclined Plane
\[ a = g\sin\theta - \mu_k g\cos\theta \]
Angle of Friction
\[ \tan\lambda = \mu_s \]
Tension in Rope (Connected Bodies)
\[ T = \frac{m_2}{m_1 + m_2} F \]
⚡

4. Work, Power & Energy

10 Formulas
Important
Work Done
\[ W = \vec{F}\cdot\vec{s} = Fs\cos\theta \]
Key
Kinetic Energy
\[ K = \frac{1}{2}mv^2 = \frac{p^2}{2m} \]
Work–Energy Theorem
\[ W_{net} = \Delta K = K_f - K_i \]
Gravitational Potential Energy
\[ U = mgh \]
Elastic Potential Energy (Spring)
\[ U = \frac{1}{2}kx^2 \]
Important
Power
\[ P = \frac{dW}{dt} = \vec{F}\cdot\vec{v} \]
Conservation of Energy
\[ K_i + U_i = K_f + U_f \]
Coefficient of Restitution
\[ e = \frac{v_2 - v_1}{u_1 - u_2} \]
0 ≤ e ≤ 1; e=1 elastic, e=0 perfectly inelastic
🔄

5. Circular Motion

10 Formulas
Key
Angular Velocity
\[ \omega = \frac{d\theta}{dt} = \frac{v}{r} \]
Linear Velocity
\[ v = r\omega \]
Important
Centripetal Acceleration
\[ a_c = \frac{v^2}{r} = \omega^2 r \]
Important
Centripetal Force
\[ F_c = \frac{mv^2}{r} = m\omega^2 r \]
Time Period
\[ T = \frac{2\pi}{\omega} = \frac{2\pi r}{v} \]
Banking of Roads (No Friction)
\[ \tan\theta = \frac{v^2}{rg} \]
Conical Pendulum
\[ T = 2\pi\sqrt{\frac{L\cos\theta}{g}} \]
Min. Speed at Top of Vertical Circle
\[ v_{min} = \sqrt{gR} \]
Min. Speed at Bottom of Vertical Circle
\[ v_{min} = \sqrt{5gR} \]
⚖️

6. Centre of Mass & Momentum

10 Formulas
Key
Centre of Mass
\[ \vec{R}_{cm} = \frac{\sum m_i\vec{r}_i}{\sum m_i} \]
Linear Momentum
\[ \vec{p} = m\vec{v} \]
Important
Impulse
\[ \vec{J} = \vec{F}\Delta t = \Delta\vec{p} \]
Law of Conservation of Momentum
\[ \vec{p}_i = \vec{p}_f \quad (\text{when } F_{ext}=0) \]
Elastic Collision Velocities
\[ v_1 = \frac{(m_1-m_2)u_1 + 2m_2 u_2}{m_1+m_2} \] \[ v_2 = \frac{(m_2-m_1)u_2 + 2m_1 u_1}{m_1+m_2} \]
Perfectly Inelastic Collision
\[ v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2} \]
🌀

7. Rotational Dynamics

12 Formulas
Key
Moment of Inertia
\[ I = \sum m_i r_i^2 \]
Moment of Inertia – Standard Bodies
BodyAxisI
Solid SphereDiameter\(\frac{2}{5}MR^2\)
Hollow SphereDiameter\(\frac{2}{3}MR^2\)
Solid CylinderOwn axis\(\frac{1}{2}MR^2\)
RingOwn axis\(MR^2\)
Thin RodCentre (⊥)\(\frac{1}{12}ML^2\)
Thin RodEnd (⊥)\(\frac{1}{3}ML^2\)
Parallel Axis Theorem
\[ I = I_{cm} + Md^2 \]
Perpendicular Axis Theorem
\[ I_z = I_x + I_y \]
(For laminar/2D bodies)
Important
Torque
\[ \vec{\tau} = \vec{r}\times\vec{F} = I\alpha \]
Important
Angular Momentum
\[ \vec{L} = I\vec{\omega} = \vec{r}\times\vec{p} \]
Rotational Kinetic Energy
\[ K_{rot} = \frac{1}{2}I\omega^2 \]
Rolling Without Slipping (Total KE)
\[ K = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 \]
🌍

8. Gravitation

10 Formulas
Important
Newton's Law of Gravitation
\[ F = \frac{Gm_1 m_2}{r^2} \]
G = 6.67×10⁻¹¹ N m² kg⁻²
Key
Acceleration due to Gravity
\[ g = \frac{GM}{R^2} \]
g at Height h
\[ g_h = g\!\left(1 - \frac{2h}{R}\right) \approx \frac{GM}{(R+h)^2} \]
g at Depth d
\[ g_d = g\!\left(1 - \frac{d}{R}\right) \]
Important
Orbital Velocity
\[ v_o = \sqrt{\frac{GM}{r}} = \sqrt{gR^2/r} \]
Escape Velocity
\[ v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR} \]
Key
Kepler's 3rd Law
\[ T^2 \propto r^3 \quad\Rightarrow\quad T^2 = \frac{4\pi^2 r^3}{GM} \]
Gravitational Potential
\[ V = -\frac{GM}{r} \]
Gravitational PE
\[ U = -\frac{GMm}{r} \]
〰️

9. Simple Harmonic Motion (SHM)

12 Formulas
Important
Restoring Force
\[ F = -kx \]
Acceleration in SHM
\[ a = -\omega^2 x \]
Key
Angular Frequency
\[ \omega = \sqrt{\frac{k}{m}} = \frac{2\pi}{T} \]
Important
Time Period (Spring–Mass)
\[ T = 2\pi\sqrt{\frac{m}{k}} \]
Important
Time Period (Simple Pendulum)
\[ T = 2\pi\sqrt{\frac{L}{g}} \]
Displacement Equation
\[ x = A\sin(\omega t + \phi) \]
A=Amplitude, φ=initial phase
Velocity in SHM
\[ v = \omega\sqrt{A^2 - x^2} \]
Maximum Velocity
\[ v_{max} = \omega A \quad (\text{at } x=0) \]
Total Energy in SHM
\[ E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2 A^2 \]
KE & PE in SHM
\[ KE = \frac{1}{2}m\omega^2(A^2-x^2) \] \[ PE = \frac{1}{2}m\omega^2 x^2 \]
💧

10. Fluid Mechanics & Properties of Matter

12 Formulas
Pressure
\[ P = \frac{F}{A},\quad P = P_0 + \rho g h \]
Key
Equation of Continuity
\[ A_1 v_1 = A_2 v_2 \]
Conservation of mass in fluid flow
Important
Bernoulli's Theorem
\[ P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant} \]
Torricelli's Theorem
\[ v = \sqrt{2gh} \]
Speed of efflux from a hole
Stokes' Law (Viscous Force)
\[ F = 6\pi\eta r v \]
Terminal Velocity
\[ v_t = \frac{2r^2(\rho_s - \rho_f)g}{9\eta} \]
Surface Tension
\[ T = \frac{F}{L} \]
Capillary Rise
\[ h = \frac{2T\cos\theta}{r\rho g} \]
Young's Modulus
\[ Y = \frac{F/A}{\Delta L/L} \]
Bulk Modulus
\[ B = -\frac{\Delta P}{\Delta V/V} \]
🌡️

11. Thermodynamics & Kinetic Theory

16 Formulas
Important
Ideal Gas Law
\[ PV = nRT \]
R = 8.314 J mol⁻¹ K⁻¹
RMS Speed
\[ v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3kT}{m}} \]
Average Speed
\[ v_{avg} = \sqrt{\frac{8RT}{\pi M}} \]
Most Probable Speed
\[ v_{mp} = \sqrt{\frac{2RT}{M}} \]
Internal Energy (Ideal Gas)
\[ U = \frac{f}{2}nRT \]
f=degrees of freedom (3 mono, 5 diatomic)
Important
First Law of Thermodynamics
\[ \Delta Q = \Delta U + \Delta W \]
Specific Heats Relation
\[ C_p - C_v = R,\quad \gamma = \frac{C_p}{C_v} \]
Thermodynamic Processes
ProcessConditionWork Done
IsothermalT=const\(nRT\ln(V_f/V_i)\)
IsobaricP=const\(P\Delta V = nR\Delta T\)
IsochoricV=const\(W=0\)
AdiabaticQ=0\(\frac{P_1V_1 - P_2V_2}{\gamma-1}\)
Key
Adiabatic Relation
\[ PV^\gamma = \text{constant} \]
Efficiency of Carnot Engine
\[ \eta = 1 - \frac{T_2}{T_1} \]
Stefan–Boltzmann Law
\[ P = e\sigma A T^4 \]
σ = 5.67×10⁻⁸ W m⁻² K⁻⁴
Newton's Law of Cooling
\[ \frac{dT}{dt} = -k(T - T_0) \]
🌊

12. Waves & Sound

14 Formulas
Key
Wave Equation
\[ v = f\lambda \]
Speed of Transverse Wave (String)
\[ v = \sqrt{\frac{T}{\mu}} \]
T=tension, μ=linear mass density
Speed of Sound (Gas)
\[ v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\gamma RT}{M}} \]
Intensity of Wave
\[ I = 2\pi^2 f^2 A^2 \rho v \]
Intensity from Point Source
\[ I = \frac{P}{4\pi r^2} \]
Important
Doppler Effect
\[ f' = f\cdot\frac{V \pm V_o}{V \mp V_s} \]
+Vo when observer moves towards source
Beats
\[ n_{beats} = |f_1 - f_2| \]
Standing Wave Condition
\[ y = 2A\sin(kx)\cos(\omega t) \]
Fundamental Frequency (Closed Pipe)
\[ f_1 = \frac{v}{4L} \]
Fundamental Frequency (Open Pipe)
\[ f_1 = \frac{v}{2L} \]
Loudness (Decibel)
\[ \beta = 10\log_{10}\!\left(\frac{I}{I_0}\right) \text{ dB} \]
I₀ = 10⁻¹² W/m²
⚡

13. Electrostatics

14 Formulas
Important
Coulomb's Law
\[ F = \frac{kq_1 q_2}{r^2} = \frac{q_1 q_2}{4\pi\varepsilon_0 r^2} \]
k = 9×10⁹ N m² C⁻²
Electric Field
\[ E = \frac{F}{q} = \frac{kQ}{r^2} \]
Electric Potential
\[ V = \frac{W}{q} = \frac{kQ}{r} \]
Relation E and V
\[ E = -\frac{dV}{dr} \]
Important
Capacitance
\[ C = \frac{Q}{V} \]
Parallel Plate Capacitor
\[ C = \frac{\varepsilon_0 A}{d} \]
Energy Stored in Capacitor
\[ U = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{QV}{2} \]
Series Capacitance
\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} \]
Parallel Capacitance
\[ C_{eq} = C_1 + C_2 \]
Gauss's Law
\[ \oint \vec{E}\cdot d\vec{A} = \frac{Q_{enc}}{\varepsilon_0} \]
Electric Dipole Moment
\[ p = q \cdot 2l \]
Torque on Dipole
\[ \tau = pE\sin\theta \]
🔌

14. Current Electricity

14 Formulas
Important
Ohm's Law
\[ V = IR \]
Resistance
\[ R = \frac{\rho L}{A} \]
ρ=resistivity, L=length, A=area
Series Resistance
\[ R_{eq} = R_1 + R_2 + \cdots \]
Parallel Resistance
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots \]
Power Dissipation
\[ P = VI = I^2 R = \frac{V^2}{R} \]
Key
Kirchhoff's Current Law (KCL)
\[ \sum I_{in} = \sum I_{out} \]
Key
Kirchhoff's Voltage Law (KVL)
\[ \sum V = 0 \text{ (around any loop)} \]
Wheatstone Bridge (balanced)
\[ \frac{P}{Q} = \frac{R}{S} \]
EMF & Internal Resistance
\[ V = \varepsilon - Ir \]
Drift Velocity
\[ v_d = \frac{I}{nAe} \]
n=electron density, e=electron charge
Temperature Coefficient of Resistance
\[ R_T = R_0(1 + \alpha\Delta T) \]
🧲

15. Magnetism & Moving Charges

12 Formulas
Important
Lorentz Force on Charge
\[ \vec{F} = q(\vec{E} + \vec{v}\times\vec{B}) \]
Force on Current-Carrying Wire
\[ \vec{F} = I\vec{L}\times\vec{B} \]
Key
Biot–Savart Law
\[ dB = \frac{\mu_0}{4\pi}\frac{I\,dl\sin\theta}{r^2} \]
B due to Long Straight Wire
\[ B = \frac{\mu_0 I}{2\pi r} \]
B at Centre of Circular Loop
\[ B = \frac{\mu_0 I}{2R} \]
B inside Solenoid
\[ B = \mu_0 n I \]
n=turns per unit length
Magnetic Moment of Loop
\[ M = NIA \]
Torque on Magnetic Dipole
\[ \tau = MB\sin\theta = \vec{M}\times\vec{B} \]
Cyclotron Frequency
\[ f = \frac{qB}{2\pi m} \]
Ampere's Law
\[ \oint\vec{B}\cdot d\vec{l} = \mu_0 I_{enc} \]
🔁

16. Electromagnetic Induction & AC Circuits

14 Formulas
Important
Magnetic Flux
\[ \Phi = \vec{B}\cdot\vec{A} = BA\cos\theta \]
Important
Faraday's Law (EMF)
\[ \varepsilon = -\frac{d\Phi}{dt} = -N\frac{d\Phi}{dt} \]
Lenz's Law
Induced EMF opposes the change in flux (negative sign in Faraday's law)
Self Inductance
\[ L = \frac{N\Phi}{I},\quad \varepsilon = -L\frac{dI}{dt} \]
Energy Stored in Inductor
\[ U = \frac{1}{2}LI^2 \]
Mutual Inductance
\[ M = \frac{N_2\Phi_{21}}{I_1},\quad \varepsilon_2 = -M\frac{dI_1}{dt} \]
Key
RMS Values (AC)
\[ I_{rms} = \frac{I_0}{\sqrt{2}},\quad V_{rms} = \frac{V_0}{\sqrt{2}} \]
Impedance of Series LCR
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
Inductive & Capacitive Reactance
\[ X_L = \omega L,\quad X_C = \frac{1}{\omega C} \]
Resonance Frequency
\[ \omega_0 = \frac{1}{\sqrt{LC}},\quad f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Power Factor (AC)
\[ \cos\phi = \frac{R}{Z},\quad P_{avg} = V_{rms}I_{rms}\cos\phi \]
Transformer (Turns Ratio)
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} \]
🔭

17. Optics

16 Formulas
Important
Mirror Formula
\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} = \frac{2}{R} \]
Magnification (Mirror)
\[ m = -\frac{v}{u} \]
Important
Snell's Law
\[ n_1\sin\theta_i = n_2\sin\theta_r \]
Refractive Index
\[ n = \frac{c}{v} = \frac{\sin\theta_i}{\sin\theta_r} \]
Critical Angle (TIR)
\[ \sin\theta_c = \frac{n_2}{n_1} = \frac{1}{\mu} \]
Important
Lens Formula
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
Magnification (Lens)
\[ m = \frac{v}{u} \]
Key
Lens Maker's Formula
\[ \frac{1}{f} = (n-1)\!\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]
Power of Lens
\[ P = \frac{1}{f}\text{ (in metres)},\quad \text{unit: Dioptre} \]
Young's Double Slit – Fringe Width
\[ \beta = \frac{\lambda D}{d} \]
D=screen distance, d=slit separation
Condition for Bright Fringes
\[ \Delta x = n\lambda,\quad n = 0,1,2,\ldots \]
Condition for Dark Fringes
\[ \Delta x = (2n-1)\frac{\lambda}{2} \]
Resolving Power (Telescope)
\[ \theta_{min} = \frac{1.22\lambda}{D} \]
Brewster's Angle
\[ \tan\theta_B = n \]
⚛️

18. Modern Physics

16 Formulas
Important
Photon Energy
\[ E = hf = \frac{hc}{\lambda} \]
h = 6.626×10⁻³⁴ J·s (Planck's constant)
Important
Photoelectric Effect (Einstein)
\[ K_{max} = hf - \phi = hf - hf_0 \]
φ=work function, f₀=threshold frequency
Key
de Broglie Wavelength
\[ \lambda = \frac{h}{p} = \frac{h}{mv} \]
Heisenberg Uncertainty Principle
\[ \Delta x\cdot\Delta p \geq \frac{\hbar}{2} \]
ℏ = h/2π
Important
Bohr's Radius (Hydrogen)
\[ r_n = \frac{0.529\,n^2}{Z}\text{ Å} \]
Important
Energy of Electron (Bohr Model)
\[ E_n = -\frac{13.6\,Z^2}{n^2}\text{ eV} \]
Wavelength of Emitted Photon
\[ \frac{1}{\lambda} = R_H Z^2\!\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \]
R_H = 1.097×10⁷ m⁻¹ (Rydberg constant)
Hydrogen Spectral Series
Seriesn₁n₂Region
Lyman12,3,4…UV
Balmer23,4,5…Visible
Paschen34,5,6…IR
Brackett45,6,7…IR
Pfund56,7,8…Far IR
Important
Radioactive Decay Law
\[ N = N_0\,e^{-\lambda t} \]
Key
Half-Life
\[ t_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda} \]
Mean Life
\[ \tau = \frac{1}{\lambda} = \frac{t_{1/2}}{0.693} \]
Mass–Energy Equivalence
\[ E = mc^2 \]
c = 3×10⁸ m/s
Nuclear Binding Energy
\[ BE = \Delta m\cdot c^2 \]
Δm = mass defect
Activity
\[ A = \lambda N = A_0\,e^{-\lambda t} \]