Physics Formula Library
Formulas are useless without meaning. Each page explains what the equation says, defines every variable, states the assumptions and works an example.
⚡ Electricity & Magnetism
C = Q/V — Capacitance
Capacitance equals charge stored divided by voltage across the capacitor.
Coulomb's Law — F = kq₁q₂/r²
The electrostatic force between two point charges is proportional to the product of the charges divided by the square of their separation.
E = kQ/r² — Electric Field of a Point Charge
Electric field equals Coulomb's constant times charge divided by distance squared.
V = kQ/r — Electric Potential of a Point Charge
Electric potential equals Coulomb's constant times charge divided by distance.
Electrical Power — P = IV
Electrical power equals current times voltage.
F = qvB·sinθ — Magnetic Force on a Moving Charge
Magnetic force equals charge times speed times field strength times the sine of the angle.
Ohm's Law — V = IR
Voltage equals current times resistance.
💧 Fluid Mechanics
Bernoulli's Equation — P + ½ρv² + ρgh = constant
Along a streamline, pressure plus kinetic-energy density plus gravitational-energy density stays constant.
F_b = ρVg — Buoyant Force (Archimedes' Principle)
Buoyant force equals fluid density times displaced volume times g.
A₁v₁ = A₂v₂ — Continuity Equation for Fluids
Cross-sectional area times speed is constant along a pipe.
Pressure — P = F/A
Pressure equals force divided by the area it acts on.
🚀 Classical Mechanics
L = Iω — Angular Momentum
Angular momentum equals moment of inertia times angular velocity.
Centripetal Force — F = mv²/r
The inward force needed for circular motion equals mass times speed squared divided by radius.
F = Gm₁m₂/r² — Newton's Law of Universal Gravitation
Gravitational force equals G times the product of the masses divided by the distance squared.
Gravitational Potential Energy — PE = mgh
Gravitational potential energy equals mass times gravity times height.
Hooke's Law — F = kx
The restoring force of a spring equals its stiffness times the displacement from equilibrium.
Kinetic Energy Formula — KE = ½mv²
Kinetic energy equals one-half times mass times velocity squared.
Momentum Formula — p = mv
Momentum equals mass times velocity.
Newton's Second Law — F = ma
The net force on an object equals its mass times its acceleration.
v = √(GM/r) — Circular Orbital Velocity
Orbital speed equals the square root of G times central mass over orbital radius.
T = 2π√(L/g) — Period of a Simple Pendulum
Period equals two pi times the square root of length over g.
Power Formula — P = W/t
Power equals work done divided by the time taken.
PE = ½kx² — Elastic Potential Energy of a Spring
Spring potential energy equals one-half times the spring constant times the stretch squared.
s = ut + ½at² — Displacement under Constant Acceleration
Displacement equals initial velocity times time plus one-half acceleration times time squared.
v = u + at — Velocity from Acceleration and Time
Final velocity equals initial velocity plus acceleration times time.
τ = rF·sinθ — Torque (Moment of Force)
Torque equals lever arm times force times the sine of the angle between them.
Work Formula — W = Fd
Work equals force times distance moved in the direction of the force.
⚛️ Modern Physics
N = N₀(½)^(t/t½) — Radioactive Half-Life Law
Remaining nuclei equal the initial number times one-half raised to the number of elapsed half-lives.
Mass-Energy Equivalence — E = mc²
Energy equals mass times the speed of light squared.
KE_max = hf − Φ — Photoelectric Equation
Maximum electron kinetic energy equals photon energy minus the metal's work function.
🔭 Optics
Lens Equation — 1/f = 1/do + 1/di
The reciprocals of image distance and object distance add up to the reciprocal of the focal length.
m = −dᵢ/dₒ — Lens Magnification
Magnification equals image height over object height, or negative image distance over object distance.
Snell's Law — n₁sinθ₁ = n₂sinθ₂
The product of refractive index and sine of the angle is conserved across a boundary.
🔥 Thermodynamics
η = 1 − T_c/T_h — Carnot Efficiency Limit
Maximum efficiency equals one minus the cold reservoir temperature over the hot reservoir temperature.
Ideal Gas Law — PV = nRT
Pressure times volume equals moles times the gas constant times absolute temperature.
v_rms = √(3RT/M) — Root-Mean-Square Molecular Speed
RMS speed equals the square root of three R T over molar mass.
Specific Heat — Q = mcΔT
Heat transferred equals mass times specific heat times temperature change.
Thermal Efficiency — η = W/Qh
Thermal efficiency equals useful work output divided by heat input.