Physics Formula Sheet
A complete, free physics formula sheet — all 174 formulas organized by topic. Use the interactive searcher to find a formula by any variable, solve for any unknown, and convert units.
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| Average velocity | v = Δx / Δt |
| Average acceleration | a = Δv / Δt |
| Velocity (constant a) | v = u + a·t |
| Displacement (suvat) | s = u·t + ½·a·t² |
| Velocity² (suvat) | v² = u² + 2·a·s |
| Displacement (avg velocity) | s = ½·(u + v)·t |
| Projectile range | R = (v²·sin2θ) / g |
| Position (general) | x = x₀ + v₀·t + ½·a·t² |
| Average speed | v̄ = d / t |
| Relative velocity | v_AB = v_A − v_B |
| Projectile time of flight | t = 2·v·sinθ / g |
| Projectile max height | H = v²·sin²θ / (2·g) |
| Free fall velocity | v = g·t |
| Free fall distance | h = ½·g·t² |
| Jerk | j = da / dt |
| Newton's second law | F = m·a |
| Weight | W = m·g |
| Friction force | f = μ·N |
| Hooke's law | F = -k·x |
| Centripetal force | F = m·v² / r |
| Centripetal acceleration | a = v² / r |
| Impulse | J = F·Δt = Δp |
| Tension (Atwood) | T = 2·m₁·m₂·g / (m₁+m₂) |
| Inclined plane (parallel) | F = m·g·sinθ |
| Inclined plane (normal) | N = m·g·cosθ |
| Static friction (max) | f_s = μ_s·N |
| Drag force | F_d = ½·ρ·v²·C_d·A |
| Terminal velocity | v_t = √(2·m·g / (ρ·A·C_d)) |
| Spring force constant | k = F / x |
| Banked curve angle | tanθ = v² / (r·g) |
| Linear momentum | p = m·v |
| Angular momentum | L = I·ω |
| Conservation of momentum | m₁·u₁ + m₂·u₂ = m₁·v₁ + m₂·v₂ |
| Elastic collision (1D) | v₁ = ((m₁−m₂)·u₁ + 2·m₂·u₂)/(m₁+m₂) |
| Coefficient of restitution | e = (v₂−v₁)/(u₁−u₂) |
| Center of mass | x_cm = Σ(mᵢ·xᵢ) / Σmᵢ |
| Rocket equation | Δv = v_e·ln(m₀/m_f) |
| Angular impulse | ΔL = τ·Δt |
| Work done | W = F·d·cosθ |
| Kinetic energy | KE = ½·m·v² |
| Gravitational PE | PE = m·g·h |
| Elastic PE | PE = ½·k·x² |
| Power | P = W / t |
| Power (force·velocity) | P = F·v |
| Efficiency | η = E_out / E_in |
| Work–energy theorem | W = ΔKE |
| Power (average) | P̄ = ΔE / Δt |
| Mechanical energy | E = KE + PE |
| Gravitational PE (orbital) | E = −G·M·m / (2·r) |
| Torque | τ = r·F·sinθ |
| Angular velocity | ω = θ / t |
| Rotational KE | KE = ½·I·ω² |
| Angular acceleration | α = Δω / Δt |
| Rotational Newton's 2nd law | τ = I·α |
| Moment of inertia (point) | I = m·r² |
| Moment of inertia (disk) | I = ½·m·r² |
| Moment of inertia (rod, center) | I = (1/12)·m·L² |
| Tangential velocity | v = r·ω |
| Tangential acceleration | a_t = r·α |
| Angular displacement | θ = ω₀·t + ½·α·t² |
| Rolling kinetic energy | KE = ½·m·v² + ½·I·ω² |
| Newton's gravitation | F = G·m₁·m₂ / r² |
| Gravitational field | g = G·M / r² |
| Gravitational PE (general) | U = −G·m₁·m₂ / r |
| Orbital velocity | v = √(G·M / r) |
| Escape velocity | v_e = √(2·G·M / r) |
| Kepler's third law | T² = (4π²/G·M)·r³ |
| Gravitational potential | V = −G·M / r |
| Orbital period | T = 2π·√(r³ / (G·M)) |
| Wave speed | v = f·λ |
| Period & frequency | T = 1 / f |
| SHM displacement | x = A·cos(ω·t) |
| Pendulum period | T = 2π·√(L / g) |
| SHM velocity | v = −A·ω·sin(ω·t) |
| SHM acceleration | a = −ω²·x |
| SHM max velocity | v_max = A·ω |
| Mass-spring period | T = 2π·√(m / k) |
| Angular frequency | ω = 2π·f |
| Wave equation (number) | k = 2π / λ |
| Doppler effect (sound) | f' = f·(v ± v_o)/(v ∓ v_s) |
| Standing wave frequency | f_n = n·v / (2·L) |
| Speed of wave on string | v = √(T / μ) |
| Intensity | I = P / A |
| Sound intensity level | β = 10·log(I / I₀) |
| Beat frequency | f_beat = |f₁ − f₂| |
| Ohm's law | V = I·R |
| Electrical power | P = V·I |
| Electrical energy | E = V·I·t |
| Charge | Q = I·t |
| Coulomb's law | F = k·q₁·q₂ / r² |
| Capacitance | C = Q / V |
| Resistivity | R = ρ·L / A |
| Magnetic force on wire | F = B·I·L |
| Force on moving charge | F = q·v·B |
| Resistors in series | R_eq = R₁ + R₂ + … |
| Resistors in parallel | 1/R_eq = 1/R₁ + 1/R₂ + … |
| Capacitors in parallel | C_eq = C₁ + C₂ + … |
| Capacitors in series | 1/C_eq = 1/C₁ + 1/C₂ + … |
| Power (I²R) | P = I²·R |
| Power (V²/R) | P = V² / R |
| Electric field (point charge) | E = k·q / r² |
| Electric field (force) | E = F / q |
| Electric potential energy | U = k·q₁·q₂ / r |
| Electric potential | V = k·q / r |
| Capacitor energy | E = ½·C·V² |
| Parallel plate capacitor | C = ε₀·A / d |
| Drift velocity | I = n·A·q·v_d |
| Magnetic flux | Φ = B·A·cosθ |
| Faraday's law | ε = −N·dΦ/dt |
| Solenoid field | B = μ₀·n·I |
| Field around wire | B = μ₀·I / (2π·r) |
| Transformer ratio | V_s/V_p = N_s/N_p |
| Heat energy | Q = m·c·ΔT |
| Latent heat | Q = m·L |
| Ideal gas law | P·V = n·R·T |
| Pressure | P = F / A |
| Density | ρ = m / V |
| First law of thermodynamics | ΔU = Q − W |
| Thermal expansion (linear) | ΔL = α·L₀·ΔT |
| Thermal expansion (volume) | ΔV = β·V₀·ΔT |
| Heat conduction | Q/t = k·A·ΔT / L |
| Carnot efficiency | η = 1 − T_c / T_h |
| Entropy change | ΔS = Q / T |
| Average KE of gas | KE = (3/2)·k_B·T |
| RMS molecular speed | v_rms = √(3·k_B·T / m) |
| Work in isobaric process | W = P·ΔV |
| Stefan–Boltzmann law | P = σ·A·e·T⁴ |
| Wien's displacement law | λ_max = b / T |
| Mass–energy | E = m·c² |
| Photon energy | E = h·f |
| de Broglie wavelength | λ = h / p |
| Photoelectric effect | E = h·f − φ |
| Relativistic momentum | p = γ·m·v |
| Lorentz factor | γ = 1 / √(1 − v²/c²) |
| Time dilation | Δt = γ·Δt₀ |
| Length contraction | L = L₀ / γ |
| Relativistic energy | E = γ·m·c² |
| Energy–momentum relation | E² = (p·c)² + (m·c²)² |
| Heisenberg uncertainty | Δx·Δp ≥ ħ / 2 |
| Bohr radius / energy | E_n = −13.6 eV / n² |
| Rydberg formula | 1/λ = R·(1/n₁² − 1/n₂²) |
| Compton wavelength shift | Δλ = (h/m_e·c)·(1 − cosθ) |
| Snell's law | n₁·sinθ₁ = n₂·sinθ₂ |
| Index of refraction | n = c / v |
| Thin lens equation | 1/f = 1/d_o + 1/d_i |
| Magnification | M = −d_i / d_o = h_i / h_o |
| Critical angle | sinθ_c = n₂ / n₁ |
| Mirror equation | 1/f = 1/d_o + 1/d_i |
| Double slit (maxima) | d·sinθ = m·λ |
| Diffraction grating | d·sinθ = n·λ |
| Lens power | P = 1 / f |
| Pressure in fluid | P = ρ·g·h |
| Buoyant force | F_b = ρ·g·V |
| Continuity equation | A₁·v₁ = A₂·v₂ |
| Bernoulli's equation | P + ½·ρ·v² + ρ·g·h = const |
| Flow rate | Q = A·v |
| Viscous drag (Stokes) | F = 6π·η·r·v |
| Reynolds number | Re = ρ·v·L / η |
| RMS voltage | V_rms = V₀ / √2 |
| RMS current | I_rms = I₀ / √2 |
| Capacitive reactance | X_C = 1 / (2π·f·C) |
| Inductive reactance | X_L = 2π·f·L |
| Impedance (RLC) | Z = √(R² + (X_L − X_C)²) |
| Resonant frequency | f₀ = 1 / (2π·√(L·C)) |
| Inductor energy | E = ½·L·I² |
| Radioactive decay | N = N₀·e^(−λ·t) |
| Half-life | t½ = ln2 / λ |
| Activity | A = λ·N |
| Mass defect energy | E = Δm·c² |
| Binding energy per nucleon | BE/A = (Δm·c²) / A |
| Schwarzschild radius | r_s = 2·G·M / c² |
| Hubble's law | v = H₀·d |
| Luminosity (inverse square) | b = L / (4π·d²) |
| Stellar luminosity | L = 4π·R²·σ·T⁴ |