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Formula Sheet Library
Clean, printable reference sheets for every AP Physics course — better than the College Board version.
AP Physics 1 — Formula Sheet
Kinematics
Avg velocityv_avg = Δx/t
Velocity (const. a)v = v₀ + at
Position (const. a)x = x₀ + v₀t + ½at²
Velocity–displacementv² = v₀² + 2aΔx
Displacement (avg v)Δx = ½(v+v₀)t
Forces
Newton's 2nd lawF = ma
Weightw = mg
Kinetic frictionf_k = μ_k · N
Max static frictionf_s ≤ μ_s · N
Hooke's lawF = −kΔx
Circular Motion & Gravity
Centripetal accel.a_c = v²/r
Centripetal forceF_c = mv²/r
Orbital speedv = 2πr/T
Period–frequencyT = 1/f
GravityF_g = GMm/r²
Energy & Work
Kinetic energyK = ½mv²
Gravitational PEU_g = mgh
Spring PEU_s = ½kΔx²
WorkW = Fd cosθ
PowerP = W/t = Fv
Momentum
Momentump = mv
ImpulseJ = FΔt = Δp
Conservation (elastic)Σp_i = Σp_f
Simple Harmonic Motion
Period — springT = 2π√(m/k)
Period — pendulumT = 2π√(L/g)
Max speedv_max = Aω
Angular frequencyω = 2πf = 2π/T
Rotation
Torqueτ = rF sinφ
Newton's 2nd (rot.)τ = Iα
Angular momentumL = Iω
Rotational KEK = ½Iω²
Angular kinematicsω = ω₀ + αt
Waves & Circuits
Wave speedv = fλ
Ohm's lawV = IR
Electric powerP = IV = I²R
Series RR_s = ΣR_i
Parallel R1/R_p = Σ1/R_i
AP Physics 2 — Formula Sheet
Electrostatics
Coulomb's lawF = k|q₁q₂|/r²
Electric fieldE = kq/r²
Force on chargeF = qE
Electric potentialV = kq/r
Potential energyU = qV = kq₁q₂/r
Capacitance
CapacitanceC = Q/V
Parallel plateC = κε₀A/d
Energy storedU = ½CV²
Series C1/C_s = Σ1/C_i
Parallel CC_p = ΣC_i
DC Circuits
Ohm's lawV = IR
PowerP = IV = I²R = V²/R
Series RR_s = ΣR_i
Parallel R1/R_p = Σ1/R_i
Terminal voltageV = ε − Ir
Magnetism
Force on chargeF = qvB sinθ
Force on wireF = ILB sinθ
Magnetic fluxΦ = BA cosθ
Faraday's lawε = −NΔΦ/Δt
Circular radiusr = mv/(|q|B)
Optics
Wave speedc = fλ
Snell's lawn₁sinθ₁ = n₂sinθ₂
Thin lens/mirror1/d_o + 1/d_i = 1/f
Magnificationm = −d_i/d_o
Double-slity = mλL/d
Modern Physics
Photon energyE = hf = hc/λ
Photoelectric effectKE_max = hf − φ
de Brogliep = h/λ
Mass-energyE = mc²
Thermodynamics & Fluids
Ideal gas lawPV = nRT = Nk_BT
Avg molecular KEKE = (3/2)k_BT
Fluid pressureP = P₀ + ρgh
AP Physics C: Mechanics — Formula Sheet
Kinematics
Velocity (const. a)v = v₀ + at
Position (const. a)x = x₀ + v₀t + ½at²
Velocity–displacementv² = v₀² + 2aΔx
Calculus formv = dx/dt, a = dv/dt
Forces & Energy
Newton's 2ndF = ma = dp/dt
Work (variable F)W = ∫F·dx
KEK = ½mv²
Spring PEU_s = ½kx²
PowerP = dW/dt = F·v
Momentum
Momentump = mv
ImpulseJ = ∫F dt = Δp
Center of massx_cm = Σmᵢxᵢ / Σmᵢ
CM velocityv_cm = Σmᵢvᵢ / Σmᵢ
Rotation
Torqueτ = r × F = Iα
Angular momentumL = Iω = r × p
Rotational KEK = ½Iω²
Rolling KEK = ½mv² + ½Iω²
Rolling constraintv_cm = Rω
Moments of Inertia
Point massI = mr²
Solid sphereI = (2/5)mr²
Hollow sphereI = (2/3)mr²
Solid cylinderI = ½mr²
Rod (center)I = (1/12)mL²
Parallel axis thm.I = I_cm + md²
SHM & Gravitation
SHM equationa = −ω²x
Period — springT = 2π√(m/k)
Period — pendulumT = 2π√(L/g)
GravityF_g = GMm/r²
Orbital speedv = √(GM/r)
Kepler's 3rdT² = (4π²/GM)r³
AP Physics C: E&M — Formula Sheet
Electrostatics
Coulomb's lawF = kq₁q₂/r²
Electric fieldE = kq/r²
Potential (point)V = kq/r
E from VE = −dV/dx
Potential energyU = qV = kq₁q₂/r
Gauss's Law
Gauss's law∮E·dA = Q_enc/ε₀
E — sphereE = kQ/r² (r > R)
E — infinite planeE = σ/(2ε₀)
E — infinite wireE = λ/(2πε₀r)
Capacitance
DefinitionC = Q/V
Parallel plateC = κε₀A/d
Energy storedU = ½CV² = Q²/2C
RC time constantτ = RC
RC chargingQ = Q_max(1 − e^(−t/τ))
DC Circuits
CurrentI = dQ/dt
Ohm's lawV = IR
ResistivityR = ρL/A
PowerP = IV = I²R
Terminal voltageV = ε − Ir
Magnetism
Force on chargeF = qv × B
Force on wireF = IL × B
B — long wireB = μ₀I/(2πr)
Ampere's law∮B·dl = μ₀I_enc
B — solenoidB = μ₀nI
Induction & RL/LC
Magnetic fluxΦ_B = ∫B·dA
Faraday's lawε = −dΦ_B/dt
Inductor EMFε = −L(dI/dt)
Energy in inductorU = ½LI²
RL time constantτ = L/R
LC frequencyω = 1/√(LC)