AP Physics Formula Sheet — Physics 1, Physics 2 and C Key Equations

Every key equation for AP Physics 1 and AP Physics 2 in one place, organised by topic, with a plain-English note on when to reach for each one. A few extra equations needed for AP Physics C are included and clearly marked [C]. Good news: the College Board hands you an equation sheet inside the exam itself — so you do not need to memorise these by rote. What scores marks is recognising which equation fits a situation and what each symbol means, and that is exactly what this page trains.

Key Constants

Acceleration due to gravity g = 9.8 m/s² (the College Board accepts g = 10 m/s² for estimates)
Speed of light in a vacuum c = 3.00 × 10⁸ m/s
Universal gravitational constant G = 6.67 × 10⁻¹¹ N m²/kg²
Coulomb’s law constant k = 8.99 × 10⁹ N m²/C²
Elementary charge e = 1.60 × 10⁻¹⁹ C
Planck’s constant h = 6.63 × 10⁻³⁴ J s
Electron mass m_e = 9.11 × 10⁻³¹ kg
Proton mass m_p = 1.67 × 10⁻²⁷ kg
Permittivity of free space ε₀ = 8.85 × 10⁻¹² C²/(N m²)
Boltzmann constant k_B = 1.38 × 10⁻²³ J/K
Gas constant R = 8.31 J/(mol K)

Kinematics & Dynamics (Physics 1)

Equation	What it is / When to use it
v = v₀ + at	Final velocity after time t under constant acceleration. The first of the three big kinematics equations.
x = x₀ + v₀t + ½at²	Position after time t under constant acceleration. Use when time is known or asked for and final velocity is not.
v² = v₀² + 2aΔx	Links velocities and displacement with no time involved. The go-to equation when a problem never mentions time.
F_net = ma	Newton’s second law: add all force vectors first, then divide by mass. Almost every dynamics problem starts here.
f ≤ μN	Friction: kinetic friction equals μ_kN; static friction adjusts up to a maximum of μ_sN. It is an inequality, not always an equality.
a_c = v²/r, F_c = mv²/r	Centripetal acceleration and the net inward force needed for circular motion. Centripetal force is a role played by tension, gravity or friction — never an extra force to add.
τ = rF sin θ	Torque: the turning effect of a force. Maximum when the force is perpendicular to the lever arm (sin θ = 1), zero when it points along it.
Δθ = ω₀t + ½αt², ω = ω₀ + αt, τ_net = Iα	Rotational analogues of the linear equations: θ (angle) → x, ω (angular velocity) → v, α (angular acceleration) → a, and torque plays the role of force. If you know the linear version, you know the rotational one.
I = Σ m_ir_i² (e.g. hoop I = MR², solid disk I = ½MR², rod about centre I = (1/12)ML²)	Moment of inertia: rotational inertia. Mass far from the axis counts much more than mass near it, because r is squared.
L = Iω = r p sin θ	Angular momentum, for a spinning object (Iω) or a moving particle (r p sin θ). Conserved whenever the net external torque is zero.
KE_rot = ½Iω²	Rotational kinetic energy. Rolling objects carry both this and ½mv² — forgetting one of them is a classic lost mark.

Energy, Work & Momentum (Physics 1)

Equation	What it is / When to use it
W = Fd cos θ	Work done by a constant force: only the component of force along the displacement does work. Work is the area under a force–position graph.
KE = ½mv²	Translational kinetic energy. Doubling speed quadruples it.
ΔKE = W_net	Work–energy theorem: the net work done on an object equals its change in kinetic energy. Often faster than Newton’s laws when only speeds matter.
GPE = mgh (near Earth’s surface)	Gravitational potential energy. Only the change in height matters; you may set h = 0 wherever is convenient.
F_s = −kx, PE_s = ½kx²	Hooke’s law and spring potential energy. The minus sign means the force always points back towards equilibrium.
P = W/t = Fv	Power: the rate of doing work or transferring energy, in watts. P = Fv applies when a force acts at constant velocity.
p = mv	Linear momentum, a vector. It depends on velocity, not speed alone.
J = Δp = FΔt	Impulse equals change in momentum, and equals the area under a force–time graph. Explains why airbags help: same Δp, longer Δt, smaller F.
m₁v₁ + m₂v₂ = constant (no external impulse)	Conservation of momentum: holds in every collision and explosion, elastic or not, as long as external impulses are negligible.
Elastic collision: KE is also conserved, and v₁ − v₂ = −(v₁′ − v₂′)	In an elastic collision both momentum and kinetic energy survive, and the relative speed of approach equals the relative speed of separation.
Perfectly inelastic collision: objects stick, only momentum is conserved	Maximum kinetic energy is lost when the objects move off together with a single shared velocity. Never apply KE conservation here.
T_spring = 2π√(m/k)	Period of a mass on a spring. Depends on mass and stiffness only — not on amplitude or gravity.
T_pendulum = 2π√(L/g)	Period of a simple pendulum for small swings. Depends on length and g only — not on the bob’s mass.
x(t) = A cos(2πft), f = 1/T	Position in simple harmonic motion. Velocity is greatest at equilibrium, acceleration is greatest (and directed back to equilibrium) at the extremes.

Fluids & Thermodynamics (Physics 2)

Equation	What it is / When to use it
ρ = m/V	Density: mass per unit volume. The property that decides floating, sinking and buoyant force.
P = F/A	Pressure: force per unit area, in pascals. A fluid pushes equally in all directions at a given depth.
P = P₀ + ρgh	Pressure at depth h in a static fluid: surface pressure plus the weight of the fluid column above.
F_b = ρ_fluidV_displacedg	Buoyant force (Archimedes’ principle): it equals the weight of displaced fluid. Use the submerged volume, not the object’s total volume.
A₁v₁ = A₂v₂	Continuity equation: for an incompressible fluid, where the pipe narrows the flow speeds up.
P + ρgy + ½ρv² = constant	Bernoulli’s equation along a streamline: where a fluid moves faster, its pressure is lower (for steady, incompressible, low-viscosity flow).
PV = nRT	Ideal gas law, with T in kelvin. Links pressure, volume, amount of gas and absolute temperature.
Average KE per molecule = (3/2)k_BT	Kinetic theory: absolute temperature is a direct measure of the average kinetic energy of the molecules.
ΔU = Q + W	First law of thermodynamics. AP sign convention: W is the work done ON the gas, so compressing a gas makes W positive; Q is positive when heat flows into the gas. (Many textbooks write ΔU = Q − W with W done BY the gas — same physics, opposite sign for W.)
Efficiency = W_out/Q_h = 1 − Q_c/Q_h	Heat engine efficiency: useful work out divided by heat taken from the hot reservoir.
Carnot efficiency = 1 − T_c/T_h	The maximum possible efficiency between two temperatures (kelvin). No real engine between the same reservoirs can beat it.

Electricity & Magnetism (Physics 2, plus Physics 1 circuits)

Equation	What it is / When to use it
F = kq₁q₂/r²	Coulomb’s law: the force between two point charges. Like charges repel, unlike charges attract, and the force falls with the square of the separation.
E = F/q, and for a point charge E = kq/r²	Electric field strength: force per unit positive test charge. Field lines point away from positive charges and towards negative ones.
V = kq/r	Electric potential of a point charge: a scalar, so potentials from several charges simply add (no directions to resolve).
U = qV, ΔU = qΔV	Electric potential energy of a charge in a potential. A charge released in a field trades this energy for kinetic energy.
C = Q/V	Capacitance: charge stored per volt. It depends on the capacitor’s geometry, not on Q or V themselves.
C = ε₀A/d	Parallel-plate capacitance: bigger plates or a smaller gap store more. Inserting a dielectric multiplies C by the dielectric constant κ.
U_C = ½QV = ½CV² = Q²/2C	Energy stored in a capacitor. The factor ½ appears because the voltage grows as the capacitor charges.
I = ΔQ/Δt	Electric current: rate of flow of charge, in amperes. Conventional current flows from + to − outside the battery.
R = ρL/A	Resistance of a uniform wire: longer and thinner means more resistance; ρ is the resistivity of the material.
V = IR	Ohm’s law. Applies to each component and to whole circuits; combine with the power forms below.
P = IV = I²R = V²/R	Electrical power dissipated. Pick the form using the quantities that stay constant in the question.
Series: R_eq = R₁ + R₂ + …; Parallel: 1/R_eq = 1/R₁ + 1/R₂ + …	Series resistors share the same current and resistances add (equivalent is bigger than the biggest). Parallel resistors share the same voltage and the equivalent is smaller than the smallest.
Capacitors: series 1/C_eq = 1/C₁ + 1/C₂ + …; parallel C_eq = C₁ + C₂ + …	Capacitor rules are the reverse of the resistor rules: parallel capacitors add, series capacitors combine reciprocally.
F = qvB sin θ	Magnetic force on a moving charge. Zero if the charge moves parallel to the field; direction from the right-hand rule (reverse it for electrons).
F = BIL sin θ	Magnetic force on a current-carrying wire of length L in a field. Maximum when the wire is perpendicular to the field.
B = μ₀I/(2πr)	Magnetic field around a long straight wire (μ₀ = 4π × 10⁻⁷ T m/A). Circles the wire; use the right-hand grip rule for direction.
Φ = BA cos θ	Magnetic flux through a loop: field × area × the cosine of the angle between the field and the loop’s normal (perpendicular) direction.
EMF = −N ΔΦ/Δt	Faraday’s law: a changing magnetic flux induces an EMF. The minus sign is Lenz’s law — the induced effect opposes the change that caused it.

Waves, Sound & Optics (Physics 1 + 2)

Equation	What it is / When to use it
v = fλ	Wave speed = frequency × wavelength. True for every wave; the medium sets the speed, the source sets the frequency.
String fixed at both ends: λ_n = 2L/n, f_n = nv/2L	Standing waves on a string: all harmonics (n = 1, 2, 3, …) are present. A node sits at each fixed end.
Open pipe (both ends open): λ_n = 2L/n	All harmonics again, with an antinode at each open end — same maths as the string.
Closed pipe (one end closed): λ_n = 4L/n for odd n only	Only odd harmonics (n = 1, 3, 5, …) fit, because the closed end must be a node and the open end an antinode.
n₁ sin θ₁ = n₂ sin θ₂	Snell’s law: how light bends at a boundary. Entering a denser medium (bigger n) bends it towards the normal, and its speed becomes v = c/n.
1/f = 1/d_o + 1/d_i	Lens/mirror equation: links focal length, object distance and image distance. Real images form on the same side light reaches (positive d_i).
m = −d_i/d_o = h_i/h_o	Magnification: image size over object size. A negative m means the image is inverted; \|m\| > 1 means enlarged.
d sin θ = mλ	Double-slit interference maxima: the path difference for a bright fringe is a whole number of wavelengths (m = 0, 1, 2, …).
x = mλL/d	Small-angle form: position of the m-th bright fringe on a screen a distance L away, where d is the slit separation. Fringe spacing Δx = λL/d.
Diffraction grating: d sin θ = mλ, with d = 1/(lines per metre)	Same form as the double slit, but with many slits the maxima are much sharper and brighter. Single-slit dark fringes instead sit at a sin θ = mλ (a = slit width, m ≠ 0).

Modern Physics (Physics 2)

Equation	What it is / When to use it
E = hf	Photon energy: light comes in packets whose energy depends only on frequency. Also E = hc/λ when you are given wavelength.
KE_max = hf − φ	Photoelectric equation: photon energy minus the work function φ (energy needed to escape the metal) leaves the fastest electrons’ kinetic energy. Below the threshold frequency f₀ = φ/h, nothing is emitted at all.
λ = h/p	de Broglie wavelength: every moving particle has wave behaviour. It only becomes noticeable for very small masses and momenta.
E_n = −13.6/n² eV	Bohr model energy levels for hydrogen. A transition’s photon energy is the difference between levels: ΔE = E_initial − E_final (emitted) or the reverse (absorbed).
r_n = n²a₀, with a₀ = 5.29 × 10⁻¹¹ m	Bohr orbit radii grow with n²: the electron’s allowed orbits spread out quickly as the energy level rises.
E = mc²	Mass–energy equivalence. The binding energy of a nucleus equals its mass defect (mass of separate nucleons minus mass of the nucleus) multiplied by c²; that loss of mass is why fused/fissioned nuclei release energy.

AP Physics C Additions [C]

Equation	What it is / When to use it
[C] W = ∫ F dx	Work by a variable force is the integral of force over displacement — this is why spring work comes out as ½kx². Rotational version: W = ∫ τ dθ, and P = τω.
[C] τ = dL/dt, I = ∫ r² dm	Rotational dynamics with calculus: net torque is the rate of change of angular momentum, and moment of inertia for a continuous body is built up by integration.
[C] Gauss’s law: Φ_E = Q_enclosed/ε₀	The electric flux through any closed surface depends only on the charge inside it. Use symmetry (spheres, cylinders, planes) to pull E out of the flux integral and find fields efficiently.
[C] Ampère’s law: ∫ B · dl = μ₀I_enclosed	The magnetic equivalent of Gauss’s law: the circulation of B around a closed loop equals μ₀ times the current passing through the loop. Best for wires, solenoids and toroids.
[C] RC circuits: charging q = Q(1 − e^−t/RC), discharging q = Qe^−t/RC, time constant τ = RC	Capacitor charge and current change exponentially, never linearly. After one time constant the quantity has moved about 63% of the way (charging) or fallen to about 37% (discharging).
[C] LC oscillation: ω = 1/√(LC), T = 2π√(LC)	An inductor–capacitor circuit oscillates as energy swaps between the capacitor’s electric field and the inductor’s magnetic field — the electrical analogue of a mass on a spring.
[C] Maxwell’s equations (idea)	Changing electric fields create magnetic fields just as changing magnetic fields create electric fields; together the four equations predict self-propagating electromagnetic waves travelling at c = 1/√(ε₀μ₀).

Keep Going with Physics on QuaidianPoint

Work through free practice questions on the Physics hub, and keep the matching formula sheet for your course open beside it:

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