AP Physics equation sheet formulas

The AP Physics equation sheet provides all essential formulas you need during the exam, organized by topic. According to expert tutors at My Physics Buddy, knowing what is given — and what is not — is one of the most strategic advantages you can have on exam day.

Every Formula on the AP Physics Equation Sheet, Explained

The College Board provides an official reference sheet for AP Physics exams. Think of it like a kitchen spice rack — every ingredient is there, but you still need to know how to cook. Having the formula does not help unless you understand what each symbol means and when to apply it. I have tutored many students who freeze during exams because they see a familiar formula but cannot connect it to the problem in front of them. The goal of this guide is to make sure that never happens to you.

The equation sheet is divided by topic. Below is a comprehensive breakdown of every major formula group, organized the same way College Board presents them. Note that AP Physics 1 and AP Physics 2 share some formulas, while AP Physics C: Mechanics includes calculus-based versions. The table below covers AP Physics 1 and AP Physics 2 combined, which is the most commonly referenced sheet.

Mechanics

These are the backbone of every classical mechanics problem you will encounter.

Formula	Variable Meanings
v = v₀ + at	v = final velocity, v₀ = initial velocity, a = acceleration, t = time
x = x₀ + v₀t + ½at²	x = final position, x₀ = initial position
v² = v₀² + 2a(x − x₀)	Velocity-displacement relation, no time needed
ΣF = Fnet = ma	F = force (N), m = mass (kg), a = acceleration (m/s²)
|Ff| ≤ μ|FN|	μ = coefficient of friction, FN = normal force
ac = v²/r	Centripetal acceleration, r = radius of circular path
p = mv	p = momentum (kg·m/s)
J = FΔt = Δp	J = impulse (N·s)
K = ½mv²	K = kinetic energy (J)
ΔE = W = F·d·cosθ	W = work (J), θ = angle between force and displacement
P = W/t = F·v	P = power (W)
Ug = mgh	Ug = gravitational potential energy, g = 9.8 m/s², h = height
Us = ½kx²	Us = spring potential energy, k = spring constant (N/m), x = compression/extension
Fs = −kx	Hooke’s Law — restoring force of a spring
θ = θ₀ + ω₀t + ½αt²	Rotational kinematics, ω = angular velocity, α = angular acceleration
ω = ω₀ + αt	Rotational analog of v = v₀ + at
x = rθ, v = rω, at = rα	Linear-rotational relationships
τ = r×F = rF sinθ	τ = torque (N·m), r = lever arm
Στ = Iα	I = rotational inertia (kg·m²) — rotational Newton’s 2nd Law
L = Iω	L = angular momentum (kg·m²/s)
K = ½Iω²	Rotational kinetic energy
FG = Gm₁m₂/r²	Newton’s Law of Gravitation, G = 6.674×10⁻¹¹ N·m²/kg²
UG = −Gm₁m₂/r	Gravitational potential energy between two masses
T = 2π√(m/k)	Period of a mass-spring system
T = 2π√(L/g)	Period of a simple pendulum, L = length

Electricity and Magnetism (AP Physics 2)

Formula	Variable Meanings
FE = kq₁q₂/r²	Coulomb’s Law, k = 8.99×10⁵ N·m²/C²
E = F/q	E = electric field (N/C), q = test charge
E = kq/r²	Electric field from a point charge
UE = kq₁q₂/r = qV	UE = electric potential energy, V = electric potential (V)
V = kq/r	Electric potential from a point charge
ΔV = W/q = E·d	Potential difference in a uniform field
C = Q/V	C = capacitance (F), Q = charge stored
C = κε₀A/d	Parallel-plate capacitor, κ = dielectric constant, A = plate area, d = separation
UC = ½QV = ½CV²	Energy stored in a capacitor
I = ΔQ/Δt	I = current (A), Q = charge (C)
R = V/I	Ohm’s Law, R = resistance (Ω)
R = ρL/A	ρ = resistivity, L = length, A = cross-sectional area
P = IΔV = I²R = (ΔV)²/R	Electric power dissipated
F = qv×B = qvB sinθ	Magnetic force on a moving charge, B = magnetic field (T)
F = IL×B = BIL sinθ	Magnetic force on a current-carrying wire
ΦB = B·A·cosθ	ΦB = magnetic flux (Wb)
ε = −ΔΦB/Δt	Faraday’s Law of Induction, ε = induced EMF

Waves, Sound, and Optics

Formula	Variable Meanings
v = fλ	v = wave speed, f = frequency (Hz), λ = wavelength (m)
T = 1/f	T = period (s)
n₁ sinθ₁ = n₂ sinθ₂	Snell’s Law, n = index of refraction
n = c/v	c = speed of light = 3×10⁴ m/s
1/do + 1/di = 1/f	Thin lens and mirror equation
m = −di/do = hi/ho	m = magnification

Thermodynamics and Fluids

Formula	Variable Meanings
PV = nRT	Ideal Gas Law, R = 8.314 J/(mol·K)
Kavg = (3/2)kBT	Average kinetic energy of a gas molecule, kB = Boltzmann constant
ΔU = Q + W	First Law of Thermodynamics
e = W/QH = 1 − QC/QH	Efficiency of a heat engine
eC = 1 − TC/TH	Carnot efficiency
P = F/A	P = pressure (Pa), A = area (m²)
P = P₀ + ρgh	Hydrostatic pressure, ρ = fluid density
Fb = ρVg	Buoyant force (Archimedes’ Principle), V = displaced volume
A₁v₁ = A₂v₂	Continuity equation for fluid flow
P + ½ρv² + ρgh = const	Bernoulli’s equation

Modern and Atomic Physics

Formula	Variable Meanings
E = hf	E = photon energy, h = Planck’s constant = 6.626×10⁻³⁴ J·s
Kmax = hf − φ	Photoelectric effect, φ = work function
λ = h/(mv)	de Broglie wavelength of a particle
E = mc²	Mass-energy equivalence

As a BSc Physical Science graduate from Hansraj College, University of Delhi, I can tell you that the single most useful habit you can develop is writing each formula with labelled variables every time you use it during practice — not just copying it. That habit alone bridges the gap between recognizing a formula and actually applying it under exam pressure. You can find the official College Board reference sheet directly on the College Board AP Physics equation tables page to compare against this guide.

One analogy I use with students: think of the equation sheet as a dictionary, not a manual. If you do not know what the words mean or how to build a sentence, having a dictionary does not help you write a paragraph. Each formula is a sentence structure — you need to know the grammar (physics principles) behind it.

Common Mistakes with the AP Physics Equation Sheet

✗ Mistake: Assuming every formula you need is on the sheet — students skip memorizing definitions and conceptual relationships that are not listed.
✓ Fix: Know that quantities like the period of a wave (T = 1/f) and definitions such as average velocity (v_avg = Δx/Δt) may appear unlisted. Learn the underlying physics, not just the sheet.

✗ Mistake: Mixing up AP Physics 1 and AP Physics 2 formula sheets — some students study from the wrong sheet entirely.
✓ Fix: Download the specific equation sheet for your exact exam from the College Board website and practice exclusively with that one.

✗ Mistake: Ignoring the constants and conversion tables at the top of the sheet — students forget that values like g = 9.8 m/s² and k_B are provided there.
✓ Fix: Spend five minutes at the start of each practice session reading the constants table. You should know every symbol and its value before exam day.

Exam Relevance: The AP Physics equation sheet is central to both the AP Physics 1 and AP Physics 2 exams administered by College Board. Similar reference sheets appear in IB Physics HL/SL and A/AS Level Physics (9702) exams as well.

💡 Pro Tip from Mohit H: During practice tests, always start by flipping to the equation sheet and spending 60 seconds reminding yourself what topics are covered — it primes your brain to spot the right formulas faster under pressure.