---
title: "Ultimate AP Physics 2 Equation Sheets"
description: "Every AP Physics 2 equation you need to know, straight from the official reference sheet, to help you get a 5 on the AP Physics 2 Exam."
url: "https://nerd-notes.com/ap-physics-2-formula-sheets/"
date_modified: "2026-10-02T05:47:10+00:00"
---

# Ultimate AP Physics 2 Equation Sheets

Every equation and constant on the official AP Physics 2 exam reference sheet, in one interactive digital sheet with each formula tagged by unit.

- [View Digital Equation Sheet](https://nerd-notes.com/ap-physics-2-formula-sheets/#eq-official) (jumps to the digital sheet at the bottom of this page)

## And even more free resources to help you get a 5

- For AP-style questions, [check out UBQ.](https://nerd-notes.com/ubq/?subject=physics-2)
- For AP-style Practice Exams, [check out UBQ Quiz Labs.](https://nerd-notes.com/quiz/?subject=physics-2)
- For AP Physics 2 practice questions sorted by unit, [click here.](https://nerd-notes.com/subjects/ap-physics-2/)
- Use Phy to solve and explain hard questions. [Try here.](https://nerd-notes.com/ai/)

## Official 2026 Digital Equation Sheet

Also built into every AP Physics 2 question on [UBQ](https://nerd-notes.com/ubq/?subject=physics-2), or [download the official PDF](https://apcentral.collegeboard.org/media/pdf/ap-physics-2-equations-sheet.pdf).

On the page this is an interactive sheet: a sticky tab bar jumps between its sections, and hovering (or focusing) an equation shows its name and the AP Physics 2 unit it belongs to. Its full content follows: College Board's "AP Physics 2 2026 Exam Reference Information", transcribed, with each equation's name and CED unit as the page shows them on hover.

AP Physics 2 units: 9 Thermodynamics · 10 Electric Force, Field, and Potential · 11 Electric Circuits · 12 Magnetism and Electromagnetism · 13 Geometric Optics · 14 Waves, Sound, and Physical Optics · 15 Modern Physics.

### Electricity Equations

- Coulomb's law (Unit 10: Electric Force, Field, and Potential): $\begin{aligned} \left|\vec{F}_E\right| &= \frac{1}{4\pi\varepsilon_0}\frac{\left|q_1 q_2\right|}{r^2} \\ &= k\frac{\left|q_1 q_2\right|}{r^2} \end{aligned}$
- Electric field (definition) (Unit 10: Electric Force, Field, and Potential): $\vec{E} = \frac{\vec{F}_E}{q}$
- Electric field of a point charge (Unit 10: Electric Force, Field, and Potential): $\left|\vec{E}\right| = \frac{1}{4\pi\varepsilon_0}\frac{\left|q\right|}{r^2} = k\frac{\left|q\right|}{r^2}$
- Electric potential energy of two point charges (Unit 10: Electric Force, Field, and Potential): $U_E = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r} = k\frac{q_1 q_2}{r}$
- Change in electric potential energy (Unit 10: Electric Force, Field, and Potential): $\Delta U_E = q\Delta V$
- Electric potential of point charges (Unit 10: Electric Force, Field, and Potential): $V = \frac{1}{4\pi\varepsilon_0}\sum_i \frac{q_i}{r_i}$
- Electric field and potential difference (Unit 10: Electric Force, Field, and Potential): $\left|\vec{E}\right| = \left|\frac{\Delta V}{\Delta r}\right|$
- Capacitance (definition) (Unit 10: Electric Force, Field, and Potential): $C = \frac{Q}{\Delta V}$
- Parallel-plate capacitance (Unit 10: Electric Force, Field, and Potential): $C = \kappa\varepsilon_0\frac{A}{d}$
- Electric field in a parallel-plate capacitor (Unit 10: Electric Force, Field, and Potential): $E_C = \frac{Q}{\kappa\varepsilon_0 A}$
- Energy stored in a capacitor (Unit 10: Electric Force, Field, and Potential): $U_C = \frac{1}{2}Q\Delta V$
- Electric current (Unit 11: Electric Circuits): $I = \frac{\Delta q}{\Delta t}$
- Resistance and resistivity (Unit 11: Electric Circuits): $R = \frac{\rho\ell}{A}$
- Electric power (Unit 11: Electric Circuits): $P = I\Delta V$
- Ohm's law (Unit 11: Electric Circuits): $I = \frac{\Delta V}{R}$
- Resistors in series (Unit 11: Electric Circuits): $R_{\text{eq},s} = \sum_i R_i$
- Resistors in parallel (Unit 11: Electric Circuits): $\frac{1}{R_{\text{eq},p}} = \sum_i \frac{1}{R_i}$
- Capacitors in series (Unit 11: Electric Circuits): $\frac{1}{C_{\text{eq},s}} = \sum_i \frac{1}{C_i}$
- Capacitors in parallel (Unit 11: Electric Circuits): $C_{\text{eq},p} = \sum_i C_i$
- RC time constant (Unit 11: Electric Circuits): $\tau = R_{\text{eq}}C_{\text{eq}}$

Variables: $A$ area; $C$ capacitance; $d$ distance; $E$ electric field; $F$ force; $I$ current; $\ell$ length; $P$ power; $q$ charge; $Q$ charge; $r$ distance, radius, or position; $R$ resistance; $t$ time; $U$ potential energy; $V$ electric potential; $\kappa$ dielectric constant; $\rho$ resistivity; $\tau$ time constant

### Magnetism Equations

- Magnetic force on a moving charge (Unit 12: Magnetism and Electromagnetism): $F_B = qvB\sin\theta$
- Magnetic field of a long straight wire (Unit 12: Magnetism and Electromagnetism): $B = \frac{\mu_0 I}{2\pi r}$
- Magnetic force on a current-carrying wire (Unit 12: Magnetism and Electromagnetism): $F_B = I\ell B\sin\theta$
- Magnetic flux (dot product) (Unit 12: Magnetism and Electromagnetism): $\Phi_B = \vec{B}\cdot\vec{A}$
- Magnetic flux (magnitudes) (Unit 12: Magnetism and Electromagnetism): $\Phi_B = \left|\vec{B}\right|\cos\theta\left|\vec{A}\right|$
- Faraday's law (Unit 12: Magnetism and Electromagnetism): $\left|\mathcal{E}\right| = \left|\frac{\Delta\Phi_B}{\Delta t}\right|$
- Motional emf (Unit 12: Magnetism and Electromagnetism): $\mathcal{E} = B\ell v$

Variables: $A$ area; $B$ magnetic field; $F$ force; $I$ current; $\ell$ length; $q$ charge; $r$ distance, radius, or position; $t$ time; $v$ velocity or speed; $\mathcal{E}$ emf; $\theta$ angle; $\Phi$ flux

### Thermal Physics Equations

- Pressure (Unit 9: Thermodynamics): $P = \frac{F_{\perp}}{A}$
- Average kinetic energy of gas particles (Unit 9: Thermodynamics): $K_{\text{avg}} = \frac{3}{2}k_B T = \frac{1}{2}mv_{\text{rms}}^2$
- Rate of thermal conduction (Unit 9: Thermodynamics): $\frac{Q}{\Delta t} = \frac{kA\Delta T}{L}$
- Ideal gas law (Unit 9: Thermodynamics): $PV = nRT = Nk_B T$
- Internal energy of a monatomic ideal gas (Unit 9: Thermodynamics): $U = \frac{3}{2}nRT = \frac{3}{2}Nk_B T$
- Work done on a gas (Unit 9: Thermodynamics): $W = -P\Delta V$
- First law of thermodynamics (Unit 9: Thermodynamics): $\Delta U = Q + W$
- Specific heat (Unit 9: Thermodynamics): $Q = mc\Delta T$

Variables: $A$ area; $c$ specific heat; $F$ force; $k$ thermal conductivity; $K$ kinetic energy; $L$ length; $m$ mass; $n$ number of moles; $N$ number of atoms; $P$ pressure; $Q$ energy transferred to a system by heating; $t$ time; $T$ temperature; $U$ internal energy; $v$ velocity or speed; $V$ volume; $W$ work done on a system

### Waves, Sound, and Optics Equations

- Wave speed (Unit 14: Waves, Sound, and Physical Optics): $\lambda = \frac{v}{f}$
- Index of refraction (Unit 13: Geometric Optics): $n = \frac{c}{v}$
- Snell's law (Unit 13: Geometric Optics): $n_1\sin\theta_1 = n_2\sin\theta_2$
- Thin lens and mirror equation (Unit 13: Geometric Optics): $\frac{1}{s_i} + \frac{1}{s_o} = \frac{1}{f}$
- Magnification (Unit 13: Geometric Optics): $\left|M\right| = \left|\frac{h_i}{h_o}\right| = \left|\frac{s_i}{s_o}\right|$
- Path length difference for interference (Unit 14: Waves, Sound, and Physical Optics): $\Delta D = m\lambda$
- Single-slit path length difference (Unit 14: Waves, Sound, and Physical Optics): $\Delta D = a\sin\theta$
- Single-slit minima (small angle) (Unit 14: Waves, Sound, and Physical Optics): $a\left(\frac{y_{\text{min}}}{L}\right) \approx m\lambda$
- Double-slit path length difference (Unit 14: Waves, Sound, and Physical Optics): $\Delta D = d\sin\theta$
- Double-slit maxima (small angle) (Unit 14: Waves, Sound, and Physical Optics): $d\left(\frac{y_{\text{max}}}{L}\right) \approx m\lambda$
- Wave speed on a string (Unit 14: Waves, Sound, and Physical Optics): $v_{\text{string}} = \sqrt{\frac{F_T}{m/\ell}}$
- Period and frequency (Unit 14: Waves, Sound, and Physical Optics): $T = \frac{1}{f}$
- Position of a periodic wave over time (Unit 14: Waves, Sound, and Physical Optics): $x(t) = A\cos(\omega t) = A\cos(2\pi ft)$
- Displacement of a periodic wave over position (Unit 14: Waves, Sound, and Physical Optics): $y(x) = A\cos\left(2\pi\frac{x}{\lambda}\right)$
- Beat frequency (Unit 14: Waves, Sound, and Physical Optics): $\left|f_{\text{beat}}\right| = \left|f_1 - f_2\right|$

Variables: $a$ width; $A$ amplitude; $d$ separation; $D$ path length; $f$ frequency or focal length; $F$ force; $h$ height; $\ell$ length; $L$ distance; $m$ order or mass; $M$ magnification; $n$ index of refraction; $s$ position; $t$ time; $T$ period; $v$ speed; $x$ position; $y$ position; $\lambda$ wavelength; $\theta$ angle; $\omega$ angular frequency

### Modern Physics Equations

- Photon energy (Unit 15: Modern Physics): $E = hf$
- de Broglie wavelength (Unit 15: Modern Physics): $\lambda = \frac{h}{p}$
- Photon wavelength and frequency (Unit 15: Modern Physics): $\lambda = \frac{c}{f}$
- Wien's displacement law (Unit 15: Modern Physics): $\lambda_{\text{max}} = \frac{b}{T}$
- Stefan-Boltzmann law (Unit 15: Modern Physics): $P = A\sigma T^4$
- Photoelectric effect (Unit 15: Modern Physics): $K_{\text{max}} = hf - \phi$
- Compton shift (Unit 15: Modern Physics): $\Delta\lambda = \frac{h}{m_e c}\left(1 - \cos\theta\right)$
- Mass-energy equivalence (Unit 15: Modern Physics): $E = mc^2$
- Radioactive decay (Unit 15: Modern Physics): $N = N_0 e^{-\lambda t}$
- Decay constant and half-life (Unit 15: Modern Physics): $\lambda = \frac{\ln 2}{t_{1/2}}$

Variables: $A$ area; $E$ energy; $f$ frequency; $K$ kinetic energy; $m$ mass; $N$ number of particles; $p$ momentum; $P$ power; $t$ time; $T$ absolute temperature; $\theta$ angle; $\lambda$ wavelength or decay constant; $\phi$ work function

### Mechanics and Fluids Equations

- Velocity (constant acceleration): $v_x = v_{x0} + a_x t$
- Position (constant acceleration): $x = x_0 + v_{x0}t + \frac{1}{2}a_x t^2$
- Velocity and displacement (constant acceleration): $v_x^2 = v_{x0}^2 + 2a_x\left(x - x_0\right)$
- Center of mass position: $\vec{x}_{\text{cm}} = \frac{\sum m_i \vec{x}_i}{\sum m_i}$
- Newton's second law (system): $\vec{a}_{\text{sys}} = \frac{\sum \vec{F}}{m_{\text{sys}}} = \frac{\vec{F}_{\text{net}}}{m_{\text{sys}}}$
- Newton's law of universal gravitation: $\left|\vec{F}_g\right| = G\frac{m_1 m_2}{r^2}$
- Friction force: $\left|\vec{F}_f\right| \le \left|\mu \vec{F}_N\right|$
- Hooke's law (spring force): $\vec{F}_s = -k\Delta\vec{x}$
- Centripetal acceleration: $a_c = \frac{v^2}{r}$
- Translational kinetic energy: $K = \frac{1}{2}mv^2$
- Work done by a constant force: $W = F_{\parallel}d = Fd\cos\theta$
- Work-energy theorem: $\Delta K = \sum W_i = \sum F_{\parallel,i}\,d_i$
- Spring potential energy: $U_s = \frac{1}{2}k(\Delta x)^2$
- Gravitational potential energy (general): $U_G = -\frac{Gm_1 m_2}{r}$
- Gravitational potential energy near Earth: $\Delta U_g = mg\Delta y$
- Average power: $P_{\text{avg}} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t}$
- Instantaneous power: $P_{\text{inst}} = F_{\parallel}v = Fv\cos\theta$
- Momentum: $\vec{p} = m\vec{v}$
- Newton's second law (momentum form): $\vec{F}_{\text{net}} = \frac{\Delta\vec{p}}{\Delta t} = m\frac{\Delta\vec{v}}{\Delta t} = m\vec{a}$
- Impulse-momentum theorem: $\vec{J} = \vec{F}_{\text{avg}}\Delta t = \Delta\vec{p}$
- Center of mass velocity: $\vec{v}_{\text{cm}} = \frac{\sum \vec{p}_i}{\sum m_i} = \frac{\sum m_i \vec{v}_i}{\sum m_i}$

Variables: $a$ acceleration; $d$ distance; $E$ energy; $F$ force; $J$ impulse; $k$ spring constant; $K$ kinetic energy; $m$ mass; $p$ momentum; $P$ power; $r$ radius or distance; $t$ time; $U$ potential energy; $v$ velocity or speed; $W$ work; $x$ position; $y$ vertical position; $\theta$ angle; $\mu$ coefficient of friction

- Angular velocity (constant angular acceleration): $\omega = \omega_0 + \alpha t$
- Angular position (constant angular acceleration): $\theta = \theta_0 + \omega_0 t + \frac{1}{2}\alpha t^2$
- Angular velocity and displacement (constant angular acceleration): $\omega^2 = \omega_0^2 + 2\alpha\left(\theta - \theta_0\right)$
- Linear and angular speed: $v = r\omega$
- Tangential acceleration: $a_T = r\alpha$
- Torque: $\tau = r_{\perp}F = rF\sin\theta$
- Rotational inertia of point masses: $I = \sum m_i r_i^2$
- Parallel axis theorem: $I' = I_{\text{cm}} + Md^2$
- Newton's second law for rotation: $\alpha_{\text{sys}} = \frac{\Sigma\tau}{I_{\text{sys}}} = \frac{\tau_{\text{net}}}{I_{\text{sys}}}$
- Rotational kinetic energy: $K = \frac{1}{2}I\omega^2$
- Work done by a torque: $W = \tau\Delta\theta$
- Angular momentum of a rigid body: $L = I\omega$
- Angular momentum of a point mass: $L = rmv\sin\theta$
- Angular impulse-momentum theorem: $\Delta L = \tau\Delta t$
- Rolling without slipping: $\Delta x_{\text{cm}} = r\Delta\theta$
- Period and frequency: $T = \frac{1}{f}$
- Period of a mass-spring system: $T_s = 2\pi\sqrt{\frac{m}{k}}$
- Period of a simple pendulum: $T_p = 2\pi\sqrt{\frac{\ell}{g}}$
- Simple harmonic motion (cosine form): $x = A\cos(2\pi ft)$
- Simple harmonic motion (sine form): $x = A\sin(2\pi ft)$
- Density: $\rho = \frac{m}{V}$
- Pressure: $P = \frac{F_{\perp}}{A}$
- Absolute pressure at depth: $P = P_0 + \rho gh$
- Gauge pressure: $P_{\text{gauge}} = \rho gh$
- Buoyant force (Archimedes' principle): $F_b = \rho Vg$
- Continuity equation: $A_1 v_1 = A_2 v_2$
- Bernoulli's equation: $P_1 + \rho g y_1 + \frac{1}{2}\rho v_1^2 = P_2 + \rho g y_2 + \frac{1}{2}\rho v_2^2$

Variables: $a$ acceleration; $A$ amplitude or area; $d$ distance; $f$ frequency; $F$ force; $h$ height; $I$ rotational inertia; $k$ spring constant; $K$ kinetic energy; $\ell$ length; $L$ angular momentum; $m$ mass; $M$ mass; $P$ pressure; $r$ radius or distance; $t$ time; $T$ period; $v$ velocity or speed; $V$ volume; $W$ work; $x$ position; $y$ vertical position; $\alpha$ angular acceleration; $\theta$ angle or angular position; $\rho$ density; $\tau$ torque; $\omega$ angular speed

### Constants and Conversion Factors

- Avogadro's number: $N_0 = 6.02\times10^{23}\ \mathrm{mol^{-1}}$
- Universal gas constant: $R = 8.31\ \mathrm{J/(mol\cdot K)}$
- Boltzmann's constant: $k_B = 1.38\times10^{-23}\ \mathrm{J/K}$
- 1 atmosphere of pressure: $1\ \mathrm{atm} = 1.0\times10^{5}\ \mathrm{N/m^2} = 1.0\times10^{5}\ \mathrm{Pa}$
- Coulomb constant: $k = \frac{1}{4\pi\varepsilon_0} = 9.0\times10^{9}\ \frac{\mathrm{N\cdot m^2}}{\mathrm{C^2}}$
- Proton mass: $m_p = 1.67\times10^{-27}\ \mathrm{kg}$
- Neutron mass: $m_n = 1.67\times10^{-27}\ \mathrm{kg}$
- Electron mass: $m_e = 9.11\times10^{-31}\ \mathrm{kg}$
- Elementary charge: $e = 1.60\times10^{-19}\ \mathrm{C}$
- Vacuum permittivity: $\varepsilon_0 = 8.85\times10^{-12}\ \mathrm{C^2/(N\cdot m^2)}$
- Vacuum permeability: $\mu_0 = 4\pi\times10^{-7}\ \mathrm{(T\cdot m)/A}$
- 1 electron volt: $1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$
- Planck's constant: $\begin{aligned} h &= 6.63\times10^{-34}\ \mathrm{J\cdot s} = 4.14\times10^{-15}\ \mathrm{eV\cdot s} \\ hc &= 1.99\times10^{-25}\ \mathrm{J\cdot m} = 1240\ \mathrm{eV\cdot nm} \end{aligned}$
- Speed of light: $c = 3.00\times10^{8}\ \mathrm{m/s}$
- Wien's constant: $b = 2.90\times10^{-3}\ \mathrm{m\cdot K}$
- Stefan-Boltzmann constant: $\sigma = 5.67\times10^{-8}\ \mathrm{W/(m^2\cdot K^4)}$
- 1 unified atomic mass unit: $1\ \mathrm{u} = 1.66\times10^{-27}\ \mathrm{kg} = 931\ \mathrm{MeV}/c^2$
- Universal gravitational constant: $\begin{aligned} G &= 6.67\times10^{-11}\ \mathrm{m^3/(kg\cdot s^2)} \\ &= 6.67\times10^{-11}\ \mathrm{N\cdot m^2/kg^2} \end{aligned}$
- Magnitude of the acceleration due to gravity at Earth's surface: $g = 9.8\ \mathrm{m/s^2}$
- Magnitude of the gravitational field strength at Earth's surface: $g = 9.8\ \mathrm{N/kg}$

### Unit Symbols

| Unit | Symbol |
|---|---|
| ampere | $\mathrm{A}$ |
| coulomb | $\mathrm{C}$ |
| degree Celsius | $^\circ\mathrm{C}$ |
| electron volt | $\mathrm{eV}$ |
| farad | $\mathrm{F}$ |
| hertz | $\mathrm{Hz}$ |
| joule | $\mathrm{J}$ |
| kelvin | $\mathrm{K}$ |
| kilogram | $\mathrm{kg}$ |
| meter | $\mathrm{m}$ |
| mole | $\mathrm{mol}$ |
| newton | $\mathrm{N}$ |
| ohm | $\Omega$ |
| pascal | $\mathrm{Pa}$ |
| second | $\mathrm{s}$ |
| tesla | $\mathrm{T}$ |
| volt | $\mathrm{V}$ |
| watt | $\mathrm{W}$ |

### Prefixes

| Factor | Prefix | Symbol |
|---|---|---|
| $10^{12}$ | tera | $\mathrm{T}$ |
| $10^{9}$ | giga | $\mathrm{G}$ |
| $10^{6}$ | mega | $\mathrm{M}$ |
| $10^{3}$ | kilo | $\mathrm{k}$ |
| $10^{-2}$ | centi | $\mathrm{c}$ |
| $10^{-3}$ | milli | $\mathrm{m}$ |
| $10^{-6}$ | micro | $\mu$ |
| $10^{-9}$ | nano | $\mathrm{n}$ |
| $10^{-12}$ | pico | $\mathrm{p}$ |

### Values of Trigonometric Functions for Common Angles

| $\theta$ | $0^\circ$ | $30^\circ$ | $37^\circ$ | $45^\circ$ | $53^\circ$ | $60^\circ$ | $90^\circ$ |
|---|---|---|---|---|---|---|---|
| $\sin\theta$ | $0$ | $1/2$ | $3/5$ | $\sqrt{2}/2$ | $4/5$ | $\sqrt{3}/2$ | $1$ |
| $\cos\theta$ | $1$ | $\sqrt{3}/2$ | $4/5$ | $\sqrt{2}/2$ | $3/5$ | $1/2$ | $0$ |
| $\tan\theta$ | $0$ | $\sqrt{3}/3$ | $3/4$ | $1$ | $4/3$ | $\sqrt{3}$ | $\infty$ |

### Exam Conventions

- The frame of reference of any problem is assumed to be inertial unless otherwise stated.
- Air resistance is assumed to be negligible unless otherwise stated.
- Springs and strings are assumed to be ideal unless otherwise stated.
- The electric potential is zero at an infinite distance from an isolated point charge.
- The direction of current is the direction in which positive charges would drift.
- All batteries, wires, and meters are assumed to be ideal unless otherwise stated.

### Geometry and Trigonometry

**Rectangle**

- Area of a rectangle: $A = bh$

**Triangle**

- Area of a triangle: $A = \frac{1}{2}bh$

**Circle**

- Area of a circle: $A = \pi r^2$
- Circumference of a circle: $C = 2\pi r$
- Arc length: $s = r\theta$

**Rectangular Solid**

- Volume of a rectangular solid: $V = \ell wh$

**Cylinder**

- Volume of a cylinder: $V = \pi r^2\ell$
- Surface area of a cylinder: $S = 2\pi r\ell + 2\pi r^2$

**Sphere**

- Volume of a sphere: $V = \frac{4}{3}\pi r^3$
- Surface area of a sphere: $S = 4\pi r^2$

**Right Triangle**

- Pythagorean theorem: $a^2 + b^2 = c^2$
- Sine: $\sin\theta = \frac{a}{c}$
- Cosine: $\cos\theta = \frac{b}{c}$
- Tangent: $\tan\theta = \frac{a}{b}$

Variables: $A$ area; $b$ base; $C$ circumference; $h$ height; $\ell$ length; $r$ radius; $s$ arc length; $S$ surface area; $V$ volume; $w$ width; $\theta$ angle

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