AP Physics 2 · 2027 exam
Equations and reference
Every equation, constant, geometry rule and exam convention you'll have on test day. Same content as the official Table of Information, dark mode, printable.
Section 1
Electricity
Force, field and potential
\(|\vec{F}_E| = \frac{1}{4\pi\varepsilon_0}\frac{|q_1q_2|}{r^2} = k\frac{|q_1q_2|}{r^2}\)
\(\vec{E} = \frac{\vec{F}_E}{q}\)
\(|\vec{E}| = \frac{1}{4\pi\varepsilon_0}\frac{|q|}{r^2} = k\frac{|q|}{r^2}\)
\(U_E = \frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r} = k\frac{q_1q_2}{r}\)
\(\Delta U_E = q\Delta V\)
\(V = \frac{1}{4\pi\varepsilon_0}\sum_i \frac{q_i}{r_i}\)
\(|\vec{E}| = \left|\frac{\Delta V}{\Delta r}\right|\)
Symbols
\(A\) = 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
Capacitors and circuits
\(C = \frac{Q}{\Delta V}\)
\(C = \kappa\varepsilon_0\frac{A}{d}\)
\(E_C = \frac{Q}{\kappa\varepsilon_0 A}\)
\(U_C = \frac{1}{2}Q\Delta V\)
\(I = \frac{\Delta q}{\Delta t}\)
\(R = \frac{\rho\ell}{A}\)
\(P = I\Delta V\)
\(I = \frac{\Delta V}{R}\)
\(R_{\mathrm{eq},s} = \sum_i R_i\)
\(\frac{1}{R_{\mathrm{eq},p}} = \sum_i \frac{1}{R_i}\)
\(\frac{1}{C_{\mathrm{eq},s}} = \sum_i \frac{1}{C_i}\)
\(C_{\mathrm{eq},p} = \sum_i C_i\)
\(\tau = R_{\mathrm{eq}}C_{\mathrm{eq}}\)
Reading these
Capacitances combine the OPPOSITE way round from resistances: they add in parallel and their reciprocals add in series.
Every angle in this course is measured from the NORMAL, never from a surface.
A negative image distance, or a negative potential energy, is a result to interpret rather than an error to hunt down.
Section 2
Magnetism
Fields, forces and induction
\(F_B = qvB\sin\theta\)
\(B = \frac{\mu_0 I}{2\pi r}\)
\(F_B = I\ell B\sin\theta\)
\(\Phi_B = \vec{B}\cdot\vec{A}\)
\(\Phi_B = |\vec{B}|\cos\theta\,|\vec{A}|\)
\(|\varepsilon| = \left|\frac{\Delta\Phi_B}{\Delta t}\right|\)
\(\varepsilon = B\ell v\)
Symbols
\(A\) = area
\(B\) = magnetic field
\(F\) = force
\(I\) = current
\(\ell\) = length
\(q\) = charge
\(r\) = distance, radius, or position
\(t\) = time
\(v\) = velocity or speed
\(\varepsilon\) = emf
\(\theta\) = angle
\(\Phi\) = flux
Section 3
Thermal Physics
Gases and the first law
\(P = \frac{F_\perp}{A}\)
\(K_{\mathrm{avg}} = \frac{3}{2}k_BT = \frac{1}{2}mv_{\mathrm{rms}}^2\)
\(\frac{Q}{\Delta t} = \frac{kA\Delta T}{L}\)
\(PV = nRT = Nk_BT\)
\(U = \frac{3}{2}nRT = \frac{3}{2}Nk_BT\)
\(W = -P\Delta V\)
\(\Delta U = Q + W\)
\(Q = mc\Delta T\)
Symbols
\(A\) = 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
Section 4
Waves, Sound, and Optics
Waves and refraction
\(\lambda = \frac{v}{f}\)
\(n = \frac{c}{v}\)
\(n_1\sin\theta_1 = n_2\sin\theta_2\)
\(v_{\mathrm{string}} = \sqrt{\frac{F_T}{m/\ell}}\)
\(T = \frac{1}{f}\)
\(x(t) = A\cos(\omega t) = A\cos(2\pi ft)\)
\(y(x) = A\cos\!\left(2\pi\frac{x}{\lambda}\right)\)
\(|f_{\mathrm{beat}}| = |f_1 - f_2|\)
Images and interference
\(\frac{1}{s_i} + \frac{1}{s_o} = \frac{1}{f}\)
\(|M| = \left|\frac{h_i}{h_o}\right| = \left|\frac{s_i}{s_o}\right|\)
\(\Delta D = m\lambda\)
\(\Delta D = a\sin\theta\)
\(a\left(\frac{y_{\min}}{L}\right) \approx m\lambda\)
\(\Delta D = d\sin\theta\)
\(d\left(\frac{y_{\max}}{L}\right) \approx m\lambda\)
Symbols
\(a\) = 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
Which length is in front of the sine
Single slit, width \(a\): the condition locates the MINIMA.
Double slit or grating, separation \(d\): the condition locates the MAXIMA.
The linear forms with \(y/L\) hold only while the angle is small, which the exam's stated conventions assume for single- and double-slit diffraction.
Magnification is written here as a magnitude; orientation is a separate reading, negative for inverted and positive for upright.
Section 5
Modern Physics
Quanta, radiation and decay
\(E = hf\)
\(\lambda = \frac{h}{p}\)
\(\lambda = \frac{c}{f}\)
\(\lambda_{\max} = \frac{b}{T}\)
\(P = A\sigma T^4\)
\(K_{\max} = hf - \phi\)
\(\Delta\lambda = \frac{h}{m_ec}\left(1 - \cos\theta\right)\)
\(E = mc^2\)
\(N = N_0 e^{-\lambda t}\)
\(\lambda = \frac{\ln 2}{t_{1/2}}\)
Symbols
\(A\) = 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
Section 6
Constants and Conversions
Constants
\(N_0 = 6.02\times10^{23}\ \mathrm{mol}^{-1}\)
\(R = 8.31\ \mathrm{J/(mol\cdot K)}\)
\(k_B = 1.38\times10^{-23}\ \mathrm{J/K}\)
\(k = \frac{1}{4\pi\varepsilon_0} = 9.0\times10^{9}\ \mathrm{N\cdot m^2/C^2}\)
\(\varepsilon_0 = 8.85\times10^{-12}\ \mathrm{C^2/(N\cdot m^2)}\)
\(\mu_0 = 4\pi\times10^{-7}\ \mathrm{(T\cdot m)/A}\)
\(e = 1.60\times10^{-19}\ \mathrm{C}\)
\(m_p = m_n = 1.67\times10^{-27}\ \mathrm{kg}\)
\(m_e = 9.11\times10^{-31}\ \mathrm{kg}\)
\(h = 6.63\times10^{-34}\ \mathrm{J\cdot s} = 4.14\times10^{-15}\ \mathrm{eV\cdot s}\)
\(hc = 1.99\times10^{-25}\ \mathrm{J\cdot m} = 1240\ \mathrm{eV\cdot nm}\)
\(c = 3.00\times10^{8}\ \mathrm{m/s}\)
\(b = 2.90\times10^{-3}\ \mathrm{m\cdot K}\)
\(\sigma = 5.67\times10^{-8}\ \mathrm{W/(m^2\cdot K^4)}\)
\(g = 9.8\ \mathrm{m/s^2}\)
Conversions
\(1\ \mathrm{atm} = 1.0\times10^{5}\ \mathrm{N/m^2} = 1.0\times10^{5}\ \mathrm{Pa}\)
\(1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}\)
\(1\ \mathrm{u} = 1.66\times10^{-27}\ \mathrm{kg} = 931\ \mathrm{MeV}/c^2\)
Prefixes
\(10^{12}\) tera, T
\(10^{9}\) giga, G
\(10^{6}\) mega, M
\(10^{3}\) kilo, k
\(10^{-2}\) centi, c
\(10^{-3}\) milli, m
\(10^{-6}\) micro, µ
\(10^{-9}\) nano, n
\(10^{-12}\) pico, p
Section 7
Geometry and Trigonometry
Areas and volumes
Rectangle: \(A = bh\)
Triangle: \(A = \frac{1}{2}bh\)
Circle: \(A = \pi r^2,\quad C = 2\pi r,\quad s = r\theta\)
Rectangular solid: \(V = \ell wh\)
Cylinder: \(V = \pi r^2\ell,\quad S = 2\pi r\ell + 2\pi r^2\)
Sphere: \(V = \frac{4}{3}\pi r^3,\quad S = 4\pi r^2\)
Right triangle
\(a^2 + b^2 = c^2\)
\(\sin\theta = \frac{a}{c}\)
\(\cos\theta = \frac{b}{c}\)
\(\tan\theta = \frac{a}{b}\)
Common angles
\(\sin\theta\): 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, \(\sqrt{3}\), \(\infty\)
at \(\theta\) = 0°, 30°, 37°, 45°, 53°, 60°, 90°
Section 8
Exam Conventions
Assumed unless stated otherwise
The frame of reference is inertial.
Frictional forces are negligible.
Strings, springs, batteries, wires, and meters are ideal.
Resistors and lightbulbs are ohmic.
Ideal gases are monatomic.
The electric potential is zero at an infinite distance from an isolated point charge.
Current is conventional current.
Capacitors are air-filled \((\kappa = 1.0)\).
The small angle approximation is valid for single- and double-slit diffraction.
What these buy you
"Ohmic" is why a resistor's \(R\) may be treated as constant while a lamp filament's may not.
"Monatomic" is why \(U = \frac{3}{2}nRT\) is the internal energy on the sheet.
"Ideal meters" is why an ammeter adds no resistance and a voltmeter draws no current.
"Zero potential at infinity" is what makes a bound pair's potential energy negative.
Based on the AP Physics 2 Table of Information in the 2026 Course and Exam Description.
Reformatted as a study sheet, not an official College Board publication.