AP Physics 2: Algebra-Based

The Physics 2 equation sheet, annotated for 2026

Transcribed from the equations table of the official AP Physics 2: Algebra-Based Course and Exam Description (Effective Fall 2024). College Board provides this sheet on both sections of the exam, so nothing here needs memorizing; knowing when each equation applies is the skill the exam actually tests. The geometry and math reference tables printed alongside the equations are not reproduced here.

For the units these equations belong to, see the Physics 2 course hub.

Constants and Conversion Factors

N0=6.02×1023 mol−1N_0 = 6.02 \times 10^{23}\ \text{mol}^{-1}

Avogadro's number

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R=8.31 J/(mol⋅K)R = 8.31\ \text{J/(mol} \cdot \text{K)}

Universal gas constant

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kB=1.38×10−23 J/Kk_B = 1.38 \times 10^{-23}\ \text{J/K}

Boltzmann's constant

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1 atm=1.0×105 N/m2=1.0×105 Pa1\ \text{atm} = 1.0 \times 10^5\ \text{N/m}^2 = 1.0 \times 10^5\ \text{Pa}

1 atmosphere of pressure

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k=14πε0=9.0×109 N⋅m2/C2k = \frac{1}{4\pi\varepsilon_0} = 9.0 \times 10^9\ \text{N} \cdot \text{m}^2/\text{C}^2

Coulomb constant

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mp=1.67×10−27 kgm_p = 1.67 \times 10^{-27}\ \text{kg}

Proton mass

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mn=1.67×10−27 kgm_n = 1.67 \times 10^{-27}\ \text{kg}

Neutron mass

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me=9.11×10−31 kgm_e = 9.11 \times 10^{-31}\ \text{kg}

Electron mass

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e=1.60×10−19 Ce = 1.60 \times 10^{-19}\ \text{C}

Elementary charge

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ε0=8.85×10−12 C2/(N⋅m2)\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N} \cdot \text{m}^2)

Vacuum permittivity

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μ0=4π×10−7 (T⋅m)/A\mu_0 = 4\pi \times 10^{-7}\ (\text{T} \cdot \text{m})/\text{A}

Vacuum permeability

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1 eV=1.60×10−19 J1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}

1 electron volt

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h=6.63×10−34 J⋅s=4.14×10−15 eV⋅sh = 6.63 \times 10^{-34}\ \text{J} \cdot \text{s} = 4.14 \times 10^{-15}\ \text{eV} \cdot \text{s}

Planck's constant

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hc=1.99×10−25 J⋅m=1240 eV⋅nmhc = 1.99 \times 10^{-25}\ \text{J} \cdot \text{m} = 1240\ \text{eV} \cdot \text{nm}
c=3.00×108 m/sc = 3.00 \times 10^8\ \text{m/s}

Speed of light

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b=2.90×10−3 m⋅Kb = 2.90 \times 10^{-3}\ \text{m} \cdot \text{K}

Wien's constant

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σ=5.67×10−8 W/(m2⋅K4)\sigma = 5.67 \times 10^{-8}\ \text{W}/(\text{m}^2 \cdot \text{K}^4)

Stefan-Boltzmann constant

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1 u=1.66×10−27 kg=931 MeV/c21\ \text{u} = 1.66 \times 10^{-27}\ \text{kg} = 931\ \text{MeV}/c^2

1 unified atomic mass unit

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G=6.67×10−11 m3/(kg⋅s2)=6.67×10−11 N⋅m2/kg2G = 6.67 \times 10^{-11}\ \text{m}^3/(\text{kg} \cdot \text{s}^2) = 6.67 \times 10^{-11}\ \text{N} \cdot \text{m}^2/\text{kg}^2

Universal gravitational constant

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g=9.8 m/s2g = 9.8\ \text{m/s}^2

Magnitude of the acceleration due to gravity at Earth's surface

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g=9.8 N/kgg = 9.8\ \text{N/kg}

Magnitude of the gravitational field strength at Earth's surface

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Electricity

∣F⃗E∣=14πε0∣q1q2∣r2=k∣q1q2∣r2\left| \vec{F}_E \right| = \frac{1}{4\pi\varepsilon_0} \frac{|q_1 q_2|}{r^2} = k \frac{|q_1 q_2|}{r^2}
E⃗=F⃗Eq\vec{E} = \frac{\vec{F}_E}{q}
∣E⃗∣=14πε0∣q∣r2=k∣q∣r2\left| \vec{E} \right| = \frac{1}{4\pi\varepsilon_0} \frac{|q|}{r^2} = k \frac{|q|}{r^2}
UE=14πε0q1q2r=kq1q2rU_E = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r} = k \frac{q_1 q_2}{r}
ΔUE=qΔV\Delta U_E = q \Delta V
V=14πε0∑iqiriV = \frac{1}{4\pi\varepsilon_0} \sum_i \frac{q_i}{r_i}
∣E⃗∣=∣ΔVΔr∣\left| \vec{E} \right| = \left| \frac{\Delta V}{\Delta r} \right|
C=QΔVC = \frac{Q}{\Delta V}
C=κε0AdC = \frac{\kappa \varepsilon_0 A}{d}
EC=Qκε0AE_C = \frac{Q}{\kappa \varepsilon_0 A}
UC=12QΔVU_C = \frac{1}{2} Q \Delta V
I=ΔqΔtI = \frac{\Delta q}{\Delta t}
R=ρℓAR = \frac{\rho \ell}{A}
P=IΔVP = I \Delta V
I=ΔVRI = \frac{\Delta V}{R}
Req,s=∑iRiR_{\text{eq,s}} = \sum_i R_i
1Req,p=∑i1Ri\frac{1}{R_{\text{eq,p}}} = \sum_i \frac{1}{R_i}
1Ceq,s=∑i1Ci\frac{1}{C_{\text{eq,s}}} = \sum_i \frac{1}{C_i}
Ceq,p=∑iCiC_{\text{eq,p}} = \sum_i C_i
τ=ReqCeq\tau = R_{\text{eq}} C_{\text{eq}}

Magnetism

FB=qvBsin⁡θF_B = q v B \sin\theta
B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}
FB=IℓBsin⁡θF_B = I \ell B \sin\theta
ΦB=B⃗⋅A⃗\Phi_B = \vec{B} \cdot \vec{A}
ΦB=∣B⃗∣cos⁡θ∣A⃗∣\Phi_B = \left| \vec{B} \right| \cos\theta \left| \vec{A} \right|
∣E∣=∣ΔΦBΔt∣\left| \mathcal{E} \right| = \left| \frac{\Delta \Phi_B}{\Delta t} \right|

emf, printed as script E on the official sheet

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E=Bℓv\mathcal{E} = B \ell v

emf

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Thermal Physics

P=F⊥AP = \frac{F_{\perp}}{A}
Kavg=32kBT=12mvrms2K_{\text{avg}} = \frac{3}{2} k_B T = \frac{1}{2} m v_{\text{rms}}^2
QΔt=kAΔTL\frac{Q}{\Delta t} = \frac{k A \Delta T}{L}
PV=nRT=NkBTP V = n R T = N k_B T
U=32nRT=32NkBTU = \frac{3}{2} n R T = \frac{3}{2} N k_B T
W=−PΔVW = -P \Delta V
ΔU=Q+W\Delta U = Q + W
Q=mcΔTQ = m c \Delta T

Waves, Sound, and Optics

λ=vf\lambda = \frac{v}{f}
n=cvn = \frac{c}{v}
n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2
1si+1so=1f\frac{1}{s_i} + \frac{1}{s_o} = \frac{1}{f}
∣M∣=∣hiho∣=∣siso∣|M| = \left| \frac{h_i}{h_o} \right| = \left| \frac{s_i}{s_o} \right|
ΔD=mλ\Delta D = m \lambda
ΔD=asin⁡θ\Delta D = a \sin\theta
ayminL≈mλa \frac{y_{\text{min}}}{L} \approx m \lambda
ΔD=dsin⁡θ\Delta D = d \sin\theta
dymaxL≈mλd \frac{y_{\text{max}}}{L} \approx m \lambda
vstring=FTm/ℓv_{\text{string}} = \sqrt{\frac{F_T}{m/\ell}}
T=1fT = \frac{1}{f}
x(t)=Acos⁡(ωt)=Acos⁡(2πft)x(t) = A \cos(\omega t) = A \cos(2\pi f t)
y(x)=Acos⁡(2πxλ)y(x) = A \cos\left( \frac{2\pi x}{\lambda} \right)
∣fbeat∣=∣f1−f2∣\left| f_{\text{beat}} \right| = |f_1 - f_2|

Modern Physics

E=hfE = h f
λ=hp\lambda = \frac{h}{p}
λ=cf\lambda = \frac{c}{f}
λmax=bT\lambda_{\text{max}} = \frac{b}{T}
P=AσT4P = A \sigma T^4
Kmax=hf−ϕK_{\text{max}} = h f - \phi
Δλ=hmec(1−cos⁡θ)\Delta \lambda = \frac{h}{m_e c} (1 - \cos\theta)
E=mc2E = m c^2
N=N0e−λtN = N_0 e^{-\lambda t}
λ=ln⁡2t1/2\lambda = \frac{\ln 2}{t_{1/2}}

Mechanics and Fluids

vx=vx0+axtv_x = v_{x0} + a_x t
x=x0+vx0t+12axt2x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2
vx2=vx02+2ax(x−x0)v_x^2 = v_{x0}^2 + 2 a_x (x - x_0)
x⃗cm=∑mix⃗i∑mi\vec{x}_{\text{cm}} = \frac{\sum m_i \vec{x}_i}{\sum m_i}
a⃗sys=∑F⃗msys=F⃗netmsys\vec{a}_{\text{sys}} = \frac{\sum \vec{F}}{m_{\text{sys}}} = \frac{\vec{F}_{\text{net}}}{m_{\text{sys}}}
∣F⃗g∣=Gm1m2r2\left| \vec{F}_g \right| = \frac{G m_1 m_2}{r^2}
∣F⃗f∣≤∣μF⃗N∣\left| \vec{F}_f \right| \leq \left| \mu \vec{F}_N \right|
F⃗s=−kΔx⃗\vec{F}_s = -k \Delta \vec{x}
ac=v2ra_c = \frac{v^2}{r}
K=12mv2K = \frac{1}{2} m v^2
W=F∥d=Fdcos⁡θW = F_{\parallel} d = F d \cos\theta
ΔK=∑Wi=∑F∥,i di\Delta K = \sum W_i = \sum F_{\parallel, i}\, d_i
Us=12k(Δx)2U_s = \frac{1}{2} k (\Delta x)^2
UG=−Gm1m2rU_G = -\frac{G m_1 m_2}{r}
ΔUg=mgΔy\Delta U_g = m g \Delta y
Pavg=WΔt=ΔEΔtP_{\text{avg}} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t}
Pinst=F∥v=Fvcos⁡θP_{\text{inst}} = F_{\parallel} v = F v \cos\theta
p⃗=mv⃗\vec{p} = m \vec{v}
F⃗net=Δp⃗Δt=mΔv⃗Δt=ma⃗\vec{F}_{\text{net}} = \frac{\Delta \vec{p}}{\Delta t} = m \frac{\Delta \vec{v}}{\Delta t} = m \vec{a}
J⃗=F⃗avgΔt=Δp⃗\vec{J} = \vec{F}_{\text{avg}} \Delta t = \Delta \vec{p}
v⃗cm=∑p⃗i∑mi=∑miv⃗i∑mi\vec{v}_{\text{cm}} = \frac{\sum \vec{p}_i}{\sum m_i} = \frac{\sum m_i \vec{v}_i}{\sum m_i}
ω=ω0+αt\omega = \omega_0 + \alpha t
θ=θ0+ω0t+12αt2\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2
ω2=ω02+2α(θ−θ0)\omega^2 = \omega_0^2 + 2 \alpha (\theta - \theta_0)
v=rωv = r \omega
aT=rαa_T = r \alpha
τ=r⊥F=rFsin⁡θ\tau = r_{\perp} F = r F \sin\theta
I=∑miri2I = \sum m_i r_i^2
I′=Icm+Md2I' = I_{\text{cm}} + M d^2
αsys=∑τIsys=τnetIsys\alpha_{\text{sys}} = \frac{\sum \tau}{I_{\text{sys}}} = \frac{\tau_{\text{net}}}{I_{\text{sys}}}
K=12Iω2K = \frac{1}{2} I \omega^2
W=τΔθW = \tau \Delta\theta
L=IωL = I \omega
L=rmvsin⁡θL = r m v \sin\theta
ΔL=τΔt\Delta L = \tau \Delta t
Δxcm=rΔθ\Delta x_{\text{cm}} = r \Delta\theta
T=1fT = \frac{1}{f}
Ts=2πmkT_s = 2\pi \sqrt{\frac{m}{k}}
Tp=2πℓgT_p = 2\pi \sqrt{\frac{\ell}{g}}
x=Acos⁡(2πft)x = A \cos(2\pi f t)
x=Asin⁡(2πft)x = A \sin(2\pi f t)
ρ=mV\rho = \frac{m}{V}
P=F⊥AP = \frac{F_{\perp}}{A}
P=P0+ρghP = P_0 + \rho g h
Pgauge=ρghP_{\text{gauge}} = \rho g h
Fb=ρVgF_b = \rho V g
A1v1=A2v2A_1 v_1 = A_2 v_2
P1+ρgy1+12ρv12=P2+ρgy2+12ρv22P_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

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