Home / Equation sheets / Physics 2 equation sheet AP Physics 2: Algebra-Based
The Physics 2 equation sheet, annotated for 2026 Print this sheet 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 N 0 = 6.02 × 10 23 mol − 1 N_0 = 6.02 \times 10^{23}\ \text{mol}^{-1} N 0 = 6.02 × 1 0 23 mol − 1 Avogadro's number
R = 8.31 J/(mol ⋅ K) R = 8.31\ \text{J/(mol} \cdot \text{K)} R = 8.31 J/(mol ⋅ K) Universal gas constant
k B = 1.38 × 10 − 23 J/K k_B = 1.38 \times 10^{-23}\ \text{J/K} k B = 1.38 × 1 0 − 23 J/K Boltzmann's constant
1 atm = 1.0 × 10 5 N/m 2 = 1.0 × 10 5 Pa 1\ \text{atm} = 1.0 \times 10^5\ \text{N/m}^2 = 1.0 \times 10^5\ \text{Pa} 1 atm = 1.0 × 1 0 5 N/m 2 = 1.0 × 1 0 5 Pa 1 atmosphere of pressure
k = 1 4 π ε 0 = 9.0 × 10 9 N ⋅ m 2 / C 2 k = \frac{1}{4\pi\varepsilon_0} = 9.0 \times 10^9\ \text{N} \cdot \text{m}^2/\text{C}^2 k = 4 π ε 0 1 = 9.0 × 1 0 9 N ⋅ m 2 / C 2 Coulomb constant
m p = 1.67 × 10 − 27 kg m_p = 1.67 \times 10^{-27}\ \text{kg} m p = 1.67 × 1 0 − 27 kg Proton mass
m n = 1.67 × 10 − 27 kg m_n = 1.67 \times 10^{-27}\ \text{kg} m n = 1.67 × 1 0 − 27 kg Neutron mass
m e = 9.11 × 10 − 31 kg m_e = 9.11 \times 10^{-31}\ \text{kg} m e = 9.11 × 1 0 − 31 kg Electron mass
e = 1.60 × 10 − 19 C e = 1.60 \times 10^{-19}\ \text{C} e = 1.60 × 1 0 − 19 C Elementary charge
ε 0 = 8.85 × 10 − 12 C 2 / ( N ⋅ m 2 ) \varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N} \cdot \text{m}^2) ε 0 = 8.85 × 1 0 − 12 C 2 / ( N ⋅ m 2 ) Vacuum permittivity
μ 0 = 4 π × 10 − 7 ( T ⋅ m ) / A \mu_0 = 4\pi \times 10^{-7}\ (\text{T} \cdot \text{m})/\text{A} μ 0 = 4 π × 1 0 − 7 ( T ⋅ m ) / A Vacuum permeability
1 eV = 1.60 × 10 − 19 J 1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J} 1 eV = 1.60 × 1 0 − 19 J 1 electron volt
h = 6.63 × 10 − 34 J ⋅ s = 4.14 × 10 − 15 eV ⋅ s h = 6.63 \times 10^{-34}\ \text{J} \cdot \text{s} = 4.14 \times 10^{-15}\ \text{eV} \cdot \text{s} h = 6.63 × 1 0 − 34 J ⋅ s = 4.14 × 1 0 − 15 eV ⋅ s Planck's constant
h c = 1.99 × 10 − 25 J ⋅ m = 1240 eV ⋅ nm hc = 1.99 \times 10^{-25}\ \text{J} \cdot \text{m} = 1240\ \text{eV} \cdot \text{nm} h c = 1.99 × 1 0 − 25 J ⋅ m = 1240 eV ⋅ nm c = 3.00 × 10 8 m/s c = 3.00 \times 10^8\ \text{m/s} c = 3.00 × 1 0 8 m/s Speed of light
b = 2.90 × 10 − 3 m ⋅ K b = 2.90 \times 10^{-3}\ \text{m} \cdot \text{K} b = 2.90 × 1 0 − 3 m ⋅ K Wien's constant
σ = 5.67 × 10 − 8 W / ( m 2 ⋅ K 4 ) \sigma = 5.67 \times 10^{-8}\ \text{W}/(\text{m}^2 \cdot \text{K}^4) σ = 5.67 × 1 0 − 8 W / ( m 2 ⋅ K 4 ) Stefan-Boltzmann constant
1 u = 1.66 × 10 − 27 kg = 931 MeV / c 2 1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg} = 931\ \text{MeV}/c^2 1 u = 1.66 × 1 0 − 27 kg = 931 MeV / c 2 1 unified atomic mass unit
G = 6.67 × 10 − 11 m 3 / ( kg ⋅ s 2 ) = 6.67 × 10 − 11 N ⋅ m 2 / kg 2 G = 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 G = 6.67 × 1 0 − 11 m 3 / ( kg ⋅ s 2 ) = 6.67 × 1 0 − 11 N ⋅ m 2 / kg 2 Universal gravitational constant
g = 9.8 m/s 2 g = 9.8\ \text{m/s}^2 g = 9.8 m/s 2 Magnitude of the acceleration due to gravity at Earth's surface
g = 9.8 N/kg g = 9.8\ \text{N/kg} g = 9.8 N/kg Magnitude of the gravitational field strength at Earth's surface
Electricity ∣ F ⃗ E ∣ = 1 4 π ε 0 ∣ q 1 q 2 ∣ r 2 = k ∣ q 1 q 2 ∣ r 2 \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} F E = 4 π ε 0 1 r 2 ∣ q 1 q 2 ∣ = k r 2 ∣ q 1 q 2 ∣ E ⃗ = F ⃗ E q \vec{E} = \frac{\vec{F}_E}{q} E = q F E ∣ E ⃗ ∣ = 1 4 π ε 0 ∣ q ∣ r 2 = k ∣ q ∣ r 2 \left| \vec{E} \right| = \frac{1}{4\pi\varepsilon_0} \frac{|q|}{r^2} = k \frac{|q|}{r^2} E = 4 π ε 0 1 r 2 ∣ q ∣ = k r 2 ∣ q ∣ U E = 1 4 π ε 0 q 1 q 2 r = k q 1 q 2 r U_E = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r} = k \frac{q_1 q_2}{r} U E = 4 π ε 0 1 r q 1 q 2 = k r q 1 q 2 Δ U E = q Δ V \Delta U_E = q \Delta V Δ U E = q Δ V V = 1 4 π ε 0 ∑ i q i r i V = \frac{1}{4\pi\varepsilon_0} \sum_i \frac{q_i}{r_i} V = 4 π ε 0 1 i ∑ r i q i ∣ E ⃗ ∣ = ∣ Δ V Δ r ∣ \left| \vec{E} \right| = \left| \frac{\Delta V}{\Delta r} \right| E = Δ r Δ V C = Q Δ V C = \frac{Q}{\Delta V} C = Δ V Q C = κ ε 0 A d C = \frac{\kappa \varepsilon_0 A}{d} C = d κ ε 0 A E C = Q κ ε 0 A E_C = \frac{Q}{\kappa \varepsilon_0 A} E C = κ ε 0 A Q U C = 1 2 Q Δ V U_C = \frac{1}{2} Q \Delta V U C = 2 1 Q Δ V I = Δ q Δ t I = \frac{\Delta q}{\Delta t} I = Δ t Δ q R = ρ ℓ A R = \frac{\rho \ell}{A} R = A ρ ℓ I = Δ V R I = \frac{\Delta V}{R} I = R Δ V R eq,s = ∑ i R i R_{\text{eq,s}} = \sum_i R_i R eq,s = i ∑ R i 1 R eq,p = ∑ i 1 R i \frac{1}{R_{\text{eq,p}}} = \sum_i \frac{1}{R_i} R eq,p 1 = i ∑ R i 1 1 C eq,s = ∑ i 1 C i \frac{1}{C_{\text{eq,s}}} = \sum_i \frac{1}{C_i} C eq,s 1 = i ∑ C i 1 C eq,p = ∑ i C i C_{\text{eq,p}} = \sum_i C_i C eq,p = i ∑ C i τ = R eq C eq \tau = R_{\text{eq}} C_{\text{eq}} τ = R eq C eq Magnetism F B = q v B sin θ F_B = q v B \sin\theta F B = q v B sin θ B = μ 0 I 2 π r B = \frac{\mu_0 I}{2\pi r} B = 2 π r μ 0 I F B = I ℓ B sin θ F_B = I \ell B \sin\theta F B = I ℓ B sin θ Φ B = B ⃗ ⋅ A ⃗ \Phi_B = \vec{B} \cdot \vec{A} Φ B = B ⋅ A Φ B = ∣ B ⃗ ∣ cos θ ∣ A ⃗ ∣ \Phi_B = \left| \vec{B} \right| \cos\theta \left| \vec{A} \right| Φ B = B cos θ A ∣ E ∣ = ∣ Δ Φ B Δ t ∣ \left| \mathcal{E} \right| = \left| \frac{\Delta \Phi_B}{\Delta t} \right| ∣ E ∣ = Δ t Δ Φ B emf, printed as script E on the official sheet
E = B ℓ v \mathcal{E} = B \ell v E = B ℓ v emf
Thermal Physics P = F ⊥ A P = \frac{F_{\perp}}{A} P = A F ⊥ K avg = 3 2 k B T = 1 2 m v rms 2 K_{\text{avg}} = \frac{3}{2} k_B T = \frac{1}{2} m v_{\text{rms}}^2 K avg = 2 3 k B T = 2 1 m v rms 2 Q Δ t = k A Δ T L \frac{Q}{\Delta t} = \frac{k A \Delta T}{L} Δ t Q = L k A Δ T P V = n R T = N k B T P V = n R T = N k_B T P V = n R T = N k B T U = 3 2 n R T = 3 2 N k B T U = \frac{3}{2} n R T = \frac{3}{2} N k_B T U = 2 3 n R T = 2 3 N k B T W = − P Δ V W = -P \Delta V W = − P Δ V Δ U = Q + W \Delta U = Q + W Δ U = Q + W Q = m c Δ T Q = m c \Delta T Q = m c Δ T Waves, Sound, and Optics λ = v f \lambda = \frac{v}{f} λ = f v n 1 sin θ 1 = n 2 sin θ 2 n_1 \sin\theta_1 = n_2 \sin\theta_2 n 1 sin θ 1 = n 2 sin θ 2 1 s i + 1 s o = 1 f \frac{1}{s_i} + \frac{1}{s_o} = \frac{1}{f} s i 1 + s o 1 = f 1 ∣ M ∣ = ∣ h i h o ∣ = ∣ s i s o ∣ |M| = \left| \frac{h_i}{h_o} \right| = \left| \frac{s_i}{s_o} \right| ∣ M ∣ = h o h i = s o s i Δ D = m λ \Delta D = m \lambda Δ D = mλ Δ D = a sin θ \Delta D = a \sin\theta Δ D = a sin θ a y min L ≈ m λ a \frac{y_{\text{min}}}{L} \approx m \lambda a L y min ≈ mλ Δ D = d sin θ \Delta D = d \sin\theta Δ D = d sin θ d y max L ≈ m λ d \frac{y_{\text{max}}}{L} \approx m \lambda d L y max ≈ mλ v string = F T m / ℓ v_{\text{string}} = \sqrt{\frac{F_T}{m/\ell}} v string = m / ℓ F T x ( t ) = A cos ( ω t ) = A cos ( 2 π f t ) x(t) = A \cos(\omega t) = A \cos(2\pi f t) x ( t ) = A cos ( ω t ) = A cos ( 2 π f t ) y ( x ) = A cos ( 2 π x λ ) y(x) = A \cos\left( \frac{2\pi x}{\lambda} \right) y ( x ) = A cos ( λ 2 π x ) ∣ f beat ∣ = ∣ f 1 − f 2 ∣ \left| f_{\text{beat}} \right| = |f_1 - f_2| ∣ f beat ∣ = ∣ f 1 − f 2 ∣ Modern Physics λ = h p \lambda = \frac{h}{p} λ = p h λ = c f \lambda = \frac{c}{f} λ = f c λ max = b T \lambda_{\text{max}} = \frac{b}{T} λ max = T b P = A σ T 4 P = A \sigma T^4 P = A σ T 4 K max = h f − ϕ K_{\text{max}} = h f - \phi K max = h f − ϕ Δ λ = h m e c ( 1 − cos θ ) \Delta \lambda = \frac{h}{m_e c} (1 - \cos\theta) Δ λ = m e c h ( 1 − cos θ ) N = N 0 e − λ t N = N_0 e^{-\lambda t} N = N 0 e − λ t λ = ln 2 t 1 / 2 \lambda = \frac{\ln 2}{t_{1/2}} λ = t 1/2 ln 2 Mechanics and Fluids v x = v x 0 + a x t v_x = v_{x0} + a_x t v x = v x 0 + a x t x = x 0 + v x 0 t + 1 2 a x t 2 x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2 x = x 0 + v x 0 t + 2 1 a x t 2 v x 2 = v x 0 2 + 2 a x ( x − x 0 ) v_x^2 = v_{x0}^2 + 2 a_x (x - x_0) v x 2 = v x 0 2 + 2 a x ( x − x 0 ) x ⃗ cm = ∑ i m i x ⃗ i ∑ i m i \vec{x}_{\text{cm}} = \frac{\sum_i m_i \vec{x}_i}{\sum_i m_i} x cm = ∑ i m i ∑ i m i x i a ⃗ sys = ∑ F ⃗ m sys = F ⃗ net m sys \vec{a}_{\text{sys}} = \frac{\sum \vec{F}}{m_{\text{sys}}} = \frac{\vec{F}_{\text{net}}}{m_{\text{sys}}} a sys = m sys ∑ F = m sys F net ∣ F ⃗ g ∣ = G m 1 m 2 r 2 \left| \vec{F}_g \right| = \frac{G m_1 m_2}{r^2} F g = r 2 G m 1 m 2 ∣ F ⃗ f ∣ ≤ ∣ μ F ⃗ N ∣ \left| \vec{F}_f \right| \leq \left| \mu \vec{F}_N \right| F f ≤ μ F N F ⃗ s = − k Δ x ⃗ \vec{F}_s = -k \Delta \vec{x} F s = − k Δ x a c = v 2 r a_c = \frac{v^2}{r} a c = r v 2 K = 1 2 m v 2 K = \frac{1}{2} m v^2 K = 2 1 m v 2 W = F ∥ d = F d cos θ W = F_{\parallel} d = F d \cos\theta W = F ∥ d = F d cos θ Δ K = ∑ i W i = ∑ i F ∥ , i d i \Delta K = \sum_i W_i = \sum_i F_{\parallel, i}\, d_i Δ K = i ∑ W i = i ∑ F ∥ , i d i U s = 1 2 k ( Δ x ) 2 U_s = \frac{1}{2} k (\Delta x)^2 U s = 2 1 k ( Δ x ) 2 U G = − G m 1 m 2 r U_G = -\frac{G m_1 m_2}{r} U G = − r G m 1 m 2 Δ U g = m g Δ y \Delta U_g = m g \Delta y Δ U g = m g Δ y P avg = W Δ t = Δ E Δ t P_{\text{avg}} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t} P avg = Δ t W = Δ t Δ E P inst = F ∥ v = F v cos θ P_{\text{inst}} = F_{\parallel} v = F v \cos\theta P inst = F ∥ v = F v cos θ p ⃗ = m v ⃗ \vec{p} = m \vec{v} p = m v F ⃗ net = Δ p ⃗ Δ t = m Δ v ⃗ Δ t = m a ⃗ \vec{F}_{\text{net}} = \frac{\Delta \vec{p}}{\Delta t} = m \frac{\Delta \vec{v}}{\Delta t} = m \vec{a} F net = Δ t Δ p = m Δ t Δ v = m a J ⃗ = F ⃗ avg Δ t = Δ p ⃗ \vec{J} = \vec{F}_{\text{avg}} \Delta t = \Delta \vec{p} J = F avg Δ t = Δ p v ⃗ cm = ∑ i p ⃗ i ∑ i m i = ∑ i m i v ⃗ i ∑ i m i \vec{v}_{\text{cm}} = \frac{\sum_i \vec{p}_i}{\sum_i m_i} = \frac{\sum_i m_i \vec{v}_i}{\sum_i m_i} v cm = ∑ i m i ∑ i p i = ∑ i m i ∑ i m i v i ω = ω 0 + α t \omega = \omega_0 + \alpha t ω = ω 0 + α t θ = θ 0 + ω 0 t + 1 2 α t 2 \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 θ = θ 0 + ω 0 t + 2 1 α t 2 ω 2 = ω 0 2 + 2 α ( θ − θ 0 ) \omega^2 = \omega_0^2 + 2 \alpha (\theta - \theta_0) ω 2 = ω 0 2 + 2 α ( θ − θ 0 ) a T = r α a_T = r \alpha a T = r α τ = r ⊥ F = r F sin θ \tau = r_{\perp} F = r F \sin\theta τ = r ⊥ F = r F sin θ I = ∑ i m i r i 2 I = \sum_i m_i r_i^2 I = i ∑ m i r i 2 I ′ = I cm + M d 2 I' = I_{\text{cm}} + M d^2 I ′ = I cm + M d 2 α sys = ∑ τ I sys = τ net I sys \alpha_{\text{sys}} = \frac{\sum \tau}{I_{\text{sys}}} = \frac{\tau_{\text{net}}}{I_{\text{sys}}} α sys = I sys ∑ τ = I sys τ net K = 1 2 I ω 2 K = \frac{1}{2} I \omega^2 K = 2 1 I ω 2 W = τ Δ θ W = \tau \Delta\theta W = τ Δ θ L = r m v sin θ L = r m v \sin\theta L = r m v sin θ Δ L = τ Δ t \Delta L = \tau \Delta t Δ L = τ Δ t Δ x cm = r Δ θ \Delta x_{\text{cm}} = r \Delta\theta Δ x cm = r Δ θ T s = 2 π m k T_s = 2\pi \sqrt{\frac{m}{k}} T s = 2 π k m T p = 2 π ℓ g T_p = 2\pi \sqrt{\frac{\ell}{g}} T p = 2 π g ℓ x = A cos ( 2 π f t ) x = A \cos(2\pi f t) x = A cos ( 2 π f t ) x = A sin ( 2 π f t ) x = A \sin(2\pi f t) x = A sin ( 2 π f t ) ρ = m V \rho = \frac{m}{V} ρ = V m P = F ⊥ A P = \frac{F_{\perp}}{A} P = A F ⊥ P = P 0 + ρ g h P = P_0 + \rho g h P = P 0 + ρ g h P gauge = ρ g h P_{\text{gauge}} = \rho g h P gauge = ρ g h F b = ρ V g F_b = \rho V g F b = ρ V g A 1 v 1 = A 2 v 2 A_1 v_1 = A_2 v_2 A 1 v 1 = A 2 v 2 P 1 + ρ g y 1 + 1 2 ρ v 1 2 = P 2 + ρ g y 2 + 1 2 ρ v 2 2 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 P 1 + ρ g y 1 + 2 1 ρ v 1 2 = P 2 + ρ g y 2 + 2 1 ρ v 2 2 The other sheets