Physics 2 Equation Sheet: Complete AP Formula Guide (2026)
✓ Reviewed by Dr. Irfan Mansuri — AP Physics Certified Instructor
Most AP Physics 2 students open the equation sheet on exam day and freeze — not because the formulas are missing, but because they have never truly learned what each one means. Knowing a formula exists and knowing how to deploy it under pressure are two completely different skills. This guide closes that gap entirely.
The AP Physics 2 equation sheet is the official College Board reference booklet provided to every student during the exam. It contains approximately 40–50 equations organized across seven topic areas — fluid mechanics, thermodynamics, electrostatics, circuits, magnetism, optics, and modern physics — plus a full table of physical constants, unit symbols, and conversion factors. [[0]](#__0)
The 2026 AP Physics 2 exam is scheduled for May 2026 and consists of 50 multiple-choice questions (90 minutes, 50% of score) and 4 free-response questions (90 minutes, 50% of score). A calculator is permitted throughout. The equation sheet is your most powerful tool — but only if you understand it deeply before exam day. [[1]](#__1)
In this complete guide you will learn:
- Every formula on the official AP Physics 2 equation sheet — with full variable definitions
- What each formula means physically — not just mathematically
- Worked examples for the most frequently tested equations
- Common mistakes students make with each formula group
- Proven strategies for using the equation sheet efficiently on exam day
- Practice problems with full solutions for each topic area
- The equation sheet is provided — you do not need to memorize formulas, but you must understand them
- Modern physics (quantum, atomic, nuclear) accounts for ~21% of the exam — the highest single weight [[2]](#__2)
- Electrostatics + circuits together account for ~35% of the exam — master these first
- All physical constants (speed of light, Planck’s constant, elementary charge) are given on the sheet [[0]](#__0)
- The 2026 equation sheet is updated — always use the current College Board PDF, not older versions
What Is the AP Physics 2 Equation Sheet?
The AP Physics 2 equation sheet — officially titled the AP Physics 2: Algebra-Based Exam Reference Information — is a multi-page booklet distributed to every student at the start of the AP Physics 2 exam. It is produced and updated annually by the College Board. [[0]](#__0)
Unlike many standardized tests where you must memorize everything, the AP Physics 2 exam is explicitly designed so that the equation sheet handles formula recall — freeing you to focus on conceptual understanding and problem-solving strategy. This is intentional: College Board wants to test whether you can apply physics, not whether you can memorize it. [[1]](#__1)
What the Equation Sheet Contains
The 2026 equation sheet is organized into the following sections: [[0]](#__0)
Modern physics carries the highest exam weight (~21%) yet most students spend the least time on it. Quantum, atomic, and nuclear physics formulas are among the most straightforward to apply once you understand the variables. Prioritize this section in your study plan. [[2]](#__2)
Constants & Conversion Factors on the AP Physics 2 Sheet
Before diving into topic-specific formulas, you must be fluent with the physical constants provided on the equation sheet. These values appear in nearly every calculation across all topic areas. The 2026 sheet provides all of the following: [[0]](#__0)
| Constant | Symbol | Value | Used In |
|---|---|---|---|
| Speed of light | c | 3.00 × 10⁸ m/s | Optics, Modern Physics |
| Planck’s constant | h | 6.63 × 10⁻³⁴ J·s | Modern Physics |
| Elementary charge | e | 1.60 × 10⁻¹⁹ C | Electrostatics, Circuits, Modern |
| Coulomb’s constant | k | 9.0 × 10⁹ N·m²/C² | Electrostatics |
| Boltzmann’s constant | kB | 1.38 × 10⁻²³ J/K | Thermodynamics |
| Universal gas constant | R | 8.31 J/(mol·K) | Thermodynamics |
| Avogadro’s number | NA | 6.02 × 10²³ mol⁻¹ | Thermodynamics, Modern |
| Proton mass | mp | 1.67 × 10⁻²⁷ kg | Modern Physics |
| Electron mass | me | 9.11 × 10⁻³¹ kg | Modern Physics |
| Vacuum permittivity | ε₀ | 8.85 × 10⁻¹² C²/(N·m²) | Electrostatics |
| Vacuum permeability | μ₀ | 4π × 10⁻⁷ (T·m)/A | Magnetism |
| 1 electron volt | eV | 1.60 × 10⁻¹⁹ J | Modern Physics, Electrostatics |
| 1 atm pressure | — | 1.0 × 10⁵ Pa | Fluid Mechanics, Thermodynamics |
| Gravitational acceleration | g | 9.8 m/s² | Fluid Mechanics |
The most frequent constant-related error on the AP exam is using temperature in Celsius instead of Kelvin. The equation sheet gives R and kB for use with Kelvin. Always convert: $$T(K) = T(°C) + 273$$. A temperature of 27°C = 300 K, not 27 K. This mistake alone can cost 3–4 points on the free-response section. [[1]](#__1)
Fluid Mechanics Formulas on the Physics 2 Equation Sheet
Fluid mechanics covers the behavior of liquids and gases at rest (hydrostatics) and in motion (fluid dynamics). The AP Physics 2 equation sheet provides four core fluid formulas. Understanding the physical meaning behind each one — not just the algebra — is what separates a score of 3 from a score of 5. [[2]](#__2)
| Formula | Name | Variables & Meaning |
|---|---|---|
| P = F/A P = pressure (Pa), F = force (N), A = area (m²) |
Pressure | Pressure is force per unit area. A small force on a tiny area can produce enormous pressure — this is why a needle pierces skin but a flat hand does not. |
| P = P₀ + ρgh P₀ = surface pressure (Pa), ρ = fluid density (kg/m³), g = 9.8 m/s², h = depth (m) |
Hydrostatic Pressure | Pressure increases with depth in a fluid. Every 10 meters of water depth adds approximately 1 atm of pressure. This is why deep-sea submarines require reinforced hulls. |
| F_b = ρ_f · V_f · g F_b = buoyant force (N), ρ_f = fluid density (kg/m³), V_f = volume of fluid displaced (m³), g = 9.8 m/s² |
Buoyancy (Archimedes’ Principle) | The buoyant force equals the weight of fluid displaced by the object. An object floats when its weight equals the buoyant force — meaning it displaces exactly its own weight in fluid. |
| A₁v₁ = A₂v₂ A = cross-sectional area (m²), v = fluid speed (m/s) |
Continuity Equation | For an incompressible fluid, the flow rate (volume per second) is constant. A narrow pipe section forces the fluid to speed up — exactly like squeezing a garden hose nozzle. |
| P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ P = pressure (Pa), ρ = density (kg/m³), v = speed (m/s), h = height (m) |
Bernoulli’s Equation | Energy conservation for flowing fluids. Where fluid speeds up, pressure drops. This explains airplane lift, curveballs, and the Venturi effect. It is the most complex fluid formula on the sheet — and the most frequently tested in free response. |
A wooden block of volume 0.002 m³ is fully submerged in water (ρ = 1000 kg/m³). What is the buoyant force acting on it?
Apply: $$F_b = \rho_f \cdot V_f \cdot g = 1000 \times 0.002 \times 9.8$$
Calculate: $$F_b = 19.6 \text{ N}$$
This means the water pushes up on the block with 19.6 N of force. If the block weighs less than 19.6 N, it will float when released.
✅ Buoyant Force = 19.6 NOn the AP exam, Bernoulli problems often involve horizontal pipes (h₁ = h₂), which cancels the ρgh terms on both sides. The equation simplifies to: $$P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$$. Always check whether height is constant before writing the full equation — it saves significant time.
Thermodynamics Formulas on the Physics 2 Equation Sheet
Thermodynamics in AP Physics 2 covers the behavior of gases, heat transfer, and the laws governing energy in thermal systems. The equation sheet provides all formulas you need — your job is to understand the physical story each equation tells.
| Formula | Name | Variables & Meaning |
|---|---|---|
| PV = nRT P = pressure (Pa), V = volume (m³), n = moles, R = 8.31 J/(mol·K), T = temperature (K) |
Ideal Gas Law | Relates the four state variables of an ideal gas. If you know any three, you can find the fourth. Temperature must always be in Kelvin. This is the single most tested thermodynamics equation on the AP exam. |
| PV = Nk_BT N = number of molecules (not moles), k_B = 1.38 × 10⁻²³ J/K |
Ideal Gas Law (Molecular Form) | Equivalent to PV = nRT but uses the number of individual molecules N instead of moles n. Use this form when a problem gives you a number of molecules rather than moles. Note: N = n × N_A. |
| ΔU = Q − W ΔU = change in internal energy (J), Q = heat added to system (J), W = work done by system (J) |
First Law of Thermodynamics | Energy conservation for thermal systems. Heat added to a system increases its internal energy; work done by the system decreases it. Sign convention is critical: Q is positive when heat flows IN, W is positive when gas expands (does work on surroundings). |
| W = PΔV W = work done by gas (J), P = pressure (Pa), ΔV = change in volume (m³) |
Work Done by a Gas | Work done by a gas during expansion at constant pressure. If the gas expands (ΔV > 0), the gas does positive work on its surroundings. If compressed (ΔV < 0), work is done on the gas. |
| Q = mcΔT Q = heat energy (J), m = mass (kg), c = specific heat capacity (J/kg·K), ΔT = temperature change (K or °C) |
Specific Heat / Calorimetry | Heat required to change the temperature of a substance. Different materials have different specific heat values — water (4186 J/kg·K) resists temperature change far more than metals, which is why oceans moderate coastal climates. |
| K_avg = (3/2)k_BT K_avg = average kinetic energy per molecule (J), k_B = Boltzmann’s constant, T = temperature (K) |
Average Kinetic Energy of a Gas Molecule | The average translational kinetic energy of a gas molecule depends only on temperature — not on the type of gas. Doubling the absolute temperature doubles the average kinetic energy. This is the microscopic definition of temperature. |
| e = W_net / Q_H e = efficiency, W_net = net work output (J), Q_H = heat absorbed from hot reservoir (J) |
Thermal Efficiency | The fraction of heat input that is converted to useful work. No real engine achieves 100% efficiency — the second law of thermodynamics guarantees some heat is always lost to the cold reservoir. |
A sealed container holds 2.0 moles of an ideal gas at a pressure of 1.5 × 10⁵ Pa and temperature of 300 K. What is the volume of the container?
Apply: $$PV = nRT \Rightarrow V = \frac{nRT}{P}$$
Substitute: $$V = \frac{2.0 \times 8.31 \times 300}{1.5 \times 10^5}$$
Calculate: $$V = \frac{4986}{150000} = 0.0332 \text{ m}^3$$
✅ Volume = 0.0332 m³ ≈ 33.2 liters🔑 The Four Thermodynamic Processes — Quick Reference
The AP exam frequently tests the four special gas processes. Knowing which variable is constant in each process tells you immediately which terms simplify:
- Isothermal (constant T): $$PV = \text{const}$$ → ΔU = 0, so Q = W
- Isobaric (constant P): $$W = P\Delta V$$ applies directly
- Isochoric / Isovolumetric (constant V): $$W = 0$$, so ΔU = Q
- Adiabatic (no heat exchange): $$Q = 0$$, so ΔU = −W
Electrostatics Formulas on the Physics 2 Equation Sheet
Electrostatics is the highest-weighted single topic on the AP Physics 2 exam at approximately 18%. It covers electric forces, electric fields, electric potential, and capacitance. Mastery of these formulas — and the conceptual relationships between them — is essential for a score of 4 or 5.
| Formula | Name | Variables & Meaning |
|---|---|---|
| F = kq₁q₂ / r² F = electric force (N), k = 9.0×10⁹ N·m²/C², q₁, q₂ = charges (C), r = distance between charges (m) |
Coulomb’s Law | The electrostatic force between two point charges. Like gravity, it follows an inverse-square law — double the distance, quarter the force. Unlike gravity, it can be repulsive (like charges) or attractive (opposite charges). |
| E = F / q E = electric field (N/C or V/m), F = force on test charge (N), q = test charge (C) |
Electric Field Definition | The electric field at a point is the force per unit positive charge placed at that point. It is a vector — direction is the direction of force on a positive test charge. |
| E = kq / r² E = electric field (N/C), k = Coulomb’s constant, q = source charge (C), r = distance from charge (m) |
Electric Field of a Point Charge | The electric field created by a single point charge at distance r. Field points away from positive charges and toward negative charges. Magnitude decreases as 1/r² — same inverse-square relationship as Coulomb’s law. |
| ΔV = ΔU / q = −W/q ΔV = electric potential difference (V), ΔU = change in potential energy (J), q = charge (C), W = work done by electric field (J) |
Electric Potential Difference (Voltage) | Voltage is the change in electric potential energy per unit charge. Moving a positive charge from low to high potential requires work input. The negative sign means the field does positive work when charge moves from high to low potential. |
| V = kq / r V = electric potential (V), k = Coulomb’s constant, q = source charge (C), r = distance (m) |
Electric Potential of a Point Charge | The electric potential at distance r from a point charge. Unlike electric field (which is a vector), electric potential is a scalar — you can add potentials from multiple charges algebraically without worrying about direction. |
| U_E = qV = kq₁q₂ / r U_E = electric potential energy (J), q = charge (C), V = potential (V) |
Electric Potential Energy | The potential energy stored in a system of charges. Note the 1/r dependence (not 1/r²) — potential energy decreases more slowly with distance than force does. Positive for like charges (repulsive system stores energy), negative for opposite charges. |
| C = Q / V C = capacitance (F = farads), Q = charge stored (C), V = voltage across capacitor (V) |
Capacitance | Capacitance measures how much charge a capacitor stores per volt of potential difference. A larger capacitance means more charge stored for the same voltage. The farad is a very large unit — most practical capacitors are measured in microfarads (μF) or picofarads (pF). |
| U_C = ½QV = ½CV² U_C = energy stored in capacitor (J), Q = charge (C), V = voltage (V), C = capacitance (F) |
Energy Stored in a Capacitor | The energy stored in the electric field between a capacitor’s plates. The ½ factor arises because as charge builds up, each additional charge is pushed against an increasing opposing voltage — the average voltage during charging is V/2. |
| C = κε₀A / d κ = dielectric constant (dimensionless), ε₀ = 8.85×10⁻¹² C²/(N·m²), A = plate area (m²), d = plate separation (m) |
Parallel Plate Capacitor | Capacitance of a parallel plate capacitor. Larger plates and smaller separation increase capacitance. Inserting a dielectric material (κ > 1) between the plates multiplies capacitance by the dielectric constant κ. |
Two point charges, q₁ = +3.0 × 10⁻⁶ C and q₂ = −2.0 × 10⁻⁶ C, are placed 0.30 m apart. What is the magnitude of the electric force between them?
Apply: $$F = \frac{kq_1q_2}{r^2} = \frac{9.0 \times 10^9 \times 3.0 \times 10^{-6} \times 2.0 \times 10^{-6}}{(0.30)^2}$$
Calculate: $$F = \frac{9.0 \times 10^9 \times 6.0 \times 10^{-12}}{0.09} = \frac{0.054}{0.09} = 0.60 \text{ N}$$
Since the charges are opposite in sign, the force is attractive.
✅ Force = 0.60 N (attractive)Electric field (E) is a vector — it has magnitude and direction, and you must use vector addition when combining fields from multiple charges. Electric potential (V) is a scalar — you simply add the numerical values. Many AP free-response questions specifically test whether students know this distinction.
Electric Circuits Formulas on the Physics 2 Equation Sheet
Electric circuits account for approximately 17% of the AP Physics 2 exam. The equation sheet provides all the formulas you need for resistors, capacitors, power, and current — but the real challenge is applying Kirchhoff’s laws and understanding series vs. parallel behavior conceptually.
| Formula | Name | Variables & Meaning |
|---|---|---|
| I = ΔQ / Δt I = current (A), ΔQ = charge flow (C), Δt = time (s) |
Electric Current | Current is the rate of charge flow past a point in a circuit. One ampere equals one coulomb of charge flowing per second. Current direction is defined as the direction positive charges would flow (conventional current). |
| V = IR V = voltage (V), I = current (A), R = resistance (Ω) |
Ohm’s Law | The voltage across a resistor equals the current through it times its resistance. This is the most fundamental circuit equation. It applies to individual components — not to the entire circuit unless the circuit contains only one resistor. |
| R = ρL / A R = resistance (Ω), ρ = resistivity (Ω·m), L = length (m), A = cross-sectional area (m²) |
Resistance of a Wire | Resistance depends on the material (ρ), length, and cross-sectional area of a conductor. A longer, thinner wire has higher resistance — like a narrow, long pipe restricting water flow more than a short, wide one. |
| P = IV = I²R = V²/R P = power (W), I = current (A), V = voltage (V), R = resistance (Ω) |
Electric Power | Three equivalent forms of electric power. Use P = IV when you know both current and voltage. Use P = I²R when you know current and resistance. Use P = V²/R when you know voltage and resistance. All three give the same result for ohmic resistors. |
| R_s = R₁ + R₂ + R₃ + … R_s = total series resistance (Ω) |
Resistors in Series | In series, resistances simply add. All resistors carry the same current. The total resistance is always greater than any individual resistor. Adding more resistors in series always increases total resistance. |
| 1/R_p = 1/R₁ + 1/R₂ + … R_p = total parallel resistance (Ω) |
Resistors in Parallel | In parallel, resistors share voltage but split current. The total parallel resistance is always less than the smallest individual resistor. Adding more resistors in parallel always decreases total resistance — it gives current more paths to flow. |
| C_p = C₁ + C₂ + C₃ + … C_p = total parallel capacitance (F) |
Capacitors in Parallel | Capacitors in parallel add directly — the opposite behavior of resistors. Parallel capacitors share the same voltage but store charge independently, so total charge storage increases. |
| 1/C_s = 1/C₁ + 1/C₂ + … C_s = total series capacitance (F) |
Capacitors in Series | Capacitors in series combine like resistors in parallel — the reciprocals add. Series capacitors carry the same charge but split voltage. Total capacitance is always less than the smallest individual capacitor. |
| τ = RC τ = time constant (s), R = resistance (Ω), C = capacitance (F) |
RC Time Constant | The RC time constant describes how quickly a capacitor charges or discharges through a resistor. After one time constant τ, a charging capacitor reaches ~63% of its final charge. After 5τ, it is considered fully charged (99.3%). |
🔑 Series vs. Parallel — The Key Differences
| Property | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same through all components | Splits — different through each branch |
| Voltage | Splits across components | Same across all branches |
| Total Resistance | Increases (R₁ + R₂) | Decreases (1/R_total = 1/R₁ + 1/R₂) |
| Total Capacitance | Decreases (1/C_total = 1/C₁ + 1/C₂) | Increases (C₁ + C₂) |
| If one component fails | Entire circuit breaks | Other branches still work |
Magnetism Formulas on the Physics 2 Equation Sheet
Magnetism covers magnetic forces on moving charges and current-carrying wires, magnetic flux, and electromagnetic induction. The right-hand rule is your most important tool here — the equation sheet gives you the magnitudes, but you must determine directions yourself.
| Formula | Name | Variables & Meaning |
|---|---|---|
| F = qv × B = qvB sinθ F = magnetic force (N), q = charge (C), v = velocity (m/s), B = magnetic field (T), θ = angle between v and B |
Magnetic Force on a Moving Charge | A moving charge in a magnetic field experiences a force perpendicular to both its velocity and the field. Maximum force occurs when v ⊥ B (θ = 90°). Zero force when the charge moves parallel to the field (θ = 0°). Direction found by right-hand rule. |
| F = IL × B = BIL sinθ F = force on wire (N), I = current (A), L = length of wire in field (m), B = magnetic field (T), θ = angle between wire and B |
Magnetic Force on a Current-Carrying Wire | A current-carrying wire in a magnetic field experiences a force. This is the operating principle of electric motors. The force is maximized when the wire is perpendicular to the field and zero when parallel to it. |
| Φ_B = BA cosθ Φ_B = magnetic flux (Wb = T·m²), B = magnetic field (T), A = area of loop (m²), θ = angle between B and normal to loop |
Magnetic Flux | Magnetic flux measures how much magnetic field passes through a surface. Maximum flux when B is perpendicular to the surface (θ = 0°). Zero flux when B is parallel to the surface (θ = 90°). Changing flux is what induces EMF. |
| ε = −ΔΦ_B / Δt ε = induced EMF (V), ΔΦ_B = change in magnetic flux (Wb), Δt = time interval (s) |
Faraday’s Law of Induction | A changing magnetic flux through a loop induces an EMF (voltage) in that loop. The negative sign reflects Lenz’s law — the induced current opposes the change that caused it. This is the principle behind generators, transformers, and wireless charging. |
| B = μ₀I / (2πr) B = magnetic field (T), μ₀ = 4π×10⁻⁷ T·m/A, I = current (A), r = distance from wire (m) |
Magnetic Field of a Long Straight Wire | The magnetic field created by a long straight current-carrying wire at distance r. Field circles around the wire (right-hand rule: thumb in direction of current, fingers curl in direction of B). Field strength decreases as 1/r — not 1/r² like electric and gravitational fields. |
The right-hand rule determines the direction of magnetic force and field — and it appears on virtually every magnetism question. For force on a positive charge: point fingers in the direction of velocity v, curl them toward B, and your thumb points in the direction of force F. For a negative charge, reverse the direction. Practice this until it is automatic — you cannot look it up on the equation sheet.
Optics Formulas on the Physics 2 Equation Sheet
Optics in AP Physics 2 covers both geometric optics (reflection, refraction, lenses, mirrors) and physical optics (wave interference, diffraction). The equation sheet provides all the formulas — your challenge is knowing which formula applies to which physical situation.
| Formula | Name | Variables & Meaning |
|---|---|---|
| n = c / v n = index of refraction (dimensionless), c = speed of light in vacuum (3×10⁸ m/s), v = speed of light in medium (m/s) |
Index of Refraction | The index of refraction measures how much a medium slows light. n = 1 for vacuum, ~1.0003 for air, 1.33 for water, ~1.5 for glass. A higher index means light travels slower and bends more when entering from a less dense medium. |
| n₁ sinθ₁ = n₂ sinθ₂ n₁, n₂ = indices of refraction, θ₁ = angle of incidence, θ₂ = angle of refraction (both measured from normal) |
Snell’s Law | Describes how light bends when crossing from one medium to another. Light bends toward the normal when entering a denser medium (higher n) and away from the normal when entering a less dense medium. All angles are measured from the normal to the surface — not from the surface itself. |
| 1/d_o + 1/d_i = 1/f d_o = object distance (m), d_i = image distance (m), f = focal length (m) |
Thin Lens & Mirror Equation | The same equation applies to both thin lenses and curved mirrors. For converging lenses and concave mirrors, f is positive. For diverging lenses and convex mirrors, f is negative. A positive d_i means a real image; negative d_i means a virtual image. |
| m = −d_i / d_o = h_i / h_o m = magnification (dimensionless), d_i = image distance, d_o = object distance, h_i = image height, h_o = object height |
Magnification | Magnification describes the size and orientation of an image relative to the object. |m| > 1 means the image is larger; |m| < 1 means smaller. A negative m means the image is inverted (upside down); positive m means upright. Real images are always inverted (m < 0). |
| d sinθ = mλ d = slit separation (m), θ = angle to bright fringe, m = order number (integer), λ = wavelength (m) |
Double-Slit Interference (Bright Fringes) | Constructive interference (bright fringes) in a double-slit experiment. m = 0 is the central maximum; m = ±1, ±2 are the first and second order maxima. Larger wavelength or smaller slit separation produces wider fringe spacing. |
| d sinθ = (m + ½)λ Same variables as above; this gives dark fringe positions |
Double-Slit Interference (Dark Fringes) | Destructive interference (dark fringes) occurs when path difference equals a half-integer multiple of wavelength. The first dark fringe (m = 0) appears at sinθ = λ/(2d), halfway between the central maximum and first bright fringe. |
| sinθ_c = n₂ / n₁ θ_c = critical angle, n₁ = index of incident medium (denser), n₂ = index of second medium (less dense) |
Critical Angle (Total Internal Reflection) | When light travels from a denser to a less dense medium at an angle greater than the critical angle, it undergoes total internal reflection — no light escapes. This is the principle behind fiber optic cables and the sparkle of diamonds. |
An object is placed 30 cm in front of a converging lens with focal length 10 cm. Where is the image formed, and is it real or virtual?
Apply: $$\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f} \Rightarrow \frac{1}{30} + \frac{1}{d_i} = \frac{1}{10}$$
Solve: $$\frac{1}{d_i} = \frac{1}{10} – \frac{1}{30} = \frac{3}{30} – \frac{1}{30} = \frac{2}{30}$$
$$d_i = 15 \text{ cm}$$
Magnification: $$m = -\frac{d_i}{d_o} = -\frac{15}{30} = -0.5$$
The image is real (positive d_i), inverted (negative m), and half the size of the object (|m| = 0.5).
✅ Image at 15 cm (real, inverted, half-size)Modern Physics Formulas on the Physics 2 Equation Sheet
Modern physics is the highest-weighted topic on the entire AP Physics 2 exam at approximately 21%. It covers quantum mechanics, atomic structure, nuclear physics, and special relativity concepts. Many students underestimate this section — but the formulas are among the most straightforward to apply once you understand the physical context.
| Formula | Name | Variables & Meaning |
|---|---|---|
| E = hf = hc / λ E = photon energy (J or eV), h = 6.63×10⁻³⁴ J·s, f = frequency (Hz), c = 3×10⁸ m/s, λ = wavelength (m) |
Photon Energy | The energy of a single photon is directly proportional to its frequency and inversely proportional to its wavelength. Higher frequency (shorter wavelength) = higher energy photon. Gamma rays carry far more energy per photon than radio waves — this is why gamma radiation is dangerous. |
| K_max = hf − φ K_max = maximum kinetic energy of ejected electron (J or eV), hf = photon energy, φ = work function of metal (J or eV) |
Photoelectric Effect | When a photon strikes a metal surface, it ejects an electron only if the photon energy exceeds the work function φ. Any excess energy becomes kinetic energy of the ejected electron. This equation proved that light behaves as discrete packets (photons) — Einstein won the Nobel Prize for this, not relativity. |
| λ = h / p = h / (mv) λ = de Broglie wavelength (m), h = Planck’s constant, p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s) |
de Broglie Wavelength | All matter has an associated wavelength — the de Broglie wavelength. Larger momentum means shorter wavelength. Electrons have measurable wavelengths (explaining electron diffraction); a baseball’s wavelength is so tiny it is physically meaningless. This is wave-particle duality. |
| E = mc² E = rest energy (J), m = mass (kg), c = speed of light (3×10⁸ m/s) |
Mass-Energy Equivalence | Mass and energy are interconvertible. A tiny amount of mass converts to an enormous amount of energy (c² = 9×10¹⁶ m²/s²). This is the energy source of nuclear reactions — fission and fusion both release energy by converting a small mass deficit into energy. |
| ΔE = Δmc² ΔE = energy released (J), Δm = mass defect (kg) |
Nuclear Binding Energy / Mass Defect | The energy released in a nuclear reaction equals the mass defect (difference between reactant and product masses) multiplied by c². In nuclear fission, a heavy nucleus splits into lighter fragments with slightly less total mass — the mass difference is released as energy. |
| N = N₀ (½)^(t/t½) N = remaining nuclei, N₀ = initial nuclei, t = elapsed time, t½ = half-life |
Radioactive Decay | After each half-life, half the remaining radioactive nuclei decay. After n half-lives, the fraction remaining is (½)ⁿ. After 10 half-lives, less than 0.1% of the original sample remains. Half-life is constant for a given isotope — it does not depend on temperature, pressure, or chemical state. |
| hf = E_i − E_f hf = photon energy emitted/absorbed, E_i = initial energy level (eV), E_f = final energy level (eV) |
Atomic Energy Level Transitions | When an electron transitions between energy levels in an atom, it emits or absorbs a photon whose energy equals the difference between the levels. Emission: electron drops to lower level, photon released. Absorption: photon absorbed, electron jumps to higher level. This produces atomic spectra. |
Light of frequency 8.0 × 10¹⁴ Hz strikes a metal with a work function of 2.0 eV. What is the maximum kinetic energy of the ejected electrons in eV?
Step 1 — Find photon energy: $$E = hf = (6.63 \times 10^{-34})(8.0 \times 10^{14}) = 5.30 \times 10^{-19} \text{ J}$$
Step 2 — Convert to eV: $$E = \frac{5.30 \times 10^{-19}}{1.60 \times 10^{-19}} = 3.31 \text{ eV}$$
Step 3 — Apply photoelectric equation: $$K_{max} = hf – \phi = 3.31 – 2.0 = 1.31 \text{ eV}$$
✅ Maximum Kinetic Energy = 1.31 eVHow to Use the AP Physics 2 Equation Sheet on Exam Day
Having the equation sheet is only useful if you know how to navigate it under time pressure. Here are the strategies that consistently separate students who score 4–5 from those who score 2–3.
Before the Exam: Build Fluency, Not Dependence
- Know the layout cold. Practice with the actual College Board PDF so you know exactly where each formula group is located. On exam day, you should be able to find any formula in under 10 seconds.
- Understand every variable. For each formula, be able to state what every letter represents, its units, and what happens to the output when each variable increases or decreases.
- Practice without the sheet first. Work practice problems from memory, then check the sheet. This builds the conceptual understanding that the exam actually tests.
- Know what is NOT on the sheet. The right-hand rule, Lenz’s law direction, sign conventions for lenses/mirrors, and Kirchhoff’s laws are not given — you must know these conceptually.
During the Exam: Strategic Sheet Use
- Read the problem first, then find the formula. Never scan the equation sheet looking for inspiration — identify what physics is happening, then look up the relevant formula.
- Check units before calculating. The equation sheet shows units implicitly through the variable definitions. If your units do not work out correctly, you have used the wrong formula or made a substitution error.
- For free-response, write the formula before substituting. AP graders award points for correct formula selection even if your arithmetic is wrong. Always write the symbolic equation first.
- Use the constants table actively. Do not try to recall constants from memory — look them up every time. A misremembered constant destroys an otherwise perfect solution.
The following are tested on the AP Physics 2 exam but are not on the equation sheet: the right-hand rule for magnetic force direction, Lenz’s law (direction of induced current), sign conventions for the mirror/lens equation, Kirchhoff’s voltage and current laws (conceptual), the definition of the mole, and the relationship between period and frequency (f = 1/T). You must know these from your coursework.
Practice Problems: Apply the AP Physics 2 Equation Sheet
Work through each problem using only the formulas covered in this guide. Attempt each one independently before revealing the solution. Each answer includes a complete step-by-step explanation.
Problem 1 — Fluid Mechanics Easy
Question: A diver is 20 m below the surface of the ocean (ρ = 1025 kg/m³). The atmospheric pressure at the surface is 1.01 × 10⁵ Pa. What is the total pressure at this depth?
Apply: $$P = P_0 + \rho g h$$
Substitute: $$P = 1.01 \times 10^5 + (1025)(9.8)(20)$$
Calculate: $$P = 101{,}000 + 200{,}900 = 301{,}900 \text{ Pa} \approx 3.02 \times 10^5 \text{ Pa}$$
This is approximately 3 atmospheres of pressure — nearly triple the surface pressure. This is why divers must equalize ear pressure as they descend.
✅ Answer: 3.02 × 10⁵ Pa
Problem 2 — Thermodynamics Easy
Question: A gas absorbs 500 J of heat and does 200 J of work on its surroundings. What is the change in the internal energy of the gas?
Apply First Law: $$\Delta U = Q – W$$
Substitute: $$\Delta U = 500 – 200 = 300 \text{ J}$$
The gas gained 300 J of internal energy. 500 J came in as heat; 200 J left as work done on the surroundings; the remaining 300 J stayed in the gas as increased molecular kinetic energy (higher temperature).
✅ Answer: ΔU = +300 J
Problem 3 — Electrostatics Medium
Question: A parallel plate capacitor has plate area 0.04 m² and plate separation 2.0 mm. It is connected to a 12 V battery. (a) Find the capacitance. (b) Find the charge stored. Assume no dielectric (κ = 1).
(a) Capacitance: $$C = \frac{\kappa \varepsilon_0 A}{d} = \frac{(1)(8.85 \times 10^{-12})(0.04)}{0.002}$$
$$C = \frac{3.54 \times 10^{-13}}{0.002} = 1.77 \times 10^{-10} \text{ F} = 177 \text{ pF}$$
(b) Charge stored: $$Q = CV = (1.77 \times 10^{-10})(12) = 2.12 \times 10^{-9} \text{ C} = 2.12 \text{ nC}$$
✅ Answer: C = 177 pF, Q = 2.12 nC
Problem 4 — Optics Medium
Question: A ray of light travels from water (n = 1.33) into glass (n = 1.50) at an angle of incidence of 40°. What is the angle of refraction?
Apply Snell’s Law: $$n_1 \sin\theta_1 = n_2 \sin\theta_2$$
Substitute: $$(1.33)\sin(40°) = (1.50)\sin\theta_2$$
$$(1.33)(0.643) = (1.50)\sin\theta_2$$
$$0.855 = 1.50 \sin\theta_2$$
$$\sin\theta_2 = \frac{0.855}{1.50} = 0.570$$
$$\theta_2 = \sin^{-1}(0.570) = 34.8°$$
Light bends toward the normal (smaller angle) when entering a denser medium — confirmed since 34.8° < 40°.
✅ Answer: θ₂ ≈ 34.8°
Problem 5 — Modern Physics Hard
Question: A radioactive isotope has a half-life of 8 days. A sample initially contains 6.4 × 10¹⁰ atoms. (a) How many atoms remain after 32 days? (b) What fraction of the original sample has decayed?
(a) Number of half-lives elapsed: $$n = \frac{t}{t_{1/2}} = \frac{32}{8} = 4 \text{ half-lives}$$
Apply decay equation: $$N = N_0 \left(\frac{1}{2}\right)^n = 6.4 \times 10^{10} \times \left(\frac{1}{2}\right)^4$$
$$N = 6.4 \times 10^{10} \times \frac{1}{16} = 4.0 \times 10^9 \text{ atoms}$$
(b) Fraction decayed: $$\text{Fraction remaining} = \frac{1}{16} = 0.0625 = 6.25\%$$
$$\text{Fraction decayed} = 1 – 0.0625 = 0.9375 = 93.75\%$$
✅ Answer: (a) 4.0 × 10⁹ atoms remain, (b) 93.75% has decayed
🧠 Quick Quiz: AP Physics 2 Equation Sheet
Select the best answer for each question. Instant feedback appears after each selection.
1. A gas molecule at 300 K has an average kinetic energy of K₁. The temperature is raised to 600 K. What is the new average kinetic energy?
2. A photon has a wavelength of 400 nm. Which of the following correctly calculates its energy? (h = 6.63 × 10⁻³⁴ J·s, c = 3.00 × 10⁸ m/s)
3. Two resistors, R₁ = 6 Ω and R₂ = 3 Ω, are connected in parallel across a 12 V battery. What is the total current drawn from the battery?
Frequently Asked Questions About the AP Physics 2 Equation Sheet
What formulas are on the AP Physics 2 equation sheet?
The official AP Physics 2 equation sheet provided by College Board includes formulas for fluid mechanics (pressure, buoyancy, flow rate, Bernoulli’s equation), thermodynamics (ideal gas law, first law, specific heat, kinetic energy), electrostatics (Coulomb’s law, electric field, potential, capacitance), circuits (Ohm’s law, power, series/parallel combinations, RC time constant), magnetism (magnetic force, flux, Faraday’s law), optics (Snell’s law, lens/mirror equation, magnification, interference), and modern physics (photon energy, photoelectric effect, de Broglie wavelength, radioactive decay, mass-energy equivalence).
Is the Physics 2 equation sheet provided during the AP exam?
Yes. The College Board provides the official AP Physics 2 equation sheet — called the Exam Reference Information — to every student at the start of the exam. It is a multi-page booklet containing all physical constants, unit symbols, conversion factors, trigonometric values for common angles, and all major physics equations organized by topic. You do not need to memorize every formula, but you absolutely must understand what each formula means and when to apply it. Students who rely on the sheet without prior understanding lose significant time and frequently misapply equations.
What physical constants are given on the AP Physics 2 formula sheet?
The AP Physics 2 formula sheet provides all essential physical constants including: speed of light (c = 3.00 × 10⁸ m/s), Planck’s constant (h = 6.63 × 10⁻³⁴ J·s), elementary charge (e = 1.60 × 10⁻¹⁹ C), Coulomb’s constant (k = 9.0 × 10⁹ N·m²/C²), Boltzmann’s constant (k_B = 1.38 × 10⁻²³ J/K), universal gas constant (R = 8.31 J/mol·K), Avogadro’s number (N_A = 6.02 × 10²³ mol⁻¹), proton mass (1.67 × 10⁻²⁷ kg), electron mass (9.11 × 10⁻³¹ kg), vacuum permittivity (ε₀ = 8.85 × 10⁻¹² C²/N·m²), vacuum permeability (μ₀ = 4π × 10⁻⁷ T·m/A), and gravitational acceleration (g = 9.8 m/s²).
What is the ideal gas law formula in AP Physics 2?
The ideal gas law in AP Physics 2 is $$PV = nRT$$, where P is pressure in Pascals, V is volume in cubic meters, n is the number of moles, R is the universal gas constant (8.31 J/mol·K), and T is absolute temperature in Kelvin. An equivalent molecular form is $$PV = Nk_BT$$, where N is the number of individual molecules and k_B is Boltzmann’s constant (1.38 × 10⁻²³ J/K). Both forms appear on the official equation sheet. Temperature must always be in Kelvin — this is the most common mistake on thermodynamics problems.
What optics formulas are on the AP Physics 2 equation sheet?
The AP Physics 2 equation sheet includes the following optics formulas: index of refraction (n = c/v), Snell’s law (n₁sinθ₁ = n₂sinθ₂), the thin lens and mirror equation (1/d_o + 1/d_i = 1/f), magnification (m = −d_i/d_o = h_i/h_o), double-slit bright fringe condition (d sinθ = mλ), double-slit dark fringe condition (d sinθ = (m + ½)λ), and the critical angle for total internal reflection (sinθ_c = n₂/n₁). The relationship between index of refraction and wave speed (n = c/v) is also provided.
Do I need to memorize the AP Physics 2 equation sheet?
You do not need to memorize the AP Physics 2 equation sheet since it is provided during the exam. However, you must understand what every formula means, what each variable represents, its units, and when to apply each equation. Students who only look up formulas during the exam without prior understanding lose significant time and often apply equations incorrectly. The goal is fluency — being able to identify which formula applies to a given physical situation within seconds, then use the sheet to confirm the exact form. Think of it like a dictionary: having it available does not help if you do not already know the language.
Which topic on the AP Physics 2 equation sheet has the most exam weight?
Modern physics (quantum mechanics, atomic structure, and nuclear physics) carries the highest exam weight at approximately 21% of the total AP Physics 2 score. This is followed by electrostatics (~18%), electric circuits (~17%), thermodynamics (~12%), optics (~12%), fluid mechanics (~10%), and magnetism (~10%). Despite its high weight, modern physics is often the most under-studied topic. The formulas for this section — photon energy, photoelectric effect, de Broglie wavelength, radioactive decay, and mass-energy equivalence — are among the most straightforward to apply once you understand the physical context.
📋 Summary: AP Physics 2 Equation Sheet — Complete Formula Guide
- The official AP Physics 2 equation sheet is provided by College Board during the exam — it contains ~40–50 equations across 7 topic areas plus all physical constants
- Fluid Mechanics (~10%): Pressure, hydrostatic pressure, buoyancy (Archimedes), continuity equation, Bernoulli’s equation
- Thermodynamics (~12%): Ideal gas law (PV = nRT and PV = Nk_BT), first law (ΔU = Q − W), specific heat (Q = mcΔT), average kinetic energy (K = 3/2 k_BT)
- Electrostatics (~18% — highest single topic): Coulomb’s law, electric field, electric potential, capacitance, energy stored in capacitor, parallel plate capacitor
- Circuits (~17%): Ohm’s law (V = IR), power (P = IV = I²R = V²/R), series/parallel resistors and capacitors, RC time constant
- Magnetism (~10%): Magnetic force on charge and wire, magnetic flux, Faraday’s law, magnetic field of a wire
- Optics (~12%): Snell’s law, thin lens/mirror equation, magnification, double-slit interference, critical angle
- Modern Physics (~21% — highest overall weight): Photon energy, photoelectric effect, de Broglie wavelength, mass-energy equivalence, radioactive decay, atomic energy transitions
- Always use temperature in Kelvin, not Celsius, in all thermodynamics and kinetic theory equations
- The right-hand rule, Lenz’s law direction, and Kirchhoff’s laws are not on the sheet — know these conceptually
Ready to go deeper? Explore our AP Physics 2 Complete Study Guide → for full unit breakdowns, past free-response walkthroughs, and score prediction tools.
📎 Sources & References
- College Board. “AP Physics 2: Algebra-Based — 2026 Exam Reference Information.” Retrieved from apcentral.collegeboard.org
- PrepScholar. “What’s the AP Physics 2 Equation Sheet? A Complete Breakdown.” Retrieved from blog.prepscholar.com
- RefreshKid. “AP Physics 2 — Syllabus, Exam Date & Formula Sheet.” Retrieved from blog.refreshkid.com
- College Board. “AP Physics 2: Algebra-Based — Table of Information and Equations (2020 Edition).” Retrieved from apcentral.collegeboard.org
📋 Editorial Standards: This content was written and reviewed by Dr. Irfan Mansuri (Ph.D. Physics Education, AP Physics Certified Instructor). All formulas have been verified against the official 2026 College Board AP Physics 2 Exam Reference Information. Last verified: March 6, 2026. IrfanEdu is committed to accuracy, depth, and genuine educational value in all published content.
📐 Curriculum Alignment: This content aligns with College Board AP Physics 2: Algebra-Based course and exam description (CED), covering all seven major units as defined in the official AP Physics 2 curriculum framework.