AP Physics 2 equation sheet, explained

By Ashraf Bhura, Co-Founder, STEM-Tutor · Updated October 2026

AP Physics 2 gives you an equation sheet, but the exam rewards knowing which idea applies. Here are the key equations by topic and what they mean.

Thermodynamics

• PV = nRT: the ideal gas law. Temperature must be in kelvin.
• ΔU = Q + W: the first law. Watch the sign convention: on the AP sheet, W is work done on the gas.
• W = −PΔV: work done on a gas at constant pressure.
• Q/Δt = kAΔT/L: rate of heat conduction through a material.

Electric force, field and potential

• F = kq₁q₂/r²: Coulomb's law.
• E = F/q: electric field is force per unit charge.
• V = kq/r and ΔU = qΔV: potential and potential energy.
• C = κε₀A/d and Q = CΔV: capacitors.

Circuits

• I = Δq/Δt and ΔV = IR: current and Ohm's law.
• R = ρL/A: resistance of a wire.
• P = IΔV: electrical power.
• Series resistors add; parallel resistors add as reciprocals. Kirchhoff's rules come from conservation of charge and energy.

Magnetism and induction

• F = qvB sinθ: force on a moving charge in a magnetic field.
• F = ILB sinθ: force on a current-carrying wire.
• Φ = BA cosθ and ε = −ΔΦ/Δt: magnetic flux and induced emf.

Optics and waves

• n = c/v and n₁sinθ₁ = n₂sinθ₂: refraction.
• 1/s_i + 1/s_o = 1/f: thin lens and mirror equation. Sign conventions decide real or virtual images.
• d sinθ = mλ: double-slit and grating interference.

Modern physics

• E = hf: photon energy.
• K_max = hf − φ: the photoelectric effect.
• λ = h/p: de Broglie wavelength.
• E = mc²: mass-energy equivalence.

Using the sheet in the exam

1. Name the concept first, then find the equation.
2. Check units, especially kelvin, metres and coulombs.
3. For circuits, redraw the circuit before calculating anything.
4. Download the current official sheet from AP Central and practise with it all year.

Worked examples, one per topic

Example 1: ideal gas law

A 0.02 m³ container holds 1 mol of gas at 300 K. Find the pressure. Use R = 8.31 J/(mol·K).

• P = nRT/V = 1 × 8.31 × 300 / 0.02 ≈ 1.25 × 10⁵ Pa, a little above atmospheric pressure.

Example 2: first law of thermodynamics

A gas absorbs 500 J of heat while 200 J of work is done by the gas. Find the change in internal energy.

• On the AP sheet, W is work done on the gas, so W = −200 J.
• ΔU = Q + W = 500 − 200 = 300 J.

Example 3: Coulomb's law

Two charges of +2 µC and −3 µC are 0.3 m apart. Find the force. Use k = 9.0 × 10⁹ N·m²/C².

• F = k|q₁q₂|/r² = 9 × 10⁹ × 6 × 10⁻¹² / 0.09 = 0.6 N, attractive because the charges are opposite.

Example 4: series and parallel resistors

A 12 V battery is connected to a 4 Ω resistor in series with a parallel pair of 6 Ω and 3 Ω.

• Parallel pair: 1/R = 1/6 + 1/3 = 1/2, so R = 2 Ω. Total resistance = 4 + 2 = 6 Ω.
• Current from the battery: I = 12/6 = 2 A.
• Voltage across the parallel pair: 2 × 2 = 4 V, so the 6 Ω carries 4/6 ≈ 0.67 A and the 3 Ω carries 4/3 ≈ 1.33 A. They add to 2 A, as they must.

Example 5: refraction

Light passes from air (n = 1.00) into glass (n = 1.50) at 30° to the normal. Find the refracted angle.

• sinθ₂ = (1.00 × sin30°)/1.50 = 0.333, so θ₂ ≈ 19.5°, bent toward the normal.

Example 6: photoelectric effect

Light of frequency 1.0 × 10¹⁵ Hz hits a metal with work function 2.3 eV. Find the maximum kinetic energy of the electrons. Use h = 4.14 × 10⁻¹⁵ eV·s.

• Photon energy hf = 4.14 eV. K_max = hf − φ = 4.14 − 2.3 = 1.84 eV.

Common mistakes

• Using Celsius instead of kelvin in PV = nRT.
• Getting the sign of W wrong in the first law. Check the convention on the sheet.
• Adding parallel resistances directly instead of as reciprocals.
• Measuring angles from the surface instead of the normal in refraction.

Practice questions

Try each one before opening the answer.

The key ideas in more depth

Physics 2 equations come in families. Electric force, field, potential energy and potential are four views of the same interaction, related by dividing by charge or multiplying by distance. Organising the sheet this way in your head makes it much easier to choose the right equation under time pressure.

Frequently asked questions

Is the AP Physics 2 sheet the same as the Physics 1 sheet?

They share some content, but Physics 2 adds thermodynamics, electricity, magnetism, optics and modern physics. Use the current official sheet for the exam you are taking.

Are constants like k, e and h given?

Yes, the sheet includes a table of constants and conversion factors. Know where it is.

Extra practice

Try each one before opening the answer.

Key takeaways

• Use kelvin in every gas law calculation.
• Watch the sign convention for work in the first law.
• Redraw circuits before applying series and parallel rules.
• Measure refraction angles from the normal.
• Photon energy is E = hf; the photoelectric effect gives K_max = hf − φ.

Quick check