FREE GRE Physics Study Guide 2026: All 9 ETS Content Areas

This free GRE Physics study guide teaches to the GRE Physics Subject Test — every content area ETS tests, organized the way the official outline groups them.^[1] The test is a standardized exam for physics graduate-school applicants: about 70 multiple-choice questions over 170 minutes, scored on a 200–990 scale.^[2]

It covers the whole undergraduate physics curriculum, so the challenge is breadth and speed more than depth. This guide is interactive, not a wall of text: every area has a built-in checkpoint quiz, hover-able glossary terms, worked examples, key formulas, and concept questions, so you learn by doing.

Read this guide area by area — lead with the heavy hitters, Classical Mechanics and Electromagnetism — test yourself at each checkpoint, then round out your free prep with our practice questions and flashcards.

GRE Physics Exam Snapshot

Because there is a quarter-point penalty for wrong answers, blind guessing is roughly break-even, but eliminating even one choice makes guessing worthwhile.^[2] Spend your study time across all nine areas, but weight it by how much each is tested:

ETS reports these area shares as approximate, so the exact mix shifts a little each form.^[1] This guide teaches all nine areas in the official order, each as a study module with its major sub-topics.

1 · Classical Mechanics

About 20% of the test — the single biggest area. Newtonian mechanics plus the Lagrangian and Hamiltonian formulations: kinematics, dynamics, energy and momentum, rotation, oscillations, gravitation, and non-inertial frames.^[2]

Kinematics & Newton’s Laws

Start with the constant-acceleration equations and Newton’s second law $\vec F = m\vec a$. Draw a free-body diagram, resolve forces along and perpendicular to the motion, and apply the law component by component. For a block on a frictionless incline of angle $\theta$, the acceleration down the slope is $g\sin\theta$.

Work, Energy & Momentum

The work-energy theorem says the net work equals the change in kinetic energy, so you can find a final speed without tracking time. Conserve momentum when no net external force acts, and conserve mechanical energy when only conservative forces act.

Rotation & Oscillations

Rotational dynamics mirror the linear laws with the moment of inertia $I$ in place of mass and torque $\tau = I\alpha$ in place of force. Conserve angular momentum $L = I\omega$when no external torque acts — the spinning skater who pulls her arms in speeds up. For simple harmonic motion, a mass–spring system has $\omega = \sqrt{k/m}$ and a simple pendulum has $T = 2\pi\sqrt{L/g}$.

Lagrangian & Hamiltonian Mechanics

The Lagrangian $L = T - V$ and the Euler-Lagrange equation $\frac{d}{dt}\frac{\partial L}{\partial \dot q} - \frac{\partial L}{\partial q} = 0$ reproduce Newton’s laws while handling constraints cleanly. The Hamiltonian $H = T + V$is the total energy in terms of coordinates and momenta, with motion set by Hamilton’s equations.

2 · Electromagnetism

About 18% of the test.Electrostatics, currents and circuits, magnetic fields and induction, and Maxwell’s equations — the second-largest area, and one where a few core laws cover most questions.^[2]

Electrostatics & Gauss’s Law

Coulomb’s law gives the force between charges; the field of a point charge is $E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}$. For symmetric distributions, Gauss’s law $\oint \vec E\cdot d\vec A = \dfrac{Q_{enc}}{\varepsilon_0}$ gives the field in one step. Inside a conductor in equilibrium the field is zero, with any excess charge on the surface.

Currents & Circuits

Apply Ohm’s law $V = IR$ and Kirchhoff’s rules. Resistors in series add; in parallel their reciprocals add. In an RC circuit the charge relaxes with time constant $\tau = RC$; in an RL circuit $\tau = L/R$.

Magnetic Fields & Induction

A moving charge feels the Lorentz force $\vec F = q\vec v\times\vec B$. The Biot-Savart and Ampere’s laws give the field of a current; a long solenoid has $B = \mu_0 n I$. Faraday’s law $\varepsilon = -\dfrac{d\Phi_B}{dt}$ gives induced EMF, and Lenz’s law fixes its direction to oppose the change.

Maxwell’s Equations & EM Waves

The four Maxwell’s equations unify all of the above and predict electromagnetic waves traveling at $c = 1/\sqrt{\mu_0\varepsilon_0}$. EM waves are transverse, need no medium, and carry energy with the Poynting vector $\vec S = \tfrac{1}{\mu_0}\vec E\times\vec B$.

3 · Optics & Wave Phenomena

About 9% of the test. Wave motion and the Doppler effect, geometric optics (mirrors and lenses), and physical optics (interference, diffraction, and polarization).^[2]

Wave Motion & the Doppler Effect

A wave obeys $v = \lambda f$. When a wave crosses into a new medium its frequency stays the same while wavelength and speed change. The Doppler effect shifts the observed frequency: approaching sources blueshift, receding sources redshift.

Geometric Optics

Refraction follows Snell’s law $n_1\sin\theta_1 = n_2\sin\theta_2$; light slows in a higher-index medium. The thin-lens and mirror equation is $\dfrac{1}{f} = \dfrac{1}{d_o} + \dfrac{1}{d_i}$.

Interference, Diffraction & Polarization

Young’s double slit gives bright fringes where $d\sin\theta = m\lambda$; halving the slit spacing or doubling the wavelength widens the fringe spacing. Single-slit diffraction has minima at $a\sin\theta = m\lambda$. An ideal polarizer passes half of unpolarized light; Malus’s law gives $I = I_0\cos^2\theta$ for already-polarized light.

4 · Thermodynamics & Statistical Mechanics

About 10% of the test. The laws of thermodynamics, ideal-gas processes and heat engines, and the statistical-mechanics distributions that connect microscopic states to macroscopic behavior.^[2]

The Laws of Thermodynamics

The first law $\Delta U = Q - W$ is energy conservation. The second law says entropy never decreases in an isolated system, setting the direction of spontaneous change; a heat pump moving heat from cold to hot needs external work because of it. The third law says entropy approaches a constant (zero for a perfect crystal) as $T\to 0$.

Ideal Gases & Processes

For an ideal gas $PV = nRT$, and internal energy depends only on temperature. Identify what is held fixed in a process, then read off the first law:

Statistical Mechanics & Distributions

The Maxwell-Boltzmann distribution gives molecular speeds in a classical gas; the average translational energy per molecule is $\tfrac{3}{2}k_B T$. At low temperature or high density, quantum statistics take over — Fermi-Dirac for fermions, Bose-Einstein for bosons. The Stefan-Boltzmann law says a blackbody radiates power $\propto T^4$.

5 · Quantum Mechanics

About 12% of the test.The Schrodinger equation and wave functions, the standard solvable potentials, and the operator formalism — spin, commutators, and uncertainty.^[2]

Wave Functions & the Schrodinger Equation

The Schrodinger equation governs the wave function $\psi$. The time-independent form is $\hat H\psi = E\psi$, and the probability of finding the particle in $[a,b]$ is $\int_a^b |\psi(x)|^2\,dx$. Wave functions must be normalized and, for bound states, vanish at infinity.

Standard Potentials & Solutions

Memorize the textbook solutions. The infinite square well of width $L$ has $E_n = \dfrac{n^2 h^2}{8mL^2}$; the harmonic oscillator has evenly spaced levels $E_n = (n+\tfrac{1}{2})\hbar\omega$. Tunneling through a barrier and the hydrogen-atom solution round out the set.

Operators, Spin & Uncertainty

Observables are operators; the Hamiltonian $\hat H$ is total energy. The canonical commutator is $[\hat x,\hat p] = i\hbar$, from which the uncertainty principle $\Delta x\,\Delta p \ge \hbar/2$ follows. The electron is a spin-$\tfrac{1}{2}$ fermion.

6 · Atomic Physics

About 10% of the test.Atomic structure and quantum numbers, spectra and selection rules, and the small splittings — fine and hyperfine structure, the Zeeman effect, and the Stern-Gerlach result.^[2]

Atomic Structure & Quantum Numbers

An electron in an atom is labeled by four quantum numbers — principal $n$, azimuthal $l$, magnetic $m_l$, and spin $m_s$. The Pauli exclusion principle forbids two electrons from sharing all four, which builds the periodic table shell by shell.

Spectra & Selection Rules

The Bohr model gives hydrogen energies $E_n = -13.6\,\text{eV}/n^2$. A photon is emitted or absorbed when an electron jumps levels, its energy equal to the gap. The longest-wavelength (lowest-energy) visible line comes from the smallest gap in the Balmer series.

Fine Structure, Zeeman & Stern-Gerlach

Fine structure comes from spin-orbit coupling; hyperfine structure from the nuclear spin. The Zeeman effect splits levels in a magnetic field, and the Stern-Gerlach experimentsplit an atomic beam into discrete components — direct evidence that angular momentum (and spin) is quantized.

7 · Special Relativity

About 6% of the test.The two postulates and their kinematic consequences — time dilation and length contraction — plus relativistic energy and momentum.^[2]

Postulates, Time Dilation & Length Contraction

Special relativity rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light $c$ is the same for every observer. From them follow time dilation $\Delta t = \gamma\,\Delta t_0$ and length contraction $L = L_0/\gamma$, both set by the Lorentz factor $\gamma = 1/\sqrt{1 - v^2/c^2}$.

Relativistic Energy & Momentum

Total energy is $E = \gamma mc^2$ and momentum $p = \gamma mv$, combined in the energy-momentum relation $E^2 = (pc)^2 + (mc^2)^2$. As $v\to c$, kinetic energy grows without bound, which is why no massive object reaches $c$.

8 · Laboratory Methods

About 6% of the test.Data and error analysis, counting statistics, and the instruments and techniques of a physics lab — the part of the exam that rewards practical, experimental knowledge.^[2]

Error Analysis & Statistics

Distinguish random from systematic error. Independent random uncertainties add in quadrature, $\sigma = \sqrt{\sigma_1^2 + \sigma_2^2}$. Counting experiments follow Poisson statistics, so a count of $N$ has uncertainty $\sqrt{N}$ and a fractional uncertainty $1/\sqrt{N}$ that shrinks as you collect more data.

Instrumentation & Techniques

Know the workhorse tools and what each is for:

9 · Specialized Topics

About 9% of the test.A grab bag of modern physics: nuclear and particle physics, condensed matter, and astrophysics. You don’t need deep mastery — recognizing the key terms and results carries most of these questions.^[2]

Nuclear & Particle Physics

Know binding energy and the magic numbers (2, 8, 20, 28, 50, 82, 126) that give nuclei extra stability, plus the basics of alpha, beta, and gamma decay. In particle physics, recall the quark model and color confinement— quarks are never isolated, only bound in hadrons.

Condensed Matter & Astrophysics

Condensed matter brings crystal structure, the free-electron model, semiconductors, superconductivity (zero resistance), and superfluidity (zero viscosity). In astrophysics, the Chandrasekhar limit(~1.4 solar masses) caps a white dwarf’s mass before it collapses into a neutron star or black hole.

How to Use This Study Guide

A study guide is a map, not the whole territory — use it alongside the official ETS GRE Physics practice book and our free tools. Because the test rewards breadth and speed, the goal is fast, accurate pattern-recognition across all nine areas, so spaced, mixed practice beats one long cram. Lead with Classical Mechanics and Electromagnetism (about 38% combined), then layer in the modern-physics areas.

GRE Physics Glossary

Quick definitions for the laws, equations, and terms you’ll meet most across the GRE Physics Subject Test:

Bohr model

A model of hydrogen with quantized angular momentum $L = n\hbar$ and energies $E_n = -13.6\,\text{eV}/n^2$. It predicts the spectral series emitted in electron transitions.

Carnot efficiency

The maximum efficiency of any heat engine between two reservoirs, $\eta = 1 - T_c/T_h$, with temperatures in kelvin. No engine between the same temperatures can do better.

Chandrasekhar limit

The maximum mass (about 1.4 solar masses) of a white dwarf supported by electron degeneracy pressure. Above it, the core collapses into a neutron star or black hole.

Commutator

For operators $\hat A$ and $\hat B$, $[\hat A,\hat B] = \hat A\hat B - \hat B\hat A$. The canonical relation is $[\hat x,\hat p] = i\hbar$, which underlies the uncertainty principle.

Diffraction

The bending and spreading of a wave around edges or through an aperture. A single slit of width $a$ has diffraction minima at $a\sin\theta = m\lambda$.

Doppler effect

The shift in observed frequency when source and observer move relative to each other. Light from a receding source is redshifted (lower frequency); from an approaching source it is blueshifted.

Energy-momentum relation

The relativistic link $E^2 = (pc)^2 + (mc^2)^2$. It gives $E = mc^2$ for a particle at rest and $E = pc$ for a massless particle such as a photon.

Entropy

A measure of disorder or the number of microstates of a system. The second law says the entropy of an isolated system never decreases, setting the arrow of time.

Faraday's law

A changing magnetic flux induces an electromotive force, $\varepsilon = -\,d\Phi_B/dt$. The minus sign (Lenz's law) makes the induced current oppose the change that created it.

Fine structure

Small splittings of atomic spectral lines caused mainly by spin-orbit coupling — the interaction of an electron's spin with its orbital motion. Hyperfine structure comes from the nuclear spin.

First law of thermodynamics

Conservation of energy for a thermodynamic system, $\Delta U = Q - W$: the change in internal energy equals heat added minus work done by the system.

Gauss's law

The net electric flux through a closed surface equals the enclosed charge over the permittivity of free space, $\Phi_E = Q_{enc}/\varepsilon_0$. It gives fields quickly when the charge has high symmetry.

GRE Physics Subject Test

A standardized exam from ETS for applicants to physics graduate programs. It has about 70 multiple-choice questions over 170 minutes and is scored 200-990, testing undergraduate physics across nine content areas.

Hamiltonian

For a time-independent potential, the total energy $H = T + V$ expressed in coordinates and momenta. Hamilton's equations $\dot q = \partial H/\partial p$ and $\dot p = -\partial H/\partial q$ govern the motion.

Lagrangian

Kinetic energy minus potential energy, $L = T - V$, written in generalized coordinates. Making the action stationary gives the Euler-Lagrange equations of motion.

Length contraction

An object moving at speed $v$ is shortened along its direction of motion: $L = L_0/\gamma$, where $L_0$ is the proper length measured in the object's rest frame.

Lenz's law

An induced current always flows in the direction that opposes the change in magnetic flux producing it — the physical content of the minus sign in Faraday's law and a statement of energy conservation.

Lorentz factor

$\gamma = 1/\sqrt{1 - v^2/c^2}$, the factor that scales relativistic time dilation, length contraction, and energy. It is ≈ 1 at low speed and diverges as $v \to c$.

Magic numbers

Proton or neutron counts (2, 8, 20, 28, 50, 82, 126) that fill nuclear shells and give extra stability — the nuclear analog of noble-gas electron configurations.

Maxwell-Boltzmann distribution

The classical distribution of molecular speeds in an ideal gas at temperature $T$. The average translational kinetic energy per molecule is $\tfrac{3}{2}k_B T$.

Maxwell's equations

The four laws of electromagnetism — Gauss's law, Gauss's law for magnetism, Faraday's law, and the Ampere-Maxwell law — that together predict electromagnetic waves traveling at $c = 1/\sqrt{\mu_0 \varepsilon_0}$.

Moment of inertia

The rotational analog of mass, $I = \sum m_i r_i^2$, measuring resistance to angular acceleration. The parallel-axis theorem $I = I_{cm} + Md^2$ shifts it to a parallel axis.

Pauli exclusion principle

No two identical fermions (half-integer spin, e.g. electrons) may occupy the same quantum state. It explains shell filling, the periodic table, and the stability of matter.

Photoelectric effect

The ejection of electrons from a metal by light, with maximum kinetic energy $KE = hf - \phi$, where $\phi$ is the work function. It is direct evidence for the photon nature of light.

Quantum numbers

The four labels of an atomic electron: principal $n$, azimuthal $l$, magnetic $m_l$, and spin $m_s$. The Pauli principle forbids two electrons sharing all four.

Scaled score

The 200-990 number reported for the GRE Physics Subject Test, in 10-point increments. The raw score (correct answers minus one-quarter of wrong answers) is converted to this scale, and a percentile rank is reported alongside it.

Schrodinger equation

The fundamental equation of quantum mechanics. Time-independent form $\hat H \psi = E\psi$ gives stationary states and energies; the wave function $\psi$ has $|\psi|^2$ as a probability density.

Snell's law

When light crosses between media, $n_1 \sin\theta_1 = n_2 \sin\theta_2$. It governs refraction; total internal reflection occurs when light moving into a less dense medium exceeds the critical angle.

Stern-Gerlach experiment

An experiment in which a beam of atoms passing through a non-uniform magnetic field splits into discrete components, demonstrating the quantization of angular momentum (and electron spin).

Time dilation

A moving clock runs slow as seen from a stationary frame: $\Delta t = \gamma\,\Delta t_0$, where $\Delta t_0$ is the proper time measured in the clock's own rest frame.

Uncertainty principle

Conjugate quantities cannot both be sharp: $\Delta x\,\Delta p \ge \hbar/2$. It is a fundamental consequence of the wave nature of matter, not a limit of measurement.

Wave function

The quantum state $\psi(x)$ of a particle. Its squared magnitude $|\psi|^2$ is the probability density, and $\int_a^b |\psi|^2\,dx$ gives the probability of finding the particle in $[a,b]$.

Work-energy theorem

The net work done on an object equals its change in kinetic energy, $W_{net} = \tfrac{1}{2}mv_f^2 - \tfrac{1}{2}mv_i^2$. It lets you find a final speed from forces without tracking time.

Zeeman effect

The splitting of atomic energy levels and spectral lines in an external magnetic field, due to the interaction of the field with the atom's magnetic moments.

Free GRE Physics Study Materials & Resources

Everything you need to prepare for the GRE Physics Subject Test is free here — no paywall, no sign-up. This guide is the foundation; pair it with the rest of our free GRE Physics study materials for active recall, timed practice, and last-minute review:

• GRE Physics Practice Test — exam-style questions across all nine content areas, with explanations.
• GRE Physics Flashcards — active-recall decks for the high-yield laws, equations, and constants.

GRE Physics Study Guide FAQ

References

1. 1.ETS. “GRE Subject Tests: Content and Structure.” ETS. ↑
2. 2.ETS. “GRE Physics Test Practice Book.” ETS. ↑
3. 3.ETS. “GRE Subject Tests: Physics.” ETS. ↑
4. 4.ETS. “GRE Subject Tests: Scores.” ETS. ↑
5. 5.NIST. “The NIST Reference on Constants, Units, and Uncertainty.” National Institute of Standards and Technology. ↑

Sources for the concept answers

Every answer in the GRE Physics concept questions above is drawn from an official primary source:

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