The test, and the physicist's shortcuts

What the test is

The GRE Subject Test in Physics measures how well you understand the fundamental principles of undergraduate physics and how readily you apply them to problems. ETS describes it this way (ETS, GRE Subject Test Content and Structure; ETS, GRE Information Bulletin 2026–27):

• About 70 questions, each with five answer choices. Some are grouped in sets, built on diagrams, graphs, experimental data or descriptions of a physical situation (ETS, GRE Physics Test fact sheet).
• 2 hours in total, computer-delivered, with no separately timed sections and no break.
• No calculator. The bulletin says an onscreen calculator is not available for the Subject Tests and personal calculators are not permitted unless approved as an accommodation.
• SI units predominantly, and the test supplies a table of physical constants and a few SI conversion factors.
• Most questions need only the first three years of undergraduate physics.

ETS's committee of examiners sets the approximate weight of each content area:

Content category (ETS)	Share	Where this course covers it
Classical Mechanics	20%	Unit 2, four lessons
Electromagnetism	18%	Unit 3, four lessons
Optics and Wave Phenomena	8%	Unit 4
Thermodynamics and Statistical Mechanics	10%	Unit 5, two lessons
Quantum Mechanics	13%	Unit 7, three lessons
Atomic Physics	10%	Unit 8, two lessons
Special Relativity	6%	Unit 6
Laboratory Methods	6%	Unit 9
Specialized Topics (nuclear and particle, condensed matter, miscellaneous such as astrophysics and mathematical methods)	9%	Unit 10, two lessons

ETS also expects working fluency with calculus in one and several variables, rectangular, cylindrical and spherical coordinates, vector calculus, Fourier series, partial differential equations and boundary-value problems, matrices and determinants, and complex functions (ETS, GRE Subject Test Content and Structure). These appear inside physics questions, and occasionally on their own under Specialized Topics.

Scoring. You receive a total score on a 200–990 scale in 10-point increments (the range for one Subject Test is usually narrower), plus three percent-correct subscores: Classical Mechanics; Electromagnetism; and Quantum Mechanics and Atomic Physics (ETS, GRE Subject Tests for score users). The score depends on the number of questions you answer correctly, and nothing is subtracted for a wrong answer (ETS, Strategies and Tips; ETS, GRE Guide to the Use of Scores 2026–27). So never leave a question blank.

Dates. For 2026–27 the test windows are September 14–27, 2026; October 19–November 1, 2026; and April 19–May 2, 2027 (ETS, GRE Information Bulletin 2026–27). Check ETS's site for appointment availability before you plan.

The pace: 1 minute 43 seconds a question

120 minutes for about 70 questions is roughly $120/70 \approx 1.7$ minutes each. Many questions take 30 seconds if you recognise the setup; a few take four minutes if you grind algebra. The winning habit is two passes:

1. First pass. Answer everything you can do quickly. If a question will clearly take more than about two minutes, pick your best guess, use the mark-and-review feature to flag it, and move on. ETS's software lets you mark questions, see a list of answered and marked questions, and change answers while time remains (ETS, Strategies and Tips).
2. Second pass. Return to the marked questions with the time you banked.

Because blanks and wrong answers both score zero, a guess always beats a blank. Eliminating two of five choices raises a blind guess from a 1-in-5 chance to 1-in-3. The tools below are mostly elimination tools.

Tool 1: Dimensional analysis

Every correct formula is dimensionally consistent. Many wrong choices are not, and you can see it in seconds.

Worked example. A particle of mass $m$ is confined to a region of width $L$. Which combination could be its ground-state energy: $\hbar/(mL^2)$, $\hbar^2/(mL^2)$ or $\hbar^2/(mL)$?

Use $[\hbar] = \text{J s}$ and $\text{J} = \text{kg m}^2/\text{s}^2$:

$$\left[\frac{\hbar^2}{mL^2}\right] = \frac{\text{J}^2\,\text{s}^2}{\text{kg}\,\text{m}^2} = \frac{\text{J}^2\,\text{s}^2}{\text{J}\,\text{s}^2} = \text{J}.$$

Only $\hbar^2/(mL^2)$ is an energy. ($\hbar/(mL^2)$ is a frequency.) That is the infinite square well's scaling, $E_n = n^2\pi^2\hbar^2/(2mL^2)$, recovered without solving anything.

Building a formula. When a quantity depends on only a few parameters, dimensions often fix the formula up to a pure number. The speed $v$ of deep-water waves can depend only on $g$, the wavelength $\lambda$ and the density $\rho$. Density is the only one containing mass, so it cannot appear; then $v = C\sqrt{g\lambda}$ with $C$ dimensionless. (The full theory gives $C = 1/\sqrt{2\pi}$; the test usually only asks how $v$ scales.) Doubling the wavelength therefore multiplies the speed by $\sqrt 2 \approx 1.41$.

Habits that make this fast:

• Arguments of $\sin$, $\cos$, $\exp$ and $\ln$ must be dimensionless. A choice containing $e^{-t}$ or $\sin(x)$ with dimensional $t$ or $x$ is wrong.
• You can only add quantities with the same dimensions: $v\sin\theta + \sqrt{2gh}$ is fine; $\sin\theta + 2gh$ is not.
• Remember useful energy combinations: $mc^2$, $k_BT$, $\hbar\omega$, $qV$, $\hbar^2/(mL^2)$, $e^2/(4\pi\varepsilon_0 r)$, $Gm_1m_2/r$, $p^2/2m$.

Tool 2: Limiting cases and special values

A correct formula must give the right answer in every case you already understand. Plug in a limit and watch wrong choices fail.

Worked example (Atwood machine). Masses $m_1 > m_2$ hang over a massless, frictionless pulley. A choice for the acceleration reads $a = (m_1 - m_2)g/(m_1+m_2)$. Check:

• $m_2 \to 0$: $a \to g$, free fall. Correct.
• $m_1 = m_2$: $a = 0$, balance. Correct.
• A rival choice, $(m_1 - m_2)g/m_1$, passes both of these tests, and the limit $m_1 \to \infty$ as well. When two choices survive the easy limits, check one special case by a different route. The net force $(m_1 - m_2)g$ must accelerate both masses, so with $m_1 = 2m_2$ it is $m_2 g$ acting on $3m_2$: $a = g/3$. The first formula gives $g/3$; the rival gives $g/2$ because it forgot that $m_2$ is accelerated too.

Good limits to try:

Parameter	Try	You should know
An angle $\theta$	$0$, $90^\circ$	Flat ground, vertical wall, head-on, grazing
A mass	$\to 0$, $\to\infty$	Massless string or pulley, immovable object
A friction or damping constant	$0$	The ideal result
A distance	$r \to 0$, $r\to\infty$	Point-charge or uniform-field behaviour
A speed	$v \ll c$	Newtonian result
A temperature	$k_BT \gg \Delta E$, $k_BT \ll \Delta E$	Equipartition, ground state only
Two equal quantities	$m_1=m_2$, $R_1 = R_2$, $n_1 = n_2$	Symmetry: no reflection, equal sharing

Worked example (a harder one). A block of mass $m$ slides on the frictionless face of a wedge (mass $M$, angle $\theta$) that is itself free to slide on a frictionless floor. Which could be the wedge's acceleration: (i) $\dfrac{mg\sin\theta\cos\theta}{M+m}$ or (ii) $\dfrac{mg\sin\theta\cos\theta}{M+m\sin^2\theta}$?

Both vanish for $\theta = 0$, $\theta = 90^\circ$ and $M\to\infty$, as they must. Now take a massless wedge, $M \to 0$. A massless wedge can carry no net force, so the block feels no normal force and falls straight down with acceleration $g$; to stay in contact the wedge must shoot sideways with acceleration $g\cot\theta$. Choice (ii) gives $g\sin\theta\cos\theta/\sin^2\theta = g\cot\theta$; choice (i) gives $g\sin\theta\cos\theta$. Only (ii) survives.

Tool 3: Symmetry and conservation before forces

Before writing $F = ma$, ask what is conserved. Energy gives speeds; momentum handles collisions and explosions; angular momentum handles anything spinning or orbiting with no external torque; charge, baryon number and lepton number decide which particle reactions are allowed. Symmetry decides which way a field points and often that it is zero (at the centre of a ring, inside a uniform shell). Each content lesson has a "Recognise the setup" section; together they are a catalogue of the conserved quantity or symmetry that unlocks each classic problem.

Tool 4: Estimation without a calculator

The choices are usually spread by factors of two or more, so one or two significant figures are enough. Round aggressively, keep powers of ten separate, and use:

• $\pi^2 \approx 10$, $\sqrt 2 \approx 1.41$, $\sqrt 3 \approx 1.73$, $\ln 2 \approx 0.69$, $e \approx 2.72$;
• $(1+x)^n \approx 1 + nx$, $\sin x \approx \tan x \approx x$, $\cos x \approx 1 - x^2/2$ for small $x$;
• $g \approx 9.8\ \text{m/s}^2$ (take $10$ when the choices are far apart).

The constants worth carrying. All values are CODATA 2022 from NIST (NIST, Fundamental Physical Constants). The test gives you a table, but recognising the combinations below saves minutes.

Quantity	Value	Use it as
$hc$	$1239.84\ \text{eV nm}$	$\approx 1240\ \text{eV nm}$: photon energy from wavelength
$\hbar c$	$197.33\ \text{MeV fm}$	$\approx 200\ \text{MeV fm}$: nuclear and particle estimates
$m_ec^2$	$0.510\,999\ \text{MeV}$	$\approx 0.511\ \text{MeV}$
$m_pc^2$	$938.272\ \text{MeV}$	$\approx 938\ \text{MeV}$, about $1836\,m_e c^2$
$\alpha$	$1/137.036$	$e^2/(4\pi\varepsilon_0) = \alpha\hbar c \approx 1.44\ \text{eV nm}$
Rydberg energy	$13.6057\ \text{eV}$	Hydrogen ground-state binding energy (with infinite nuclear mass)
$a_0$	$0.0529\ \text{nm}$	Bohr radius
$k_B$	$8.617\times10^{-5}\ \text{eV/K}$	$k_BT \approx 0.026\ \text{eV} \approx 1/40\ \text{eV}$ at $300\ \text{K}$
$e$	$1.602\times10^{-19}\ \text{C}$	$1\ \text{eV} = 1.602\times10^{-19}\ \text{J}$
$N_A$	$6.022\times10^{23}\ \text{mol}^{-1}$	$R = N_Ak_B = 8.314\ \text{J/(mol K)}$
$c$	$2.998\times10^{8}\ \text{m/s}$	$\approx 3\times10^8\ \text{m/s}$

Worked example (photon). The energy of a 500 nm photon: $E = hc/\lambda \approx 1240/500\ \text{eV} \approx 2.5\ \text{eV}$. Visible light, roughly 400 to 700 nm, spans about 3.1 to 1.8 eV.

Worked example (electron wavelength). An electron accelerated through 100 V has kinetic energy 100 eV, far below $m_ec^2$, so it is non-relativistic and $p = \sqrt{2mK}$. Multiply top and bottom by $c$:

$$\lambda = \frac{h}{p} = \frac{hc}{\sqrt{2\,(m_ec^2)\,K}} \approx \frac{1240\ \text{eV nm}}{\sqrt{2\times 5.1\times10^{5}\times 10^{2}}\ \text{eV}} = \frac{1240}{\sqrt{1.02\times10^{8}}}\ \text{nm} \approx \frac{1240}{1.01\times10^{4}}\ \text{nm} \approx 0.12\ \text{nm}.$$

That is atomic size, which is why electron diffraction from crystals works. The trick of multiplying by $c$ to use $hc$ and $mc^2$ in eV is the single most useful arithmetic habit on this test.

Worked example (ratio of forces). How much weaker is gravity than the electric force between two protons? The distance cancels:

$$\frac{F_g}{F_e} = \frac{Gm_p^2}{e^2/(4\pi\varepsilon_0)} \approx \frac{(6.7\times10^{-11})(1.67\times10^{-27})^2}{(9.0\times10^{9})(1.60\times10^{-19})^2} \approx \frac{1.9\times10^{-64}}{2.3\times10^{-28}} \approx 8\times10^{-37}.$$

Keep the mantissas and the powers of ten in separate columns and this takes under a minute.

Recognise the classic setups

Much of the test rewards recognising a situation you have met before. A few cues, each developed in its own lesson:

Cue in the question	Think
"Small oscillations about equilibrium"	$\omega^2 = U''(x_0)/m$ (or the rotational analogue)
"Rolls without slipping"	$a = g\sin\theta/(1 + I/mR^2)$; friction does no work
"Grounded conducting plane"	Image charge
"Charging capacitor, field between the plates"	Displacement current
"Infinite square well"	$E_n \propto n^2/(mL^2)$
"Two slits" or "grating"	$d\sin\theta = m\lambda$
"Adiabatic"	$PV^\gamma$ constant, $Q = 0$
"Thermal equilibrium, two levels"	Boltzmann factor $e^{-\Delta E/k_BT}$
"Particle of energy $E$ much greater than $mc^2$"	$E \approx pc$
"Counts in a detector"	Poisson: uncertainty $\sqrt N$

How to use this course

Work through the units in order, or start with your weakest category. In each lesson, read the worked examples with a pencil, try the practice set, and read every explanation, including the ones for questions you got right: they show the fastest route and name the traps. When you have covered most units, sit the full-length practice test in one 2-hour session, with scratch paper and no calculator. Then take ETS's own free practice test from the official practice book under the same conditions (ETS, Practice Book for the GRE Subject Test in Physics). Nothing in this course is drawn from it, so it remains a genuinely fresh rehearsal.

No course can promise a particular score, and this one does not. What steady practice does is make the classic setups familiar and the shortcuts automatic, so that on the day your time goes into thinking, not searching.

Check yourself

• How many questions, how much time and how many answer choices does the Physics Test have, and is a calculator available?
• Which three categories carry the most weight, and what are the three subscores?
• Why should you answer every question, and what does the mark-and-review feature let you do?
• Can you show in two lines that $\hbar^2/(mL^2)$ is an energy and $\hbar/(mL^2)$ is not?
• Name three limits you would try on a formula containing an angle and two masses.
• What are $hc$ in eV nm, $\hbar c$ in MeV fm, and $k_BT$ at room temperature in eV?
• Estimate the de Broglie wavelength of a 100 eV electron without a calculator.