AP Physics Constants Sheet: Every Value, All 4 Courses

Every constant printed in any AP Physics booklet

There is no single AP Physics constants sheet. There are four, one per Course and Exam Description, and they are not the same. The table below is the union of all four, written at the precision the booklet actually prints, with the last column saying which courses get it.

Twenty one rows, and twenty labels, because Planck's constant is one labeled entry that runs onto a second printed line to give you $hc$. Nothing else in any of the four boxes appears that is not in this table.

Every value above is copied at the precision the College Board prints. Do not upgrade any of them. The sheet says $9.8$, not $9.81$. It says $9.0 \times 10^{9}$, not $8.99 \times 10^{9}$. It says $3.00 \times 10^{8}$, not $2.998 \times 10^{8}$. Those are the numbers a grader expects your arithmetic to be consistent with.

What each course actually gets

AP Physics 1: four entries. The whole box is the universal gravitational constant, one atmosphere of pressure, and gravity at Earth's surface written out twice. That is it. If a Physics 1 problem needs a mass, a density or a spring constant, the problem gives it to you, because the sheet will not.

AP Physics C: Mechanics: three entries. The same as Physics 1 minus the atmosphere. C: Mechanics has no fluids unit, so the pressure conversion has nothing to do. This is the smallest constants box of the four.

AP Physics C: Electricity and Magnetism: thirteen entries. The Coulomb constant, the two vacuum constants, the three particle masses, the elementary charge, the electron volt conversion, the speed of light, the atomic mass unit, and then the same three gravitational lines every course gets.

AP Physics 2: twenty entries. Everything C: E&M has, plus one atmosphere, plus the six that belong to nobody else: Avogadro's number, the universal gas constant, Boltzmann's constant, Planck's constant, Wien's constant and the Stefan-Boltzmann constant. Those six are exactly the thermal physics and modern physics content that only Physics 2 carries.

Work through that and a clean relationship falls out: the AP Physics 2 constants box contains every constant printed in any of the four booklets. The other three boxes are subsets of it. Check it against the table above if you want to be sure, quantity by quantity, because it is the sort of tidy claim that is usually false.

One consequence catches people out. AP Physics C: Electricity and Magnetism does not print Planck's constant. Neither $h$ nor $hc$ is in that box, because the C: E&M course does not cover photons. If you are working a photon problem, you are working in AP Physics 2.

Why gravity is printed twice

Every one of the four booklets spends two of its scarce lines on the same number:

Those are the same quantity in algebraically identical units. A newton is a $\text{kg} \cdot \text{m}/\text{s}^2$, so a $\text{N}/\text{kg}$ reduces to $\text{m}/\text{s}^2$ exactly. Nothing numerical changes.

What changes is what the number is being used for, and the redesigned courses care about that distinction. Written as $\text{m}/\text{s}^2$, $g$ is the acceleration of a freely falling object: an effect. Written as $\text{N}/\text{kg}$, $g$ is the gravitational field strength: force per unit mass, a property of the region of space, which exists whether or not anything is falling through it. The label on each line says so. The first reads "Magnitude of the acceleration due to gravity at Earth's surface" and the second reads "Magnitude of the gravitational field strength at Earth's surface".

The printing is a hint about how the field is meant to be discussed, not a second number to keep track of.

The precision trap, and the g = 9.8 versus g = 10 question

The Table of Information prints $g = 9.8$. It does not print $9.81$, and it does not print $10$.

That is not the whole story, and pretending it is has misled a lot of students. The AP Physics 1 Course and Exam Description states elsewhere, in the Unit 1 material, that the exam will use $g \approx 10\ \text{m}/\text{s}^2$ where a numerical value for $g$ is required, and in the same breath says students will not be penalized for correctly using the more precise commonly accepted values of $9.81\ \text{m}/\text{s}^2$ or $9.8\ \text{m}/\text{s}^2$. So both live in the same document: the exam questions may round to $10$ to keep the arithmetic mental, and $9.8$ is explicitly sanctioned. Pick one, say which you picked, and use it to the end of the problem.

The same discipline applies to the rest of the box:

• The Coulomb constant is given as $9.0 \times 10^{9}$, two significant figures. Using $8.99 \times 10^{9}$ is not wrong physics, but it can shift a two-figure answer, and it is not what the sheet handed you.
• The speed of light is $3.00 \times 10^{8}$, three figures.
• $G$ is $6.67 \times 10^{-11}$, three figures.
• The particle masses are $1.67 \times 10^{-27}$ kg for the proton and the neutron, printed identically, and $9.11 \times 10^{-31}$ kg for the electron. The proton and neutron differ in reality, and the sheet does not distinguish them.

If your answer changes at the second significant figure depending on which version of a constant you used, the grader is not going to mind. If you mixed a two-figure constant into a computation and then reported six figures, that is a different problem.

The three entries that save the most time

Three entries in the AP Physics 2 box are pre-converted for you, and each exists to remove an arithmetic step people routinely get wrong.

$hc = 1240\ \text{eV} \cdot \text{nm}$. Wavelengths of visible light are quoted in nanometers and photon energies in electron volts, so this form lets you divide directly and read an answer in eV with no unit conversion at all. The box also gives $hc = 1.99 \times 10^{-25}\ \text{J} \cdot \text{m}$ for when you want joules and meters.

$h = 4.14 \times 10^{-15}\ \text{eV} \cdot \text{s}$. The same idea applied to $E = hf$. If a frequency is in hertz and you want energy in electron volts, use this rather than converting through joules.

$1\ \text{u} = 931\ \text{MeV}/c^2$. Mass defect in a nuclear problem is naturally expressed in atomic mass units, and the answer is wanted in MeV. This line is the conversion, already carrying the $c^2$.

Notice also what the Coulomb constant line does. It prints $k$ and $\dfrac{1}{4\pi\varepsilon_0}$ as the same object, on one line, because the AP Physics 2 equation sheet writes Coulomb's law and the point charge field both ways and students otherwise treat them as two different constants.

Notation the booklet uses that textbooks do not

A few of the printed symbols do not match what a general physics textbook would show, and copying the textbook version into an AP answer is a small avoidable friction.

• Avogadro's number is $N_0$, not $N_A$. The subscript is a zero. On the same sheet, $N$ on its own is the number of atoms in the thermal physics list and the number of particles in the modern physics list.
• Boltzmann's constant is $k_B$ with a subscript B, which matters because plain $k$ is already doing duty as the Coulomb constant, the spring constant and thermal conductivity elsewhere in the same booklet.
• Wien's constant is $b$. It is stated as a plain constant with units $\text{m} \cdot \text{K}$, and the displacement law itself, $\lambda_{max} = b/T$, appears in the modern physics equations rather than in the constants box.
• The universal gravitational constant is written two ways on one line, as $\text{m}^3/(\text{kg} \cdot \text{s}^2)$ and as $\text{N} \cdot \text{m}^2/\text{kg}^2$. Same constant. The second form is the one that cancels cleanly in Newton's law of gravitation.

The constants box also holds three unit conversions rather than constants of nature: one atmosphere, one electron volt, and one unified atomic mass unit. The header says "CONSTANTS AND CONVERSION FACTORS" for that reason.

What is not in the box

Students look for these and they are not there, in any of the four booklets:

• Densities of anything, including water. A fluids problem states the density it wants.
• Specific heats, latent heats and thermal conductivities. Physics 2 defines $c$ as specific heat and $k$ as thermal conductivity in its symbol list and gives numerical values in the problem.
• Coefficients of friction for named surfaces.
• Resistivities, dielectric constants and indices of refraction. The index of refraction of water and of glass are not printed.
• Moments of inertia of standard shapes. AP Physics 1 and C: Mechanics print the definition $I = \sum m_i r_i^2$ and the parallel axis theorem, and expect a specific problem to supply or derive the rest.
• The mass or radius of the Earth, the Sun or the Moon. A gravitation problem gives them.
• The Rydberg constant, and any table of atomic energy levels.

The pattern is consistent: the sheet gives you universal constants and unit conversions, and every material property comes from the question. If you are stuck because you think a number should be on the sheet, reread the problem instead of hunting for it.