Is g 9.8 or 10 in AP Physics 1? Both Earn Credit

Both numbers are College Board's, from different pages

The confusion is real and it is not your fault. The AP Physics 1 Course and Exam Description, effective fall 2024, prints two different values for $g$ in two different places, and both are current.

The course framework says about 10. Essential knowledge 1.3.A.3, on printed page 30 under Topic 1.3, reads: "Near the surface of Earth, the vertical acceleration caused by the force of gravity is downward, constant, and has a measured value approximately equal to $a_g = g \approx 10\ \mathrm{m/s^2}$."

It says it again in Unit 2. Essential knowledge 2.6.B.2, on printed page 51: "Near the surface of Earth, the strength of the gravitational field is $g \approx 10\ \mathrm{N/kg}$."

The equation sheet says 9.8. The AP Physics 1 Table of Information, which is the sheet you are handed in the exam room, prints $g$ twice in its constants block: "Magnitude of the acceleration due to gravity at Earth's surface, $g = 9.8\ \mathrm{m/s^2}$", and "Magnitude of the gravitational field strength at Earth's surface, $g = 9.8\ \mathrm{N/kg}$". The whole sheet is transcribed on the AP Physics 1 formula sheet page.

Four entries, two numbers, one physical quantity. The two units are not two constants. Essential knowledge 2.6.A.2.ii, on that same printed page 51, is why they can share a symbol: "If the gravitational force is the only force exerted on an object, the observed acceleration of the object (in $\mathrm{m/s^2}$) is numerically equal to the magnitude of the gravitational field strength (in N/kg) at that location." Read $g$ as an acceleration in kinematics and as a field strength in force problems. Same number either way, as Gravitational Force works through.

The boundary statement that settles it, quoted whole

One paragraph in the CED reconciles the two. It sits at the foot of Topic 1.3, on printed page 31, labelled BOUNDARY STATEMENT. Here it is with nothing cut:

"For all situations in which a numerical quantity is required for $g$, the value $g \approx 10\ \mathrm{m/s^2}$ will be used. However, students will not be penalized for correctly using the more precise commonly accepted values of $g = 9.81\ \mathrm{m/s^2}$ or $g = 9.8\ \mathrm{m/s^2}$."

Two sentences, two different jobs.

The first tells you what the exam does. Not what you must do: what it will do. Wherever a question needs a number for $g$, the number behind it is about 10. That is why AP free-fall problems land on suspiciously round times, and it is the reason to reach for 10 when you are estimating.

The second tells you what happens to you. Using 9.81 or 9.8 correctly is not penalized. That is explicit, it is in the course description rather than in somebody's advice column, and it names the two values it covers.

Three words in that second sentence are load-bearing:

• "penalized". The statement is about scoring. It is not a stylistic preference.
• "correctly". The permission covers using 9.8 correctly. It does not repair a wrong method, and it does not cover starting a problem with 9.8 and finishing it with 10.
• "9.81 or 9.8". Two values are named. This is not a licence to use any figure you like.

Watch the scope, too, which is set by the statement's own first four words: "For all situations". The paragraph is printed under Topic 1.3, inside Unit 1, but it does not limit itself to kinematics. Every place in the course where $g$ needs a number is covered.

The same wording covers both AP Physics C courses. On printed page 32 of the AP Physics C: Mechanics course description: "AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism expects that for all situations in which a numerical quantity is required for $g$, the value $g \approx 10\ \mathrm{m/s^2}$ will be used. However, students will not be penalized for correctly using the more precise commonly accepted values of $g = 9.81\ \mathrm{m/s^2}$ or $g = 9.8\ \mathrm{m/s^2}$." One statement, both C exams, named in it.

AP Physics 2 carries no equivalent statement. Nothing in that course description sets a numerical value for $g$ the way these two do, and its Table of Information prints the same two 9.8 lines the Physics 1 sheet does. The equation sheet comparison covers what else differs between them.

Which value to use, situation by situation

Work down this list and stop at the first line that matches what you are looking at.

1. The problem states a value for $g$. Use the stated value, whatever it is, including on another planet. A number the question gives you outranks everything else on this page.
2. You are estimating, or doing the arithmetic in your head. Use 10. That is what it is for. Dividing by 10 needs no calculator, and the boundary statement says the exam's own numbers were built on it.
3. Multiple choice, and two options sit close together. Try 10 first, then check with 9.8. The option the question intends as correct was generated with about 10, so if your result from 9.8 falls between two options, rerun it with 10 and see which one it lands on.
4. Free response, work shown. Either value earns the point. Write the number into your substitution line so a reader can follow your arithmetic without guessing which $g$ you took.
5. Homework, lab work, and everything on this site. 9.8. The reasons are two sections down.

One rule outranks all five: whichever value you pick, keep it for the whole problem. Launching a projectile with 10 and landing it with 9.8 is not more accurate than either. It is inconsistent, and on a free-response question the inconsistency is written down in front of the reader.

Then say which one you used. One clause, "taking $g = 9.8\ \mathrm{m/s^2}$", turns a slightly different last digit into an obviously deliberate choice rather than an arithmetic slip.

How far apart are they? Two percent

Get the size of the thing straight before worrying about it. The ratio is

so 10 is about 2.0% larger than 9.8, and 9.8 is exactly 2.0% smaller than 10. There is no third value hiding in the gap.

That 2% does not land on every answer the same way. What decides it is how $g$ enters the equation you used.

• Proportional to $g$: the full 2%. Weight $mg$, potential energy $mg\Delta y$, the $\rho g h$ pressure term, the buoyant force $\rho V g$.
• Proportional to $1/g$: also 2%, in the opposite direction, so 9.8 gives the larger answer. A projectile's range, maximum height and time of flight for a fixed launch all sit here.
• Under a square root: about 1.0%, because a root halves a small fractional change: $\sqrt{10/9.8} = 1.0102$. Impact speed after a drop, time to fall a fixed height, and the period of a pendulum.

The pressure row takes the density of water as $1000\ \mathrm{kg/m^3}$, which is not a constant the sheet prints.

Now round that table to two significant figures, which is all $g = 9.8$ supports, and most of it collapses. 19.8 m/s and 20.0 m/s are both 20 m/s; 2.02 s and 2.00 s are both 2.0 s; so are 2.01 s and 1.99 s. What survives are the rows where $g$ enters linearly and the answer sits near a rounding boundary: 49 N against 50 N, and 63 m against 62 m for the range. That is the honest summary of the whole question. The choice of $g$ changes your last digit, sometimes, and nothing else.

Every equation on the AP Physics 1 sheet that contains g

It is a shorter list than most students expect. The sheet carries 4 constants and 48 equations. Six of the 48 contain $g$:

Four of the six are fluids equations, so Unit 8, Fluids is where a 2% shift in $g$ is likeliest to move an answer, not Unit 1. See the AP Physics 1 fluids guide. The pendulum line is the one exception to the 2% rule, because $g$ sits under a root there; simple harmonic motion works through it.

Two absences from that list matter more than the entries.

Weight is not printed on the sheet. There is no $F_g = mg$ anywhere on the AP Physics 1 Table of Information. The universal form is printed,

but the near-Earth shortcut is not. The CED supplies it under essential knowledge 2.6.A.3, labelled Derived Equation: "Weight $= F_g = mg$". Printed page 12 says what that label means: "Not all equations in this course framework appear on the equation sheet provided to students while taking the AP Physics 1 Exam. Many of the equations in this document are provided for reference and guidance, or to demonstrate the final results of derivations expected of students on the exam. These equations are denoted as 'Derived Equations.'" So $F_g = mg$ is required content you bring with you.

No kinematic equation contains $g$ either. Free fall is where most students meet the constant, but the three constant-acceleration equations printed on the sheet carry $a_x$, not $g$. You are the one who decides $a_x$ is $-9.8\ \mathrm{m/s^2}$ here, and the sign comes from the axis you chose. That is why the kinematics calculator asks you for an acceleration rather than assuming one, and why the kinematic equations guide picks equations by what is missing, not by a constant.

Why this site computes with 9.8

Every calculator, interactive and worked example on PhysicsLearn uses $g = 9.8\ \mathrm{m/s^2}$. This page is the only place that departs from that, and only where it is deliberately running the same problem twice. Four reasons, in order of weight:

1. It is the value on the sheet you are handed. The Table of Information prints 9.8 in the exam room. A student checking our arithmetic against the constants actually in front of them should get our number.
2. The CED names it. The boundary statement lists $g = 9.8\ \mathrm{m/s^2}$ by value as a figure that is not penalized. Nothing here is being slipped past the exam.
3. It is the more precise of the two. 10 is a rounding of 9.8, not the other way round. Computing with the finer value and telling you the size of the gap is more useful than computing with the coarser one and saying nothing.
4. One constant, site-wide. All the physics here runs through a single module with a single gravitational constant, so the projectile calculator and the pendulum page cannot quietly disagree. A site using 10 on some pages and 9.8 on others would be worse than one consistently using either.

Comparing our answers to your class's: expect the last digit to differ sometimes, by about 2% on forces and energies and 1% on speeds and times, and do not read that as an error in either place. If your teacher works in 10, our numbers run slightly low on weights and slightly high on ranges. Both sets are correct.

Topic 1.3, Representing Motion carries the same explanation sitting next to the CED text it comes from, and the rest of Unit 1, Kinematics is where you meet $g$ first.

Significant figures, and when 2% actually matters

Most of the worry about this question is worry about precision, and the CED itself takes the pressure off.

Its appendix, on printed page 207, describes what an introductory physics model throws away. In the standard block-on-a-ramp problem, it lists friction, air resistance, the slight increase in gravitational field as the block slides down, and the energy lost to vibrations, sound and thermal energy, and then says those effects "are considered negligible and are ignored in favor of obtaining an answer that is within the level of accuracy needed for the course."

A course that discards air resistance entirely is not a course where the third digit of $g$ decides anything. That is not sloppiness. It is the stated modelling boundary, and the same appendix sets out the full list of what students may assume unless otherwise stated: frames of reference are inertial, air resistance is negligible, frictional and drag forces are negligible, edge effects of charged plates are negligible, and strings, springs and pulleys are ideal.

So, four practical rules:

• Report the significant figures your data supports, not the ones the calculator prints. A 5.0 kg mass with $g = 9.8$ gives a weight of 49 N, not 49.000 N.
• 9.8 has two significant figures. Written plainly, 10 has one. Neither justifies a four-digit answer, and one built on either advertises a precision you do not have.
• Compare your candidates to the spacing of the answer options. If the options are 30% apart, the choice of $g$ is irrelevant. If two are 2% apart, run the number both ways.
• Expect the difference on forces and energies, not on speeds and times. Anything linear in $g$ carries the whole 2%; anything under a square root carries about half and usually rounds away.

There is one place the difference genuinely bites, and it is not the exam: a lab. Measure $g$ from a pendulum or a photogate and get 9.7, and your percent error is 1% against 9.8 but 3% against 10. Say which reference value you compared to. That one sentence costs nothing and settles the analysis.

Mistakes this confusion actually causes

• Mixing the two inside one problem. Compute the weight with 10, then the impact speed with 9.8, and your energy check fails to close by about 2% for no reason a reader can see. Pick one at the top of the page.
• Treating $9.8\ \mathrm{N/kg}$ as a second constant. It is the same number. EK 2.6.A.2.ii says the acceleration in $\mathrm{m/s^2}$ and the field strength in N/kg are numerically equal when gravity is the only force acting. There is nothing extra to memorise.
• Overriding a value the question handed you. If a problem says to take $g = 9.80\ \mathrm{m/s^2}$, or puts you on Mars, use that. The boundary statement is about what happens when nothing is specified.
• Confusing $g$ with $G$. $g$ is about $9.8\ \mathrm{m/s^2}$ at Earth's surface and changes with where you are. $G$, the universal gravitational constant, is printed on the sheet as $6.67 \times 10^{-11}\ \mathrm{m^3/(kg \cdot s^2)}$ and changes nowhere. They turn up in the same problems and are not interchangeable.
• Forgetting that $g$ is a magnitude. The Table of Information calls it the magnitude of the acceleration due to gravity. Whether it enters your equation as $+9.8$ or $-9.8$ is decided by the axis you declared, not by the constant. See how to draw a free-body diagram for the habit that prevents this.
• Assuming a rounder $g$ means a rounder everything. The exam rounding $g$ to 10 says nothing about how it treats a mass, a length or an angle. Take every other given at the precision it was written.
• Worrying about it at all. Both values are in the course description, both earn credit, and the gap between them is smaller than the air resistance the course already discards. Choose, note the choice, and get back to the physics the question is testing.