AP Physics 1 Formula Sheet: Equations by Unit, Study Guide

This AP Physics 1 formula sheet is a study summary of the equations the course leans on, grouped by unit and led by Newton's second law, $\sum F = ma$ . It is not the official sheet. The exam board provides its own equation sheet and table of constants for the exam, with its own layout and wording, and that is the version you will see on test day.

Use this page to learn what each symbol means, which unit it carries, and when an equation is allowed. The symbols follow US textbooks: $v_0$ for initial velocity and $\Delta x$ for displacement, where Indian books would write u and s. For the other courses, see the AP Physics formula sheets hub.

Quick facts

What this is
A study summary, not the official exam sheet
Official sheet
Provided by the exam board with the exam
Most used
$\sum F = ma$
Math level
Algebra and trigonometry, no calculus
Units covered
Kinematics, dynamics, energy, momentum, rotation, oscillations, fluids
Symbols
US style: $v_0$ , $\Delta x$ , $\Delta y$

How to use an AP Physics 1 formula sheet well

An exam equation sheet saves you from memorising every line, but it does not tell you which line to use, what the symbols stand for in a given setup, or when a relation stops being true. Those three skills are what the free response questions test.

Learn the conditions. The kinematics equations need constant acceleration. Conservation of momentum needs zero net external force on the system.
Learn the definitions the sheet leaves short. Know that impulse is the area under a force against time graph and that work is the area under a force against position graph.
Practise with the official layout. Download the current sheet from the exam board and keep it beside you while you do practice questions, so finding a line takes seconds.

The unit names below follow the current course outline. Check your teacher's outline in case the order differs.

Unit 1: Kinematics

Motion equations for constant acceleration
Formula	What it gives	SI unit	More on this site
$v_x = v_{x0} + a_x t$	velocity after time t	m/s	Final velocity
$x = x_0 + v_{x0}t + \frac{1}{2}a_x t^2$	position after time t	m	Displacement
$v_x^2 = v_{x0}^2 + 2a_x(x - x_0)$	velocity without needing the time	m/s	Equations of motion
$\bar{v} = \frac{\Delta x}{\Delta t}$	average velocity	m/s	Average velocity
$\bar{a} = \frac{\Delta v}{\Delta t}$	average acceleration	m/s²	Acceleration

For projectiles, apply these separately to x (with $a_x = 0$ ) and y (with $a_y = -g$ ). The full chain of ideas is on the kinematics hub.

Units 2 and 3: Force, dynamics, work, energy and power

Force and energy relations
Formula	What it gives	SI unit	More on this site
$\sum F = ma$	acceleration from the net force	N	Net force
$F_g = mg$	weight near Earth	N	Weight
$f_k = \mu_k F_N$ , $f_s \le \mu_s F_N$	kinetic and static friction	N	Friction force
$F_s = -k\,\Delta x$	spring force (Hooke's law)	N	Spring force
$F_g = \frac{G m_1 m_2}{r^2}$	gravitational attraction	N	Gravitation
$a_c = \frac{v^2}{r}$	centripetal acceleration	m/s²	Centripetal acceleration
$K = \frac{1}{2}mv^2$	kinetic energy	J	Kinetic energy
$W = Fd\cos\theta$	work by a constant force	J	Work
$\Delta U_g = mg\,\Delta y$	gravitational potential energy change	J	Potential energy
$U_s = \frac{1}{2}k\,\Delta x^2$	elastic energy in a spring	J	Spring energy
$U_G = -\frac{G m_1 m_2}{r}$	potential energy of two masses a distance r apart	J	Gravitation
$P = \frac{\Delta E}{\Delta t} = Fv\cos\theta$	power, the rate of energy transfer	W	Work and energy

Example: one cart, three units

A 2.0 kg cart starts from rest on a level track. A net force of 6.0 N pushes it for 4.0 s. Find its acceleration, final speed and kinetic energy, then check with work.

$a = \frac{6.0}{2.0} = 3.0\ \text{m/s}^2$ , and $v = 0 + (3.0)(4.0) = 12\ \text{m/s}$ .

$K = \frac{1}{2}(2.0)(12)^2 = 144\ \text{J}$

Check: distance $\Delta x = \frac{1}{2}(3.0)(4.0)^2 = 24\ \text{m}$ , so work $W = (6.0)(24) = 144\ \text{J}$ . The work energy theorem holds, and the answer is about 140 J to two significant figures.

Unit 4: Linear momentum

Momentum and impulse
Formula	What it gives	SI unit	More on this site
$\vec{p} = m\vec{v}$	momentum of one object	kg m/s	Momentum
$\vec{J} = \vec{F}_{avg}\,\Delta t = \Delta\vec{p}$	impulse and its effect	N s	Impulse
$\sum m\vec{v}_i = \sum m\vec{v}_f$	conservation for an isolated system	kg m/s	Conservation of momentum
$\vec{v}_{cm} = \frac{\sum m\vec{v}}{\sum m}$	velocity of the center of mass	m/s	Center of mass

Momentum is conserved in every collision when the system is isolated. Kinetic energy is conserved only in elastic collisions. A question that says the objects stick together is telling you it is perfectly inelastic.

Units 5 and 6: Torque, rotation and rotating systems

Rotational equations, the twins of the linear ones
Formula	What it gives	SI unit	More on this site
$\omega = \omega_0 + \alpha t$	angular velocity after time t	rad/s	Angular velocity
$\theta = \theta_0 + \omega_0 t + \frac{1}{2}\alpha t^2$	angle turned	rad	Angular acceleration
$v = r\omega$ , $a_T = r\alpha$	link between linear and angular	m/s, m/s²	Tangential acceleration
$\tau = rF\sin\theta$	torque about an axis	N m	Torque
$\alpha = \frac{\sum \tau}{I}$	angular acceleration from net torque	rad/s²	Rotation hub
$I = \sum m r^2$ , $I' = I_{cm} + Md^2$	rotational inertia and the parallel axis theorem	kg m²	Moment of inertia
$K = \frac{1}{2}I\omega^2$	rotational kinetic energy	J	Kinetic energy
$L = I\omega$ , $\Delta L = \tau\,\Delta t$	angular momentum and angular impulse	kg m²/s	Angular momentum

For rolling without slipping, $v_{cm} = r\omega$ and the total kinetic energy is the translational part plus the rotational part. A rolling ball reaches the bottom of a ramp slower than a frictionless sliding block because some energy goes into spin.

Units 7 and 8: Oscillations and fluids

Simple harmonic motion and fluid relations
Formula	What it gives	SI unit	More on this site
$T = \frac{1}{f}$	period from frequency	s	Period
$T_s = 2\pi\sqrt{\frac{m}{k}}$	period of a mass on a spring	s	Frequency
$T_p = 2\pi\sqrt{\frac{\ell}{g}}$	period of a pendulum at small angles	s	Period
$x = A\cos(2\pi f t)$	position in SHM, starting at the maximum	m	Amplitude
$\rho = \frac{m}{V}$	density	kg/m³	Density
$P = \frac{F}{A}$ , $P = P_0 + \rho g h$	pressure and pressure at depth	Pa	Pressure
$F_b = \rho V g$	buoyant force (fluid density, displaced volume)	N	Buoyant force
$A_1 v_1 = A_2 v_2$	continuity for an incompressible fluid	m³/s	Fluids hub
$P_1 + \rho g y_1 + \frac{1}{2}\rho v_1^2 = P_2 + \rho g y_2 + \frac{1}{2}\rho v_2^2$	Bernoulli's equation along a streamline	Pa	Fluids hub

Neither period formula depends on amplitude. The pendulum period does not depend on the bob mass either, while the spring period does not depend on g.

Mistakes the formula sheet for AP Physics 1 cannot prevent

Using a net force equation with one force. $\sum F = ma$ needs the vector sum of every force, so draw a free body diagram first.
Forgetting the radian mode. $v = r\omega$ and $a_T = r\alpha$ only work with angles in radians.
Applying energy conservation with friction present. Friction turns mechanical energy into thermal energy, so include its work.
Using the wrong density in buoyancy. $F_b = \rho V g$ uses the fluid density, not the density of the object.

When the course moves on to circuits, waves and optics, continue with the AP Physics 2 formula sheet. If you want the calculus version of mechanics, compare with the AP Physics C mechanics sheet.

Frequently asked questions

Is this the official AP Physics 1 formula sheet?

No. This page is a study summary written to help you learn the equations. The exam board publishes and provides the official equation sheet, so practise with that version before the exam.

Do you get a formula sheet for AP Physics 1 in the exam?

Yes, the exam board provides an equation sheet with a table of constants. It lists equations but does not explain when each one applies, so you still need to know the conditions.

What should I memorise even with a physics 1 formula sheet?

Learn the meaning of every symbol, the conditions for each equation and the definitions behind the graphs. Also learn how to draw free body diagrams and energy bar charts, since no sheet gives those.

What is the difference between the AP Physics 1 and AP Physics C sheets?

AP Physics 1 uses algebra and trigonometry. AP Physics C mechanics covers similar topics but writes many relations with derivatives and integrals, such as force as the rate of change of momentum.

Which value of g should I use in AP Physics 1?

Use 9.8 m/s² unless the question or the constants table says otherwise. Keep a few significant figures through the working and round at the end.