AP Physics 1 Formula Sheet

The full equation and constants reference for AP Physics 1 (2026 format), reorganized by unit so you can see where each formula belongs. Every equation links to the Mistake Master lesson that teaches and applies it. The official equation sheet is provided on both sections of the exam, but knowing what each formula means and when to reach for it is what separates a 3 from a 5.

Constants and conversions

Provided on the official AP Physics 1 equation sheet

$g$Acceleration due to gravity at Earth's surface 9.8 m/s² (10 m/s² acceptable for AP scoring)

$G$Universal gravitational constant 6.67 × 10⁻¹¹ N·m²/kg²

$\rho_w$Density of water 1.0 × 10³ kg/m³

$P_{atm}$Atmospheric pressure 1.0 × 10⁵ Pa

Unit 1

Kinematics

Position, velocity, acceleration, and the kinematic equations for motion in one and two dimensions.

$$ \bar{v} = \dfrac{\Delta x}{\Delta t} $$

Average velocity

Displacement divided by elapsed time. Slope of a position vs time graph.

Lesson 1.2 ›

$$ \bar{a} = \dfrac{\Delta v}{\Delta t} $$

Average acceleration

Change in velocity divided by elapsed time. Slope of a velocity vs time graph.

Lesson 1.2 ›

$$ v_f = v_i + a t $$

Velocity from acceleration

Final velocity given initial velocity, constant acceleration, and time.

Lesson 1.4 ›

$$ x_f = x_i + v_i t + \tfrac{1}{2} a t^2 $$

Position from constant acceleration

Position as a function of time under constant acceleration.

Lesson 1.4 ›

$$ v_f^{\,2} = v_i^{\,2} + 2 a \,\Delta x $$

Time-independent kinematic

Relates velocities and displacement without using time. Useful when time is unknown.

Lesson 1.4 ›

Unit 2

Force and Translational Dynamics

Newton's three laws, free-body diagrams, gravity, friction, springs, and circular motion.

$$ \vec{F}_{\text{net}} = m \vec{a} $$

Newton's second law

Net force on an object equals its mass times its acceleration. Force and acceleration share a direction.

Lesson 2.4 ›

$$ F_g = m g $$

Weight near Earth

Gravitational force on a mass near the surface of a planet. On Earth, g is approximately 9.8 m/s squared.

Lesson 2.5 ›

$$ F_g = \dfrac{G m_1 m_2}{r^2} $$

Universal gravitation

Gravitational attraction between two masses separated by distance r.

Lesson 2.5 ›

$$ f_s \le \mu_s F_N $$

Static friction (max)

Static friction adjusts up to a maximum proportional to the normal force.

Lesson 2.6 ›

$$ f_k = \mu_k F_N $$

Kinetic friction

Kinetic friction has a fixed magnitude proportional to the normal force.

Lesson 2.6 ›

$$ F_s = -k x $$

Spring (Hooke's law)

Restoring force of a spring is proportional to displacement from equilibrium and points back toward it.

Lesson 2.7 ›

$$ a_c = \dfrac{v^2}{r} $$

Centripetal acceleration

Acceleration of an object moving in a circle at constant speed. Always points toward the center.

Lesson 2.8 ›

$$ F_c = \dfrac{m v^2}{r} $$

Centripetal force

Net inward force required to maintain circular motion. Not a new kind of force; the label describes the role.

Lesson 2.8 ›

Unit 3

Work, Energy, and Power

Translational kinetic energy, work, gravitational and elastic potential energy, conservation of energy, and power.

$$ K = \tfrac{1}{2} m v^2 $$

Translational kinetic energy

Energy of motion for an object moving with speed v. Scalar, never negative.

Lesson 3.1 ›

$$ W = F d \cos\theta $$

Work done by a constant force

Work equals force component along displacement times displacement magnitude. Can be positive, negative, or zero.

Lesson 3.2 ›

$$ W_{\text{net}} = \Delta K $$

Work-energy theorem

Net work on an object equals its change in kinetic energy.

Lesson 3.2 ›

$$ U_g = m g h $$

Gravitational potential energy (near surface)

Energy stored in the Earth-object system due to height above a chosen reference.

Lesson 3.3 ›

$$ U_s = \tfrac{1}{2} k x^2 $$

Elastic potential energy

Energy stored in a spring stretched or compressed by distance x from equilibrium.

Lesson 3.3 ›

$$ P_{\text{avg}} = \dfrac{W}{\Delta t} $$

Average power

Rate at which work is done. Watts equal joules per second.

Lesson 3.4

Unit 4

Linear Momentum

Impulse, momentum, and conservation in collisions and explosions.

$$ \vec{p} = m \vec{v} $$

Linear momentum

Product of mass and velocity. A vector quantity that points in the direction of motion.

Lesson 4.1

$$ \vec{J} = \vec{F}_{\text{avg}} \Delta t = \Delta \vec{p} $$

Impulse-momentum theorem

Impulse delivered to an object equals its change in momentum.

Lesson 4.2

$$ \vec{p}_{i,\text{total}} = \vec{p}_{f,\text{total}} $$

Conservation of momentum

Total momentum of an isolated system is conserved. Applies to collisions and explosions.

Lesson 4.3

Unit 5

Torque and Rotational Dynamics

Angular kinematics, torque, rotational inertia, and the rotational analog of Newton's second law.

$$ \tau = r F \sin\theta $$

Torque

Rotational effect of a force about a pivot. Depends on lever arm and the angle between force and arm.

Lesson 5.3

$$ \omega_f = \omega_i + \alpha t $$

Angular velocity (constant alpha)

Rotational analog of the linear kinematic equation. Holds when angular acceleration is constant.

Lesson 5.2

$$ \theta_f = \theta_i + \omega_i t + \tfrac{1}{2} \alpha t^2 $$

Angular position (constant alpha)

Angular position as a function of time under constant angular acceleration.

Lesson 5.2

$$ \tau_{\text{net}} = I \alpha $$

Newton's second law (rotation)

Net torque equals rotational inertia times angular acceleration.

Lesson 5.4

$$ I = \textstyle\sum m_i r_i^{\,2} $$

Rotational inertia (point masses)

Sum over each particle of mass times distance squared from the axis.

Lesson 5.4

Unit 6

Energy and Momentum of Rotating Systems

Rotational kinetic energy and angular momentum.

$$ K_{\text{rot}} = \tfrac{1}{2} I \omega^2 $$

Rotational kinetic energy

Energy of rotation. Adds to translational kinetic energy when an object both rotates and translates.

Lesson 6.1

$$ L = I \omega $$

Angular momentum of a rigid body

Rotational analog of linear momentum.

Lesson 6.2

$$ L_i = L_f $$

Conservation of angular momentum

Total angular momentum of an isolated system stays constant when no external torque acts on it.

Lesson 6.3

Unit 7

Oscillations

Simple harmonic motion for springs and pendulums.

$$ T = 2\pi \sqrt{\dfrac{m}{k}} $$

Period of a spring

Period of a mass on an ideal spring. Independent of amplitude in the SHM regime.

Lesson 7.2

$$ T = 2\pi \sqrt{\dfrac{\ell}{g}} $$

Period of a pendulum

Period of a simple pendulum for small angles. Independent of mass.

Lesson 7.2

$$ f = \dfrac{1}{T} $$

Frequency and period

Frequency is the reciprocal of the period. Units are hertz, equal to one per second.

Lesson 7.1

Unit 8

Fluids

Density, pressure, buoyancy, continuity, and Bernoulli's equation.

$$ \rho = \dfrac{m}{V} $$

Density

Mass per unit volume. A property of the material.

Lesson 8.1

$$ P = \dfrac{F}{A} $$

Pressure

Force per unit area. Acts in all directions inside a fluid.

Lesson 8.2

$$ P = P_0 + \rho g h $$

Pressure with depth

Pressure at depth h below the surface of a fluid in static equilibrium.

Lesson 8.2

$$ F_b = \rho_{\text{fluid}} V_{\text{displaced}} g $$

Buoyant force (Archimedes)

Upward force on a submerged or floating object equals the weight of the fluid it displaces.

Lesson 8.3

$$ A_1 v_1 = A_2 v_2 $$

Continuity equation

Conservation of fluid volume in steady flow through a pipe.

Lesson 8.4

$$ P_1 + \tfrac{1}{2} \rho v_1^2 + \rho g y_1 = P_2 + \tfrac{1}{2} \rho v_2^2 + \rho g y_2 $$

Bernoulli's equation

Energy conservation for ideal fluid flow. Trades pressure, kinetic energy density, and potential energy density.

Lesson 8.5

Don't just memorize. Diagnose.

Knowing the formula sheet by heart is necessary but not sufficient. Most AP Physics 1 points are lost to misconceptions: applying centripetal force as if it were a new physical force, treating mass as weight, confusing average and instantaneous quantities. Mistake Master is built around fixing these specific failure modes.

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