Physics 1 Formula Sheet: Equations, Constants, and Exam Rules for 8 Units
A Physics 1 formula sheet is a reference document that lists the equations, constants, and unit symbols for introductory mechanics. The AP Physics 1 version covers 8 units, from kinematics to fluids. This guide lists the equations by unit, compares AP and college sheets, and explains the exam rules.
For a related explanation, see Kinematics Equations.
What Is a Physics 1 Formula Sheet?
A Physics 1 formula sheet is a reference document that lists the equations, constants, and unit symbols used in introductory mechanics. It is also called an equation sheet or reference information. Formula sheets for Physics 1 come in 2 main types. Examples include the AP Physics 1 exam reference information from the College Board and instructor-written course sheets such as the University of Illinois Physics 101 formula sheet.
What Topics Does AP Physics 1 Cover?
AP Physics 1 is an algebra-based course with 8 units. The College Board lists each unit's weight in the multiple-choice section:
- Kinematics (10% to 15%)
- Force and translational dynamics (18% to 23%)
- Work, energy, and power (18% to 23%)
- Linear momentum (10% to 15%)
- Torque and rotational dynamics (10% to 15%)
- Energy and momentum of rotating systems (5% to 8%)
- Oscillations (5% to 8%)
- Fluids (10% to 15%)
Fluids joined the course in the 2024-25 revision.
What Is on the AP Physics 1 Formula Sheet?
The AP Physics 1 formula sheet contains mechanics and fluids equations, constants, SI prefixes, unit symbols, and trigonometric values. The College Board calls it exam reference information and prints a booklet for schools. The same content appears in the Bluebook app. Only College Board reference information is permitted on exam day.
Where Can the AP Physics 1 Formula Sheet Be Downloaded?
The College Board publishes the sheet as a free, printable PDF on AP Central. The file is titled AP Physics 1 Exam Reference Information. The current edition carries a 2025 College Board copyright and includes fluids.
Which Constants and Conventions Appear on the Sheet?
The sheet lists 4 constants and conversion values, 9 SI prefixes, 8 unit symbols, 7 trigonometric angles, and 4 problem conventions. The table below shows the 4 constants and conversion values with the symbol, value, and unit of each.
| Constant | Symbol | Value | Unit |
|---|---|---|---|
| Universal gravitational constant | G | 6.67 × 10⁻¹¹ | N·m²/kg² |
| Atmospheric pressure (1 atmosphere) | 1 atm | 1.01 × 10⁵ | Pa |
| Acceleration due to gravity at Earth's surface | g | 9.8 | m/s² |
| Gravitational field strength at Earth's surface | g | 9.8 | N/kg |
The 9 prefixes run from tera (10¹²) to pico (10⁻¹²). The 8 unit symbols include Hz, J, kg, m, N, Pa, s, and W. The 7 angles are 0°, 30°, 37°, 45°, 53°, 60°, and 90°. The sheet sets 4 conventions unless a problem states otherwise:
- Inertial frames of reference
- Negligible air resistance
- Ideal springs and strings
- Ideal fluids in completely filled pipes
What Is Not on the AP Physics 1 Formula Sheet?
The sheet does not state when each equation applies, according to The Science Cube. ++tutors reports that it also omits rotational inertia formulas for specific shapes such as disks, spheres, rods, and hoops.
What Are the Physics 1 Formulas by Unit?
Physics 1 formulas fall into 7 groups that cover the 8 units: kinematics, forces, energy, momentum, rotation, oscillations, and fluids. Each table defines every symbol. The official PDF remains the authoritative source for exact notation.
Which Kinematics Formulas Apply to Constant Acceleration?
Three kinematics equations describe motion with constant acceleration. The table below lists each equation, the variable it omits, and every symbol.
| Equation | Name | Omitted Variable | Symbol Definitions |
|---|---|---|---|
| v = v₀ + at | Velocity-time equation | Position (x) | v = final velocity, v₀ = initial velocity, a = acceleration, t = time |
| x = x₀ + v₀t + ½at² | Position-time equation | Final velocity (v) | x = final position, x₀ = initial position, v₀ = initial velocity, a = acceleration, t = time |
| v² = v₀² + 2a(x − x₀) | Velocity-position equation | Time (t) | v = final velocity, v₀ = initial velocity, a = acceleration, x = final position, x₀ = initial position |
Which Force Formulas Appear in Physics 1?
Six equations cover Newton's second law, weight, friction, springs, circular motion, and gravitation. The table below lists each equation with its name and symbols.
| Equation | Name | Symbol Definitions |
|---|---|---|
| a = ΣF/m | Newton's second law | a = acceleration, ΣF = net force, m = mass |
| F_g = mg | Weight | F_g = gravitational force, m = mass, g = gravitational field strength |
| |F_f| ≤ μ|F_N| | Friction force | F_f = friction force, μ = coefficient of friction, F_N = normal force |
| F_s = −kx | Spring force (Hooke's law) | F_s = spring force, k = spring constant, x = displacement from equilibrium |
| a_c = v²/r | Centripetal acceleration | a_c = centripetal acceleration, v = speed, r = radius |
| F_g = Gm₁m₂/r² | Universal gravitation | F_g = gravitational force, G = gravitational constant, m₁ and m₂ = masses, r = distance between centers |
Which Energy and Power Formulas Does Physics 1 Use?
Six equations cover work, kinetic energy, potential energy, and power. The table below lists each equation with its name and symbols.
| Equation | Name | Symbol Definitions |
|---|---|---|
| K = ½mv² | Kinetic energy | K = kinetic energy, m = mass, v = speed |
| ΔU_g = mgΔy | Gravitational potential energy change | ΔU_g = potential energy change, m = mass, g = gravitational field strength, Δy = vertical position change |
| U_s = ½kx² | Elastic potential energy | U_s = spring potential energy, k = spring constant, x = stretch or compression |
| W = Fd cos θ | Work by a constant force | W = work, F = force, d = distance, θ = angle between force and displacement |
| P = ΔE/Δt | Average power | P = power, ΔE = energy change, Δt = time interval |
| W_net = ΔK | Work-energy theorem | W_net = net work, ΔK = kinetic energy change |
Which Momentum and Impulse Formulas Are on the Sheet?
Three equations relate momentum to force, time, and collisions. The table below lists each equation with its name and symbols.
| Equation | Name | Symbol Definitions |
|---|---|---|
| p = mv | Linear momentum | p = momentum, m = mass, v = velocity |
| J = FΔt = Δp | Impulse-momentum theorem | J = impulse, F = average net force, Δt = time interval, Δp = momentum change |
| Σp_i = Σp_f | Conservation of momentum (isolated system) | Σp_i = total initial momentum, Σp_f = total final momentum |
Which Rotation Formulas Appear in Units 5 and 6?
Six equations cover torque, rotational kinematics, kinetic energy, and angular momentum. The table below lists each equation with its name and symbols.
| Equation | Name | Symbol Definitions |
|---|---|---|
| τ = rF sin θ | Torque | τ = torque, r = distance from the axis, F = force, θ = angle between r and F |
| τ_net = Iα | Newton's second law for rotation | τ_net = net torque, I = rotational inertia, α = angular acceleration |
| ω = ω₀ + αt | Angular velocity-time equation | ω = final angular speed, ω₀ = initial angular speed, α = angular acceleration, t = time |
| θ = θ₀ + ω₀t + ½αt² | Angular position-time equation | θ = final angular position, θ₀ = initial angular position, ω₀ = initial angular speed, α = angular acceleration, t = time |
| K_rot = ½Iω² | Rotational kinetic energy | K_rot = rotational kinetic energy, I = rotational inertia, ω = angular speed |
| L = Iω | Angular momentum | L = angular momentum, I = rotational inertia, ω = angular speed |
Which Oscillation Formulas Are Used in Unit 7?
Four equations describe the period and position of springs and pendulums in simple harmonic motion. The table below lists each equation with its name and symbols.
| Equation | Name | Symbol Definitions |
|---|---|---|
| T = 1/f | Period-frequency relation | T = period, f = frequency |
| T_s = 2π√(m/k) | Period of a mass-spring system | T_s = period, m = mass, k = spring constant |
| T_p = 2π√(ℓ/g) | Period of a simple pendulum | T_p = period, ℓ = length, g = gravitational field strength |
| x = A cos(2πft) | Position in simple harmonic motion | x = position, A = amplitude, f = frequency, t = time |
Which Fluids Formulas Were Added to Physics 1?
Six equations cover density, pressure, buoyancy, continuity, and Bernoulli's principle. Bernoulli's equation is known for relating pressure, height, and speed in an ideal flowing fluid. The table below lists each equation with its name and symbols.
| Equation | Name | Symbol Definitions |
|---|---|---|
| ρ = m/V | Density | ρ = density, m = mass, V = volume |
| P = F/A | Pressure | P = pressure, F = perpendicular force, A = area |
| P = P₀ + ρgh | Pressure at depth | P = pressure at depth, P₀ = surface pressure, ρ = fluid density, g = gravitational field strength, h = depth |
| F_b = ρVg | Buoyant force | F_b = buoyant force, ρ = fluid density, V = displaced volume, g = gravitational field strength |
| A₁v₁ = A₂v₂ | Continuity equation | A = cross-sectional area, v = fluid speed |
| P + ρgy + ½ρv² = constant | Bernoulli's equation | P = pressure, ρ = fluid density, g = gravitational field strength, y = vertical position, v = fluid speed |
How Does a College Physics 1 Formula Sheet Differ From the AP Sheet?
College formula sheets differ from the AP sheet because each instructor sets the content and the rules. The University of Illinois PHYS 211 exams allow a formula sheet in electronic or printed form, scratch paper, and a calculator. A University of Florida calculus-based physics course (PHY 2049, Spring 2014) allowed 1 handwritten sheet for the first midterm, 2 for the second midterm, and 3 for the final exam.
Calculus-based courses add derivative and integral forms. Examples include v = dx/dt, a = dv/dt, and W = ∫F dx. The table below compares the AP sheet and college sheets across 5 features.
| Feature | AP Physics 1 Sheet | College Physics 1 Sheet |
|---|---|---|
| Source | College Board | Course instructor |
| Course math level | Algebra-based | Algebra-based or calculus-based |
| Content | 8 units of mechanics and fluids | Varies by course |
| Student-written sheets | Not allowed | Allowed where the instructor permits |
| Calculator | Permitted | Set by instructor |
How Is the AP Physics 1 Exam Structured?
The AP Physics 1 exam has 2 sections that each carry 50% of the score. The May 2027 exam is a hybrid digital exam on Wednesday, May 5, 2027, in Session 2. Students answer multiple-choice questions in Bluebook and handwrite free-response answers in paper booklets. Calculators are permitted. The table below lists the 2 sections by question type, number of questions, time, and score weight.
| Section | Question Type | Number of Questions | Time | Score Weight |
|---|---|---|---|---|
| Section I | Multiple choice | 42 | 85 minutes | 50% |
| Section II | Free response | 4 | 95 minutes | 50% |
Earlier revised exams used 40 multiple-choice questions in 80 minutes and 4 free-response questions in 100 minutes.
What Rules Apply to the Reference Booklet?
The College Board sets 3 rules for the reference booklet:
- Only College Board reference information is permitted.
- Writing on the booklet is permitted, but nothing written there is scored.
- Booklets stay in the exam room during breaks and after the exam.
Does a Formula Sheet Improve Physics Exam Scores?
Students with formula sheets scored higher on factual and routine questions in a 2012 study by Wheijen Chang at Feng Chia University in Taiwan. The study compared students with and without formula sheets in an introductory physics course. The sheet group outperformed the other group on 7 of 9 questions, and 3 differences reached statistical significance. The largest deficit for the sheet group appeared on a conceptual question.
Sheet quality, rated by completeness, showed a positive correlation of r = 0.461 with exam scores among 50 students. Across 4 classes, 80% to 92% of surveyed students agreed with the formula sheet policy. Educators disagree on the effect. Moses (2000) and Rehfuss (2003) argued that sheets may reduce study effort and conceptual thinking. Cone (2003) argued that sheets lessen exam tension.
How Do You Choose the Right Physics 1 Formula?
Choose a formula in 7 steps:
- List the known quantities with units.
- Identify the unknown quantity.
- Match the problem to a unit, such as kinematics or energy.
- Select the equation that contains the unknown and omits any variable that is neither given nor required.
- Check the condition of use, such as constant acceleration.
- Substitute the values with units.
- Verify the units and the size of the answer.
According to the 2025 College Board free-response questions, derivations begin with a fundamental physics principle or an equation from the reference information.
How Can Students Make a Physics 1 Formula Sheet?
Make a formula sheet by grouping equations by unit, defining every symbol, and stating each condition of use. Handwritten sheets apply only where instructors allow them, because the AP exam permits only College Board reference information. A complete sheet includes 5 elements:
- Equations grouped by the 8 units
- Definitions of every symbol and unit
- Conditions of use, such as constant acceleration
- One worked example per unit
- Constants, including g = 9.8 m/s² and G = 6.67 × 10⁻¹¹ N·m²/kg²
In Chang's survey of 216 students, respondents reported that making the sheet reinforced their review of the full course content.
What Mistakes Do Students Make With Physics 1 Formulas?
Five mistakes lose points in Physics 1 problems:
- Applying kinematics equations when acceleration changes
- Treating static friction as an equality instead of the upper limit |F_f| ≤ μ|F_N|
- Omitting rotational kinetic energy, ½Iω², in rolling problems
- Leaving the positive direction undefined in force and momentum problems
- Assuming kinetic energy is conserved in inelastic collisions, where only momentum is conserved
What Are People Also Asking About the Physics 1 Formula Sheet?
Is a formula sheet provided on the AP Physics 1 exam?
Yes, the College Board provides printed reference information and a digital copy in Bluebook.
Can a calculator be used on the AP Physics 1 exam?
Calculators are permitted, and the College Board publishes a list of permitted models.
Is AP Physics 1 algebra-based or calculus-based?
AP Physics 1 is algebra-based.
Can students write on the AP Physics 1 formula sheet?
Yes, scratch writing is allowed on the booklet, but the College Board does not score it.
When is the next AP Physics 1 exam?
The next AP Physics 1 exam is on Wednesday, May 5, 2027, in Session 2.
Why Does a Physics 1 Formula Sheet Matter for Mechanics Exams?
A Physics 1 formula sheet matters because it organizes 8 units of mechanics and fluids into 1 reference document. The AP version is set by the College Board and is free to download. College versions follow instructor policies. Chang's 2012 study reports a positive correlation between formula sheet quality and exam scores.
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Meta description: Net force definition: the vector sum of all forces on an object. Learn the formula, 5 calculation steps, 4 examples, and balanced vs unbalanced forces.
For the official reference, consult College Board AP Physics reference information.
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