If you’ve ever stared at a physics problem and gone completely blank on the formula you need, you’re not alone. Physics covers everything from falling apples to orbiting satellites — and the equations that describe all of it can feel overwhelming without a reliable reference. That’s exactly why a well-built physics formula sheet is one of the most powerful study tools you can have.
This guide isn’t just a list of equations. It walks you through what each formula actually means, what the variables represent, what units to use, and where you’ll apply it in real problems. Whether you’re prepping for AP Physics, a college exam, or just trying to wrap your head around the fundamentals, this is your one-stop physics equation reference.
1. Kinematics & Motion Equations
Kinematics is the branch of physics that describes how things move — without worrying about why they move (that’s dynamics). You’re dealing with displacement, velocity, acceleration, and time.
The Core Kinematic Variables
| Symbol | Meaning | SI Unit |
|---|---|---|
| u | Initial velocity | m/s |
| v | Final velocity | m/s |
| a | Acceleration | m/s² |
| s | Displacement | m |
| t | Time | s |
Average Velocity and Acceleration
Average velocity:
v̄ = Δx / Δt
Acceleration (rate of change in velocity):
a = (v − u) / t
The Four SUVAT Equations (Constant Acceleration)
These are sometimes called the equations of motion or SUVAT equations, and they’re the backbone of kinematics problems:
- v = u + at — final velocity from initial velocity and constant acceleration
- s = ut + ½at² — displacement when you know initial velocity and time
- v² = u² + 2as — final velocity when time isn’t given
- s = ½(u + v)t — displacement using average velocity
Practical example: A car starts from rest (u = 0) and reaches 30 m/s in 10 seconds. Its acceleration is a = (30 − 0) / 10 = 3 m/s². Using equation 2, its displacement over that time is s = 0 + ½(3)(10²) = 150 meters.
Quick tip: Always write down your knowns and unknowns before picking a SUVAT equation. The one with no unknowns except the one you’re solving for is the right one.
2. Forces & Newton’s Laws
Forces cause changes in motion. Newton’s three laws are the foundation of classical mechanics, and the equations that come from them appear constantly — from introductory physics to engineering.
Newton’s Second Law (The Most Used Formula in Physics)
F = ma
Force (N) equals mass (kg) times acceleration (m/s²). This single equation connects almost every dynamics problem you’ll encounter.
Net force: When multiple forces act on an object, you sum them as vectors:
ΣF = ma
If ΣF = 0, the object either stays still or moves at constant velocity — that’s Newton’s First Law (inertia) in action.
Weight
W = mg
where g = 9.8 m/s² near Earth’s surface. A 70 kg person weighs 70 × 9.8 = 686 N — not 70 kg (that’s mass, not weight).
Friction
| Type | Formula | When It Applies |
|---|---|---|
| Static friction | f_s ≤ μ_s × F_N | Object not yet moving |
| Kinetic friction | f_k = μ_k × F_N | Object already sliding |
F_N is the normal force (the surface pushing back). The coefficients μ_s and μ_k are dimensionless and depend on the material pair.
Newton’s Law of Universal Gravitation
F_G = G × (m₁m₂) / r²
where G = 6.674 × 10⁻¹¹ N·m²/kg². This describes the gravitational attraction between any two masses separated by distance r. It applies from falling objects to planetary orbits.
3. Energy, Work & Power Formulas
Energy is the capacity to do work. These formulas connect force, displacement, motion, and rate — three concepts that dominate both high school and college physics.
Work
W = Fd cosθ
Work (joules) is done when a force moves an object through a displacement. The angle θ matters: if the force is perfectly aligned with motion, cosθ = 1 and all force contributes to work. If force is perpendicular to motion (like gravity on a horizontal slide), it does zero work.
Kinetic Energy
KE = ½mv²
This is the energy an object has because of its motion. Double the speed? Quadruple the kinetic energy (velocity is squared).
Potential Energy
Gravitational:
PE_g = mgh
Elastic (spring):
PE_s = ½kx²
where k is the spring constant (N/m) and x is the compression or extension from equilibrium.
Conservation of Mechanical Energy
In a system without friction or air resistance:
KE_initial + PE_initial = KE_final + PE_final
This is one of the most powerful problem-solving tools in physics. A ball dropped from 10 m converts all its gravitational PE into KE just before hitting the ground.
Power
P = W/t = Fv
Power (watts) is the rate of energy transfer. A 100 W lightbulb uses 100 joules of energy every second.
4. Momentum & Impulse
Momentum is what makes a moving truck far more dangerous than a moving bicycle, even at the same speed.
Linear Momentum
p = mv
Momentum is a vector — it has both magnitude and direction. Units: kg·m/s.
Impulse-Momentum Theorem
J = FΔt = Δp
A force applied over time changes an object’s momentum. This is why airbags work — they increase the time of impact, reducing the peak force on the passenger.
Conservation of Momentum
When no external forces act on a system:
p_initial (total) = p_final (total)
This applies to all collisions and explosions. In an elastic collision, kinetic energy is also conserved. In an inelastic collision, momentum is conserved but some KE converts to heat or deformation.
5. Circular Motion & Gravity
When an object moves in a circle at constant speed, it’s constantly accelerating — toward the center. That’s centripetal acceleration, and these formulas describe it.
Centripetal Acceleration & Force
a_c = v²/r (or rω²)
F_c = mv²/r
The centripetal force isn’t a new type of force — it’s whatever force (tension, gravity, friction) is directed toward the center.
Angular Motion Relationships
| Formula | Meaning |
|---|---|
| v = rω | Linear speed from angular speed |
| ω = Δθ/Δt | Angular velocity |
| α = Δω/Δt | Angular acceleration |
Orbital Mechanics
Orbital velocity (circular orbit):
v = √(GM/r)
Orbital period:
T² = (4π²/GM) × r³
Kepler’s Third Law (comparing two orbiting bodies):
T₁²/T₂² = r₁³/r₂³
These formulas are how NASA calculates satellite trajectories and orbital insertion burns — the same equations, just applied at massive scale.
6. Waves & Optics Formulas
Waves carry energy without carrying matter. These equations describe everything from sound in a concert hall to light bending through a camera lens.
The Wave Equation
v = fλ
Wave speed equals frequency times wavelength. For light in a vacuum, v = c = 3.0 × 10⁸ m/s. Sound in air at room temperature travels at about 343 m/s.
Snell’s Law (Refraction)
n₁ sinθ₁ = n₂ sinθ₂
When light moves from one medium to another (say, air into glass), it bends. The refractive index n describes how much. This is why a straw appears bent in a glass of water.
The Thin Lens Equation
1/f = 1/d_o + 1/d_i
where f is focal length, d_o is the object distance, and d_i is the image distance. Use sign conventions carefully (real vs. virtual images flip the sign of d_i).
Magnification:
m = −d_i / d_o
A negative magnification means the image is inverted — which is exactly what your eye’s lens does.
7. Electricity & Magnetism
Electrical formulas dominate modern technology. These are the equations behind every circuit, motor, and electronic device.
Ohm’s Law
V = IR
Voltage (volts) = Current (amperes) × Resistance (ohms). This is the most used formula in circuit analysis. If you double the resistance, current is halved at the same voltage.
Electric Power
P = VI = I²R = V²/R
All three forms are equivalent (just substituting Ohm’s Law). In circuit problems, use whichever version has two of your known quantities.
Coulomb’s Law
F = k × (q₁q₂) / r²
where k = 8.99 × 10⁹ N·m²/C². Like gravitational force, the electric force between charges follows an inverse-square law. Unlike gravity, it can repel.
Capacitance & Energy Storage
Q = CV (charge on a capacitor)
U = ½CV² (energy stored)
Magnetic Force on a Charge
F = qvB sinθ
where q is charge, v is velocity, B is magnetic field strength (teslas), and θ is the angle between velocity and field.
8. Thermodynamics & Heat
Thermodynamics governs engines, refrigerators, stars, and the fundamental limits of what’s physically possible.
The Ideal Gas Law
PV = nRT
Pressure (Pa) × Volume (m³) = moles × gas constant × Temperature (K).
R = 8.314 J/(mol·K)
Critical: Temperature must always be in Kelvin (K = °C + 273.15). Plugging in Celsius values is one of the most common errors in thermodynamics problems.
The First Law of Thermodynamics
ΔU = Q − W
The change in a system’s internal energy equals the heat added to it minus the work done by it. Energy is always conserved — it just changes form.
Example: A gas absorbs 800 J of heat and does 300 J of work expanding against a piston. Its internal energy increases by ΔU = 800 − 300 = 500 J.
Heat Transfer Equations
| Formula | Application |
|---|---|
| Q = mcΔT | Heating or cooling a substance (c = specific heat capacity) |
| Q = mL | Phase changes — melting or boiling (L = latent heat) |
9. How to Build a Physics Formula Sheet That Actually Works
Most students make the same mistake: they copy down formulas without understanding them, then struggle to apply them under pressure. Here’s how to build a reference sheet that genuinely helps you think.
Organize by Topic, Not by Equation Number
Group your formulas under clear headings — Kinematics, Forces, Energy, and so on. When you’re mid-problem and need a formula fast, you’ll know exactly where to look.
Include Context, Not Just Equations
For each formula, note:
- What the symbols mean
- The SI units for each variable
- A one-line description of when to use it
For example, instead of just writing v² = u² + 2as, write: “Use when time (t) is unknown.”
Add Your Key Constants
Don’t leave these out:
| Constant | Value |
|---|---|
| g (Earth’s gravity) | 9.8 m/s² |
| c (speed of light) | 3.0 × 10⁸ m/s |
| G (gravitational constant) | 6.674 × 10⁻¹¹ N·m²/kg² |
| k (Coulomb’s constant) | 8.99 × 10⁹ N·m²/C² |
| R (gas constant) | 8.314 J/(mol·K) |
| e (elementary charge) | 1.602 × 10⁻¹⁹ C |
Practice With It Before the Exam
Use your formula sheet while doing practice problems — not just the night before a test. The goal is to know which formula to reach for, not just what the formula says.
Keep It Clean
A cluttered sheet slows you down. Use columns, consistent formatting, and limit yourself to one formula per line. Highlight the equations you’re most likely to confuse with each other.
Conclusion
Physics can feel like an endless sea of equations, but when you understand what each formula is actually describing — a force, a transfer of energy, a wave moving through space — the math stops feeling arbitrary and starts feeling inevitable. This physics formula sheet isn’t meant to replace understanding; it’s designed to support it.
Bookmark this page, build your own handwritten version, and most importantly: practice applying every equation here until reaching for the right formula becomes second nature. That’s when physics gets genuinely exciting.
Frequently Asked Questions (FAQ Schema Ready)
Q: What is a physics formula sheet?
A physics formula sheet is a condensed reference document listing the essential equations, constants, and units used across major physics topics — including motion, forces, energy, waves, and electricity. It’s designed for quick lookup during problem-solving or exam review, not as a substitute for understanding the concepts behind each formula.
Q: What formulas should be on a physics formula sheet?
At minimum, include: the four SUVAT (kinematic) equations, F = ma, W = mg, work-energy theorem, KE = ½mv², PE = mgh, p = mv, V = IR, P = VI, Coulomb’s Law, PV = nRT, and ΔU = Q − W. Add topic-specific equations based on your course (AP Physics 1 vs. AP Physics C, for example, have very different equation needs).
Q: How do I use a physics formula sheet effectively?
Use it while practicing, not just during exams. For each formula, make sure you can identify every variable, know its unit, and recognize the type of problem it solves. If you can explain why an equation works — not just what it says — you’ll apply it correctly under pressure.
Q: Is a formula sheet allowed on AP Physics exams?
Yes. The College Board provides an official reference sheet for AP Physics 1, AP Physics 2, and AP Physics C exams. It includes most of the core equations, so students don’t need to memorize every formula — but they do need to know how to apply them correctly and quickly.
Q: How can I memorize physics formulas faster?
The most effective approach is understanding-first, memorization-second. Derive the formula if you can, then use it in at least five different practice problems. Spaced repetition (reviewing formulas over days rather than cramming) dramatically improves long-term retention. Group related formulas together — KE, PE, and W are more intuitive as a cluster than as isolated equations.
Q: What are the SI units used in a physics formula sheet?
The International System of Units (SI) is the standard for physics. Key base units include meters (m) for length, kilograms (kg) for mass, seconds (s) for time, amperes (A) for current, kelvin (K) for temperature, and newtons (N) for force. Derived units like joules (J = kg·m²/s²) and watts (W = J/s) follow from these.
Q: What’s the difference between scalar and vector quantities in physics formulas?
Scalars have magnitude only (speed, mass, energy). Vectors have magnitude and direction (velocity, force, momentum). This distinction matters when applying formulas — for example, momentum p = mv is a vector, so direction must be tracked in collision problems. Kinetic energy KE = ½mv² is scalar, so it’s always positive.
https://shorturl.fm/h69Gq