Physics Formula Sheet by Topic: Equations, Units, and When to Use Them

Overview

This physics formula sheet by topic is designed as a reference hub rather than a cram sheet. The aim is simple: help you move from “I have seen this equation before” to “I know when to use it.” That difference matters because many physics mistakes come from choosing the wrong model, mixing units, or applying a formula without checking assumptions.

For each topic below, focus on four things:

• Equation: the relationship you are likely to use often
• Symbols: what each variable means
• SI units: the standard units expected in most school and introductory university problems
• When to use it: the physical situation where the equation makes sense

One useful habit is to think in layers. First identify the topic: motion, forces, energy, electricity, waves, or circular motion. Then choose the equation family that matches the information given. Finally, check whether the units and assumptions fit the problem. If you want a stronger foundation before using this hub, start with College Physics Study Guide: What to Review Before Intro Physics.

Also remember that formulas are compressed ideas. They do not replace understanding. A reference sheet works best when you pair it with worked examples, unit checks, diagrams, and practice. For exam technique, it also helps to review How to Check if Your Physics Answer Makes Sense and The Most Common Physics Mistakes Students Make in Exams.

Topic map

Below is a practical map of the most-used introductory physics formulas. It is not every equation you may ever meet, but it covers the set students revisit repeatedly across GCSE, A-Level, AP Physics, and first-year college physics.

1. Kinematics: describing motion

Use kinematics when you are tracking position, displacement, velocity, acceleration, and time.

• Average speed: speed = distance / time
  Units: m/s
  Use when you know total distance traveled and total time.
• Average velocity: velocity = displacement / time
  Units: m/s
  Use when direction matters and you are working with displacement, not total path length.
• Acceleration: a = (v - u) / t
  Symbols: a acceleration, u initial velocity, v final velocity, t time
  Units: m/s²
  Use when velocity changes over time.
• Constant-acceleration equation: v = u + at
  Use for straight-line motion with constant acceleration.
• Constant-acceleration equation: s = ut + 1/2 at²
  Symbol: s displacement in m
  Use when you need displacement after time t.
• Constant-acceleration equation: v² = u² + 2as
  Use when time is not given.

When to be careful: these SUVAT-style equations only work when acceleration is constant. For practice, see Projectile Motion Problems: Horizontal and Angled Launch Questions Solved.

2. Forces and Newton’s laws

Use these formulas when motion changes because of interactions such as pushes, pulls, friction, tension, or weight.

• Newton’s second law: F = ma
  Symbols: F resultant force in N, m mass in kg, a acceleration in m/s²
  Use when net force causes acceleration.
• Weight: W = mg
  Symbol: g gravitational field strength in N/kg or acceleration due to gravity in m/s²
  Use for the gravitational force on a mass near a planet.
• Momentum: p = mv
  Units: kg·m/s
  Use for collisions and motion involving moving objects.
• Impulse: J = FΔt = Δp
  Units: N·s or kg·m/s
  Use when a force acts over a time interval and changes momentum.

When to use this set: choose these equations when the problem talks about causes of motion rather than just describing motion. A strong companion page is Mechanics Revision Guide: Forces, Motion, Energy, and Momentum in One Place.

3. Work, energy, and power

These formulas are useful when forces transfer energy or when systems speed up, slow down, lift, heat, or store energy.

• Work done: W = Fd
  Units: J
  Use when a force acts through a distance in the direction of motion.
• Kinetic energy: KE = 1/2 mv²
  Units: J
  Use for energy due to motion.
• Gravitational potential energy: GPE = mgh
  Units: J
  Use for changes in vertical height near Earth’s surface.
• Elastic potential energy: E = 1/2 kx²
  Symbols: k spring constant in N/m, x extension in m
  Use for stretched or compressed springs.
• Power: P = W / t
  Units: W
  Use for rate of energy transfer.
• Efficiency: efficiency = useful output / total input
  Often written as a decimal or percentage
  Use in machines, circuits, and energy transfer questions.

Common trap: students often confuse force and energy because both can appear in the same problem. Force is measured in newtons; energy and work are measured in joules.

4. Circular motion and gravitation

These are common once motion stops being purely straight-line.

• Centripetal acceleration: a = v² / r
  Units: m/s²
  Use for motion in a circle of radius r.
• Centripetal force: F = mv² / r
  Units: N
  Use when an inward resultant force keeps an object moving in a circle.
• Universal gravitation: F = Gm₁m₂ / r²
  Use when dealing with gravitational attraction between masses.

When to be careful: centripetal force is not a new separate force. It is the name for the net inward force, which could be provided by tension, friction, gravity, or a normal force.

5. Waves and oscillations

Use these formulas when working with sound, light, water waves, or simple harmonic motion.

• Wave speed: v = fλ
  Symbols: v wave speed in m/s, f frequency in Hz, λ wavelength in m
  Use for any periodic wave.
• Period and frequency: T = 1/f
  Units: s and Hz
  Use to switch between time per cycle and cycles per second.
• Hooke’s law: F = kx
  Use for spring force within the limit of proportionality.

If your course includes oscillations in more depth, revisit Simple Harmonic Motion Explained: Equations, Graphs, and Common Traps.

6. Electricity and circuits

These equations appear constantly in introductory electricity.

• Charge: Q = It
  Symbols: Q charge in C, I current in A, t time in s
  Use when current flows for a time interval.
• Potential difference definition: V = W / Q
  Use when voltage is treated as energy transferred per unit charge.
• Ohm’s law: V = IR
  Symbol: R resistance in Ω
  Use for ohmic components and basic circuit calculations.
• Electrical power: P = IV
  Units: W
  Use for power supplied or used in a circuit.
• Electrical energy: E = Pt
• Alternative power forms: P = I²R and P = V² / R
  Use when you know current and resistance, or voltage and resistance.

Common trap: current is not used up in a series circuit. Energy is transferred, but charge is conserved.

7. Thermal physics

Thermal formulas often look simple but require careful interpretation of the physical situation.

• Specific heat capacity: Q = mcΔT
  Symbols: Q thermal energy in J, c specific heat capacity in J/kg·°C or J/kg·K, ΔT temperature change
  Use when temperature changes without a change of state.
• Density: ρ = m / V
  Units: kg/m³
  Use for mass-volume relationships.
• Pressure: p = F / A
  Units: Pa
  Use when a force acts over an area.

When to be careful: if a problem involves melting or boiling, you may need latent heat rather than specific heat capacity.

Related subtopics

A formula sheet is strongest when it connects to neighboring reference tools. Physics problems rarely arrive labeled with the exact equation to use, so students benefit from seeing formulas alongside units, constants, and worked examples.

Three related subtopics are especially worth keeping nearby:

Units and prefixes

Many wrong answers come from unit mismatch, not concept failure. Converting cm to m, g to kg, or ms to s can completely change a result. Keep a separate units reference and review Physics Units and SI Prefixes Guide: Conversions Students Always Need.

Constants and standard symbols

Some equations depend on values such as g, G, or other standard constants. It helps to separate “formula structure” from “number to substitute.” For that, use Physics Constants List: Values, Units, and What They Mean.

Practice by topic

Reference alone is not enough. You need repetition to recognize patterns and choose equations quickly. A useful next step is Physics Practice Questions by Topic: A Revision Hub for Mechanics, Waves, Electricity, and More.

You may also want to build your own layered formula sheet. One version can be a clean exam-facing page with just equations and units. Another can be a study version with notes like “use only for constant acceleration” or “works when force is along displacement.” That second version often does more for understanding than a polished one-page summary.

How to use this hub

The most effective way to use a physics equations list is not to memorize everything at once. Instead, use a repeatable routine each time you solve a problem.

1. Read for the topic first. Is this a motion problem, a force problem, an energy problem, or a circuit problem? Labeling the topic narrows the formula choice.
2. List the known and unknown quantities. Write the symbols with units. For example, u = 4 m/s, a = 2 m/s², find s.
3. Match the equation to the variables you have. Choose the formula that contains the unknown and the known quantities with the fewest extra steps.
4. Check the conditions. Ask whether the formula assumes constant acceleration, proportional behavior, straight-line motion, or an ideal component.
5. Convert units before substitution. Do not wait until the end if the conversion is simple.
6. Substitute carefully and keep units visible. This catches algebra slips early.
7. Sense-check the answer. Does the sign, size, and unit make physical sense?

This workflow is especially useful for students who feel that physics is too abstract. It turns a word problem into a sequence of manageable decisions. If you are revising from an official formula sheet, compare your habits with AP Physics 1 Formula Sheet Guide: How to Use It Efficiently.

It also helps to organize formulas by question type:

• Finding a rate: speed, velocity, acceleration, power, current
• Relating cause and effect: force and acceleration, voltage and current
• Conservation ideas: energy and momentum
• Oscillation and periodic motion: frequency, period, wave speed
• Geometry-driven problems: pressure, circular motion, electric fields in some courses

If you keep a notebook, reserve one page per topic with four headings: equation, units, assumptions, and common traps. That format naturally answers the question students ask most often: “Which formula should I use here?”

When to revisit

Come back to this hub whenever your course moves into a new topic, when you start mixing topics in revision, or when you notice that you can remember formulas but still struggle to choose them. Those are signs that the issue is not memorization alone but classification, conditions, or units.

A practical revisit schedule looks like this:

• At the start of a new unit: scan the relevant section and add any course-specific notation your teacher or textbook uses.
• After finishing a topic: condense the formulas you actually used most often into a one-page revision sheet.
• Before a test or exam: review the “when to use it” notes, not just the equations themselves.
• After marked practice: update your sheet with mistakes you repeated, such as confusing displacement with distance or voltage with energy.
• When topics begin to overlap: compare similar formulas side by side, such as F = ma versus W = mg, or P = W/t versus P = IV.

To make this hub genuinely useful over time, treat it as editable. Add examples, highlight formulas your course emphasizes, and mark the ones that only apply under special conditions. Physics becomes more manageable when your reference sheet grows with your understanding rather than remaining a static list.

Your next step is simple: pick one current topic, copy its key equations into your notes, add units and a short “use when...” phrase for each, then test yourself with a few questions. If your answers still feel uncertain, move from the formula sheet to worked practice and answer-checking. That loop—reference, apply, check, revise—is what turns formulas into usable tools.