Physics Formulas Cheat Sheet: Core Equations by Topic With Units and When to Use Them

Overview

This is a practical reference for students who want a reusable set of physics revision formulas with context. The aim is simple: when you face a problem, you should be able to answer four questions quickly.

1. What physical principle is involved?
2. Which equation matches that principle?
3. What units and symbols should appear?
4. What assumptions make the equation valid?

That last question matters more than many formula sheets admit. A formula can be correct and still be the wrong tool. For example, constant-acceleration kinematics only works when acceleration is constant; the ideal gas law is most useful when a gas can reasonably be treated as ideal; nonrelativistic momentum is fine at everyday speeds, but not when speeds approach the speed of light.

Use this article as a checklist, not just a memorization list. If you want broader concept refreshers, it pairs well with Best Physics Textbooks by Subject and Level and Best Physics YouTube Channels, Simulations, and Free Learning Tools.

A quick note on symbols and SI units

Many symbols vary by textbook, but these are common conventions:

• Displacement: x or s in meters (m)
• Velocity: v in meters per second (m/s)
• Acceleration: a in meters per second squared (m/s²)
• Force: F in newtons (N)
• Mass: m in kilograms (kg)
• Energy/work/heat: E, W, Q in joules (J)
• Power: P in watts (W)
• Charge: q in coulombs (C)
• Electric field: E in N/C or V/m
• Potential difference: V in volts (V)
• Resistance: R in ohms (Ω)
• Frequency: f in hertz (Hz)
• Wavelength: λ in meters (m)
• Temperature: T in kelvin (K)

Whenever possible, convert to SI units before substituting values. That single habit prevents a large share of avoidable mistakes.

Checklist by scenario

If you are wondering when to use physics formulas, start with the scenario, not the equation. The sections below group common problems by topic and point to the formulas most often needed.

1) Motion in a straight line: kinematics

Use these when acceleration is constant.

• v = u + at
  Use when you know initial velocity u, acceleration a, and time t.
  Units: m/s = m/s + (m/s²)(s)
• s = ut + 1/2 at²
  Use for displacement under constant acceleration.
  Units: m
• v² = u² + 2as
  Use when time is not given.
• s = (u + v)t/2
  Use when velocity changes uniformly.

Checklist: Is acceleration constant? Are signs defined clearly? Is the motion one-dimensional?

2) Forces and Newton's laws: classical mechanics explained

• F = ma
  Core relation between net force and acceleration.
  Units: N = kg·m/s²
• W = mg
  Weight near Earth's surface, where g ≈ 9.8 m/s².
• f = μN
  Frictional force, where μ is the coefficient of friction and N is the normal force.
• p = mv
  Linear momentum for nonrelativistic motion.
• J = FΔt = Δp
  Impulse-momentum theorem.

Checklist: Draw a free-body diagram. Distinguish between net force and individual forces. Decide whether friction is static or kinetic. Resolve forces into components when using inclined planes.

3) Work, energy, and power

• W = Fd cos θ
  Work done by a constant force over displacement d.
• K = 1/2 mv²
  Kinetic energy.
• U = mgh
  Gravitational potential energy near Earth's surface.
• U = 1/2 kx²
  Elastic potential energy in a spring.
• P = W/t = E/t
  Power as rate of energy transfer.
• ΔE = 0 for conservative mechanical systems, or more explicitly K₁ + U₁ = K₂ + U₂.

Checklist: Is energy conserved, or are nonconservative forces doing work? Is the force constant? Is the angle between force and displacement important?

4) Circular motion and gravitation

• a_c = v²/r
  Centripetal acceleration.
• F_c = mv²/r
  Required net inward force for circular motion.
• F = Gm₁m₂/r²
  Newton's law of gravitation.
• g = GM/r²
  Gravitational field strength at distance r from a mass.
• v = 2πr/T
  Speed in uniform circular motion.

Checklist: Remember that centripetal force is not an extra force; it is the net inward force supplied by tension, gravity, friction, or another real interaction.

5) Oscillations, waves, and optics

• v = fλ
  Wave speed relation.
• T = 1/f
  Period-frequency relation.
• ω = 2πf
  Angular frequency.
• F = -kx
  Hooke's law for springs.
• T = 2π√(m/k)
  Period of a mass-spring system.
• T = 2π√(L/g)
  Small-angle pendulum period.
• n = c/v
  Refractive index.
• 1/f = 1/d_o + 1/d_i
  Thin lens or mirror equation.
• m = h_i/h_o = -d_i/d_o
  Magnification.

Checklist: Do not confuse frequency with angular frequency. Keep track of sign conventions in optics. For pendulums, the standard period formula assumes small oscillations.

6) Electricity and circuits: electromagnetism tutorial essentials

• F = kq₁q₂/r²
  Coulomb's law.
• E = F/q
  Electric field definition.
• V = W/q
  Electric potential difference.
• I = Q/t
  Current.
• V = IR
  Ohm's law.
• P = IV = I²R = V²/R
  Electrical power.
• R_series = R₁ + R₂ + ...
• 1/R_parallel = 1/R₁ + 1/R₂ + ...
• C = Q/V
  Capacitance.
• U = 1/2 CV²
  Energy stored in a capacitor.

Checklist: In series circuits, current is the same. In parallel circuits, voltage is the same. Be careful about whether the problem asks for field, force, potential, current, or power; these are related but not interchangeable.

For a larger concept review, see Magnetism and Electromagnetic Induction Explained Simply.

7) Magnetism and induction

• F = qvB sin θ
  Magnetic force on a moving charge.
• F = BIL sin θ
  Force on a current-carrying wire.
• Φ = BA cos θ
  Magnetic flux.
• ε = -dΦ/dt
  Faraday's law of induction.

Checklist: Magnetic force changes direction but does no work on a moving point charge because it acts perpendicular to velocity. Watch the angle used in flux and force formulas.

8) Thermodynamics and statistical mechanics

• pV = nRT
  Ideal gas law.
• Q = mcΔT
  Thermal energy transfer without phase change.
• Q = mL
  Latent heat during phase change.
• ΔU = Q - W
  First law of thermodynamics, with a common sign convention where W is work done by the system.
• η = W_out/Q_in
  Efficiency.

Checklist: Confirm the sign convention your course uses for work. Convert temperature to kelvin when required. Distinguish between heating that changes temperature and heating that changes phase.

For a concept-first review, see Thermodynamics Laws Explained: Internal Energy, Heat, Work, and Entropy.

9) Modern physics explained: photons, atoms, and nuclei

• E = hf = hc/λ
  Photon energy.
• p = h/λ
  de Broglie momentum relation.
• K_max = hf - ϕ
  Photoelectric equation, where ϕ is the work function.
• E = mc²
  Mass-energy relation.
• N = N₀e^-λt
  Radioactive decay.
• t_1/2 = ln 2 / λ
  Half-life relation.

Checklist: Keep Planck's constant and the speed of light in consistent units. Decide whether the problem is about total photon energy, kinetic energy of emitted electrons, or wavelength of matter waves.

10) Relativity

• γ = 1/√(1 - v²/c²)
  Lorentz factor.
• Δt = γΔt₀
  Time dilation.
• L = L₀/γ
  Length contraction.
• E = γmc²
  Relativistic total energy.

Checklist: Identify which frame measures proper time or proper length. Relativity problems are often frame-labeling problems before they are algebra problems. For a fuller walkthrough, read Special Relativity Explained: Time Dilation, Length Contraction, and E=mc².

What to double-check

Before finalizing any answer, run through this short verification list. It is one of the most reliable ways to improve accuracy in physics homework help and exam prep.

Units

Every term in an equation must have compatible units. If one side is in joules and the other ends up in newton-seconds, something went wrong. Dimensional checking is fast and often catches algebra slips immediately.

Signs and directions

Choose a coordinate system early. State what counts as positive. This matters in kinematics, electric fields, forces on slopes, and circular motion. Many wrong answers come from changing sign conventions halfway through.

Knowns, unknowns, and constraints

List what is given and what must be found. Also write the hidden constraints: constant acceleration, isolated system, ideal gas behavior, small-angle approximation, negligible air resistance, steady current, or nonrelativistic speeds.

Appropriate model

Ask whether the equation matches the physical setting. If acceleration changes with time, constant-acceleration formulas may fail. If a circuit includes non-ohmic components, simple Ohm's law may not tell the whole story. If the speed is close to c, classical momentum may not be adequate.

Reasonable magnitude

Use estimation. A falling object near Earth does not usually accelerate at 500 m/s². A classroom resistor does not usually dissipate megawatts. Even rough physical intuition can flag an answer that is mathematically neat but physically implausible.

Graphs and data

In lab work, formulas are not only for substitution. They also guide plotting and interpretation. A linearized equation can suggest what to graph and what slope to expect. If that is part of your workflow, How to Plot Physics Data in Python: Error Bars, Fits, and Residuals is a useful companion.

Common mistakes

Most errors on formula-heavy physics problems are not caused by forgetting an equation. They come from applying a familiar equation in the wrong context or skipping basic checks.

• Using memorized formulas without identifying the principle. Start with conservation of energy, Newton's second law, Gauss-style symmetry arguments if applicable, or the first law of thermodynamics before hunting for symbols.
• Mixing scalar and vector quantities. Speed is not velocity, distance is not displacement, and electric field direction matters.
• Forgetting unit conversion. Centimeters, electron-volts, degrees Celsius, and hours often need conversion before substitution.
• Confusing net force with one force. In circular motion especially, the inward net force may be provided by tension, gravity, friction, or several forces together.
• Dropping negative signs mechanically. A negative result can be meaningful: opposite direction, opposite charge effect, or energy decrease relative to a chosen reference.
• Using special-case formulas as universal formulas. Examples include small-angle pendulum period, near-Earth potential energy mgh, and constant-acceleration equations.
• Not checking definitions of symbols. In one chapter U may mean internal energy; in another it may mean potential energy. Textbook conventions vary.
• Solving too early with numbers. Algebra first, numbers last is usually cleaner and easier to debug.

If you regularly feel stuck before the algebra starts, it can help to build a concept-to-formula map in your notes. That is often more durable than a longer equation list.

When to revisit

This cheat sheet works best as a living reference. Revisit and update it at moments when your study workflow changes or when you are shifting topics.

• Before a new exam block: Condense course-specific formulas onto one page and mark which assumptions your instructor emphasizes.
• When starting a new unit: Add the new equations beside older related ones. For example, place momentum conservation next to impulse, or photon energy next to the photoelectric equation.
• Before lab reports: Note which formulas produce derived quantities and which suggest a graph, fit, or uncertainty analysis.
• When switching textbooks or courses: Compare notation, sign conventions, and the level of approximation assumed.
• When your mistakes repeat: Add a warning note beside formulas you often misuse, such as “constant acceleration only” or “temperature must be in kelvin.”

A practical next step is to make your own three-column sheet for each topic: formula, when to use it, and what to check. That format turns passive physics notes into an active problem-solving tool. If you want to strengthen the bigger study system around it, you may also find How to Read a Physics Research Paper Without Getting Lost, Physics Breakthroughs Explained: A Monthly Research Digest to Watch, and Graduate School in Physics: Requirements, Applications, and Timeline useful for long-term academic planning.

Keep this page bookmarked, but do not stop at bookmarking it. The most useful physics equations list is the one you regularly revise, annotate, and test against real problems with solutions. That is how formulas become usable physics rather than isolated symbols.