A-Level Physics Equations List with Definitions and Unit Checks

Overview

This article gives you a practical A-Level physics equations list with definitions and unit checks. The aim is not to replace your specification or formula sheet, since those vary by board, but to help you use equations correctly under exam pressure. If you know what the symbols represent, what unit pattern should appear, and which assumptions are built into the formula, you will solve more problems accurately and faster.

A good revision method for A-Level physics formulas has four parts:

• Recognize the situation: identify the topic and physical model.
• Select the equation: choose a formula that matches the known and unknown quantities.
• Check symbols and units: confirm each variable means what you think it means and that units are consistent.
• Judge the result: ask whether the magnitude and sign are physically sensible.

That process works across mechanics, electricity, waves, materials, and modern physics. It also turns equations from a memorization task into a problem-solving tool.

Before the checklist, keep three broad reminders in view:

1. Definitions matter as much as formulas. Students often lose marks not because they forgot an equation, but because they confused similar symbols such as velocity and acceleration, or emf and potential difference.
2. Unit checks are fast error checks. If the right-hand side of an equation does not reduce to the unit on the left-hand side, something is wrong.
3. Equations come with conditions. Many formulas assume constant acceleration, ideal components, small oscillations, or no resistive forces.

If you want a broader cross-topic reference, see Physics Formulas List by Topic: Equations, Units, and When to Use Them.

Checklist by scenario

Use this section as a working checklist by topic and exam scenario. For each area, revise the equation, the symbol definitions, and the unit pattern together.

1. Motion and kinematics questions

Use these when a problem involves displacement, velocity, acceleration, and time.

• v = u + at
  Definitions: v final velocity, u initial velocity, a acceleration, t time.
  Units: m s^-1 = m s^-1 + (m s^-2)(s).
  Use when acceleration is constant.
• s = ut + 1/2 at²
  Definitions: s displacement.
  Units: m = (m s^-1)(s) + (m s^-2)(s²).
  Check that the motion is along one line or that you are applying components separately.
• v² = u² + 2as
  Units: m² s^-2 on both sides.
  Useful when time is not given.
• s = (u + v)t / 2
  Use for constant acceleration when average velocity is the mean of initial and final velocity.

Quick check: in many kinematics problems with solutions, the biggest mistake is mixing up distance and displacement, especially when direction matters.

2. Forces, Newton's laws, and momentum

• F = ma
  Definitions: F resultant force, m mass, a acceleration.
  Units: N = kg m s^-2.
  Always use the resultant force, not just one force from the diagram.
• W = mg
  Definitions: W weight, g gravitational field strength.
  Units: N = kg × N kg^-1 or kg × m s^-2.
  Do not confuse weight with mass.
• p = mv
  Definitions: p momentum.
  Units: kg m s^-1.
  A vector quantity, so direction matters.
• FΔt = Δp
  Impulse equals change in momentum.
  Units: N s = kg m s^-1.

For rotation topics, pair this section with Torque and Rotational Motion Formulas, Concepts, and Worked Problems.

3. Work, energy, and power

• W = Fs
  Work done equals force × distance moved in the direction of the force.
  Units: J = N m.
• E_k = 1/2 mv²
  Kinetic energy.
  Units: J = kg m² s^-2.
• E_p = mgh
  Gravitational potential energy change near Earth's surface.
  Units: J = kg × m s^-2 × m.
• P = E/t and P = IV
  Power as energy transferred per second, and electrical power.
  Units: W = J s^-1 and W = A V.

Checklist item: when energy appears to be “lost,” ask where it went. In most exam questions it has been transferred to thermal energy, sound, or internal energy.

4. Materials and deformation

• ρ = m/V
  Density equals mass per unit volume.
  Units: kg m^-3.
• stress = F/A
  Units: Pa = N m^-2.
• strain = ΔL/L
  No unit, because it is a ratio.
• Young modulus = stress/strain
  Units: Pa.

Common trap: strain is dimensionless, so if you attach units to it, revisit the setup.

5. Electricity and circuits

• Q = It
  Charge transferred.
  Units: C = A s.
• V = W/Q
  Potential difference as work done per unit charge.
  Units: V = J C^-1.
• V = IR
  Ohm's law for ohmic conductors under suitable conditions.
  Units: V = A Ω.
• R = ρL/A
  Resistance of a uniform conductor.
  Definitions: ρ resistivity, L length, A cross-sectional area.
  Units: Ω = (Ω m)(m)/m².
• P = IV, P = I²R, P = V²/R
  Electrical power relationships.

For practice with basic circuit reasoning, see Ohm's Law Problems and Circuit Basics: Solved Questions for Beginners.

6. Waves and optics

• v = fλ
  Wave speed equals frequency × wavelength.
  Units: m s^-1 = Hz × m.
• T = 1/f
  Period and frequency relation.
  Units: s = 1/Hz.
• n = c/v
  Refractive index.
  No unit for n.

When working on image formation, equations help, but so do diagrams. For that, use Optics Ray Diagrams Explained for Mirrors and Lenses.

7. Circular motion and oscillations

• a = v²/r
  Centripetal acceleration.
  Units: m s^-2.
• F = mv²/r
  Centripetal force.
  Units: N.
• T = 2π/ω
  Period and angular frequency.
• a = -ω²x
  Simple harmonic motion model.
  The negative sign indicates acceleration is directed toward equilibrium.

Checklist item: centripetal force is not an extra force added to the diagram. It is the name for the resultant inward force.

8. Thermal physics

• ΔE = mcΔθ
  Thermal energy change.
  Definitions: c specific heat capacity, Δθ temperature change.
  Units: J = kg × J kg^-1 K^-1 × K.
• pV = nRT
  Ideal gas equation.
  Units: Pa m³ = mol × J mol^-1 K^-1 × K.

For a dedicated reference, see Thermodynamics Formulas Sheet: Laws, Processes, and Units.

9. Electric fields and potential

• E = F/Q
  Electric field strength.
  Units: N C^-1.
• V = W/Q
  Electric potential.
  Units: J C^-1.

Do not assume field strength and potential are interchangeable. They are related ideas, but they are not the same physical quantity.

10. Quantum and nuclear basics

• E = hf
  Photon energy.
  Units: J = J s × s^-1.
• c = fλ
  For electromagnetic waves in vacuum.
• E = mc²
  Mass-energy equivalence.

In modern physics questions, unit conversion is often the hidden challenge. Move carefully between joules, electronvolts, and SI units if your course uses both.

What to double-check

This is the part many students skip, even though it often separates a complete answer from an almost-correct one.

1. Symbol meanings

The same letter can represent different things in different topics. For example, v may mean velocity or wave speed depending on context. W may mean work done, while lowercase w is often not used the same way. Never lift letters from memory without reading the question carefully.

2. SI units

Most physics equations with units work cleanly in SI form. Convert before substituting:

• cm to m
• g to kg
• ms to s
• μC to C
• kV to V

A result can be numerically wrong by a factor of 100 or 1000 even when the algebra is right.

3. Scalars and vectors

Quantities such as velocity, acceleration, force, momentum, and electric field have direction. If the problem is one-dimensional, choose a positive direction early and stay consistent.

4. Conditions of the formula

Ask what the equation assumes. Constant acceleration formulas fail if acceleration changes significantly. Ohm's law applies to ohmic behavior under suitable conditions. SHM equations rely on the restoring effect being proportional to displacement.

5. Significant figures and uncertainty

For exam answers, reported precision should usually match the data given. For practical work, uncertainties matter as much as the central value. These two guides are useful companions: Significant Figures Rules in Physics: How to Round, Multiply, and Report Results and Uncertainty and Error in Physics Labs: Rules, Examples, and Calculation Methods.

6. Does the answer make physical sense?

Final answers should pass a quick reasonableness test. A refractive index below 1 in an ordinary school-level optics problem, a negative resistance, or a speed wildly above expected conditions usually signals an earlier mistake.

Common mistakes

Most errors in A-Level revision physics are repeat errors. If you know them in advance, you can actively look for them.

• Using the right equation in the wrong situation. A memorized formula is not enough; check assumptions first.
• Confusing weight and mass. Mass is in kg. Weight is a force in N.
• Mixing up current, charge, and voltage. These are related but not interchangeable.
• Forgetting area conversions. If a length is converted from cm to m, area must be converted as cm² to m², not just divided by 100.
• Dropping direction signs. Negative values often carry physical meaning.
• Using distance where displacement is needed. This matters in motion and energy questions.
• Writing no unit or the wrong unit. Units are not decoration; they are part of the answer.
• Rounding too early. Keep extra digits until the final line, then round appropriately.
• Treating derived equations as isolated facts. It is easier to remember formulas when you understand where they come from conceptually.

If you want a useful comparison framework, the article AP Physics Formula Sheet Guide: What Every Equation Means shows the same principle in another exam context: formula recall improves when definitions and use-cases are attached to each equation.

When to revisit

This page works best as a return-to resource, not a one-time read. Revisit your equations list at moments when your revision inputs change or when exam demands shift.

Use this revisit checklist

• At the start of a new topic: build a mini sheet with formula, symbol definitions, and one worked example.
• Before mocks or end-of-term tests: check which equations you can recall, which you can use, and which you still confuse.
• Before required practical write-ups: review uncertainty, units, gradients, and proportional relationships.
• When switching exam boards or classes: confirm notation and formula sheet expectations.
• During final revision season: turn this guide into a personal checklist and tick off each equation only after you can explain it aloud.

A practical 15-minute routine

1. Pick one topic, such as mechanics or electricity.
2. Write five key equations from memory.
3. Add the definition and SI unit for every symbol.
4. Do one quick unit check for each equation.
5. Solve one short question using at least two of those equations.
6. Mark any symbol, unit, or condition that caused hesitation.

This small routine is often more effective than rereading pages of notes. It forces retrieval, application, and correction in one sitting. For a broader study approach, Why Real-Time Feedback Works: The Physics of Faster Learning Loops is a useful companion piece.

The most reliable way to use an A-Level physics equations list is to treat it as a live document. Update it when your course moves on, when your teacher emphasizes a different method, or when past-paper mistakes reveal a weak spot. Over time, your goal is not just to recognize formulas, but to know what they mean, when they apply, and how to check them quickly under pressure.