GCSE Physics Formula Sheet – Every Equation You Need (AQA 8463)
Every AQA GCSE Physics equation in one place, organised by topic, so you can revise the whole course from a single page. AQA hands you some equations on an insert in the exam hall but expects you to recall the rest from memory, so each row below is tagged [Memorise] or [Given in exam] — spend your revision time on the ones you actually have to learn.
Forces & Motion
| Equation | What it means / When to use it |
|---|---|
| Weight: W = m g | The force of gravity on an object: weight (N) = mass (kg) × gravitational field strength (N/kg). Use it whenever a question swaps between mass and weight. [Memorise] |
| Distance travelled: s = v t | Distance (m) = speed (m/s) × time (s), for motion at a steady speed. [Memorise] |
| Acceleration: a = Δv / t | Acceleration (m/s2) = change in velocity (m/s) ÷ time taken (s). [Memorise] |
| Resultant force: F = m a | Newton’s second law: force (N) = mass (kg) × acceleration (m/s2). [Memorise] |
| Momentum: p = m v | Momentum (kg m/s) = mass (kg) × velocity (m/s). Momentum is conserved in collisions when no external force acts. [Memorise] |
| Force and momentum change: F = m Δv / Δt | Force (N) = (mass × change in velocity) ÷ time. Explains why crumple zones and air bags cut injury: they stretch the time of the change. [Given in exam] |
| Moment: M = F d | The turning effect of a force: moment (N m) = force (N) × perpendicular distance from the pivot (m). [Memorise] |
| Pressure: p = F / A | Pressure (Pa) = force normal to a surface (N) ÷ area of that surface (m2). [Memorise] |
| Pressure in a liquid: p = h ρ g | Pressure (Pa) = height of the liquid column (m) × density (kg/m3) × gravitational field strength (N/kg). Pressure grows with depth. [Given in exam] |
| Force on a spring: F = k e | Hooke’s law: force (N) = spring constant (N/m) × extension (m). Only holds up to the limit of proportionality. [Memorise] |
| Elastic potential energy: Ee = ½ k e2 | Energy stored in a stretched spring (J) = ½ × spring constant (N/m) × extension2 (m2). [Given in exam] |
Energy
| Equation | What it means / When to use it |
|---|---|
| Kinetic energy: Ek = ½ m v2 | Energy of a moving object (J) = ½ × mass (kg) × speed2 (m/s). Doubling the speed quadruples the energy. [Memorise] |
| Gravitational potential energy: Ep = m g h | Energy stored by height (J) = mass (kg) × gravitational field strength (N/kg) × height (m). [Memorise] |
| Elastic potential energy: Ee = ½ k e2 | Energy stored in springs and elastic materials — see the Forces & Motion table above for the full working. [Given in exam] |
| Power: P = E / t | Power (W) = energy transferred (J) ÷ time (s). One watt is one joule per second. [Memorise] |
| Power: P = W / t | Power (W) = work done (J) ÷ time (s). The work-done version of the same idea. [Memorise] |
| Efficiency (energy form) = useful energy output / total energy input | Multiply by 100 to give a percentage. No device is 100% efficient because some energy is always wasted, usually as heat. [Memorise] |
| Efficiency (power form) = useful power output / total power input | Use this version when the question gives powers in watts instead of energies in joules. [Memorise] |
| Change in thermal energy: ΔE = m c Δθ | Specific heat capacity equation: change in thermal energy (J) = mass (kg) × specific heat capacity (J/kg °C) × temperature change Δθ (°C). [Given in exam] |
| Energy for a change of state: E = m L | Specific latent heat equation: energy (J) = mass (kg) × specific latent heat (J/kg). The temperature does not change during the change of state. [Given in exam] |
Electricity
| Equation | What it means / When to use it |
|---|---|
| Charge flow: Q = I t | Charge (C) = current (A) × time (s). Links the current in a circuit to the total charge passed. [Memorise] |
| Potential difference: V = I R | Potential difference (V) = current (A) × resistance (Ω). The starting point for most circuit calculations. [Memorise] |
| Electrical power: P = V I | Power (W) = potential difference (V) × current (A). Rates how fast a component transfers energy. [Memorise] |
| Electrical power: P = I2 R | Power (W) = current2 (A2) × resistance (Ω). Handy when you know the current and resistance but not the voltage; it comes from combining P = V I with V = I R. [Memorise] |
| Energy transferred: E = P t | Energy (J) = power (W) × time (s). Use it for appliance energy use over a period of time. [Memorise] |
| Energy transferred: E = Q V | Energy (J) = charge flow (C) × potential difference (V). Energy given to or taken from each coulomb of charge. [Memorise] |
| Resistors in series: Rtotal = R1 + R2 + … | Resistances simply add in series, so the total is bigger than any single resistor. [Memorise] |
| Resistors in parallel: total resistance is less than the smallest resistor | Adding a resistor in parallel gives the current an extra path, so the total resistance always drops below the smallest branch. [Memorise] |
Waves
| Equation | What it means / When to use it |
|---|---|
| Wave speed: v = f λ | Wave speed (m/s) = frequency (Hz) × wavelength λ (m). Applies to every wave, from ripples to light. [Memorise] |
| Period: T = 1 / f | Time period (s) = 1 ÷ frequency (Hz). The time for one complete wave to pass a point. [Given in exam] |
| Magnification = image height / object height | How many times bigger a lens or mirror makes the image. A value below 1 means the image is smaller than the object. [Given in exam] |
Matter & Pressure
| Equation | What it means / When to use it |
|---|---|
| Density: ρ = m / V | Density (kg/m3) = mass (kg) ÷ volume (m3). Rearrange it to find a mass or an unknown volume. [Memorise] |
| Internal energy (no single equation) | The total kinetic energy plus potential energy of all the particles in a system. Heating raises it: particles move faster and, during a change of state, move further apart. [Memorise] |
Key Constant
Gravitational field strength on Earth: g = 9.8 N/kg. Unless a question tells you otherwise, use 9.8 in every weight, GPE and liquid-pressure calculation.
Practise with more free resources
Work through topic-by-topic questions on the Physics hub – all boards, and keep the matching formula sheets open while you revise: IGCSE Physics Formula Sheet, A-Level Physics Formula Sheet and AP Physics Formula Sheet.
An original revision aid from QuaidianPoint, not affiliated with AQA.