Pearson Edexcel International GCSE in Physics · 4PH1 · Free · no account needed
Physics equations
Every equation on the Pearson Edexcel International GCSE Physics (4PH1) course — 38 of them, each with what its symbols stand for and the units the examiner expects, in specification order and linked to the lesson that teaches it.
Some of these are printed on the equation list at the front of the exam paper — the formula sheet — and some must be recalled from memory; either way the marks are for choosing the right one, rearranging it, substituting with the right units and stating the unit of the answer. An equation you can write is not yet one you can use: each lesson below puts it to work in a worked example, then in five marked questions. Learn the list here; then open the lesson, prove it, teach it back to an AI pupil and defend it. Completely free.
Topic 1 · Forces and motion
| Equation | Where | Units | Lesson |
|---|---|---|---|
| average speed = distance moved ÷ time taken | Rearranged: distance = speed × time · time = distance ÷ speed | m/s. Distance in m, time in s. | Speed, and What a Distance–Time Graph Is Telling You |
| a = (v − u) ÷ t | Rearranged: v = u + at · u = v − at · t = (v − u) ÷ a. Valid only for UNIFORM acceleration — a straight line on the velocity–time graph. | a in m/s², u and v in m/s, t in s. Use when a time is given or asked for. | Acceleration and the Velocity–Time Graph |
| v² = u² + 2as | Rearranged: a = (v² − u²) ÷ 2s · s = (v² − u²) ÷ 2a. Also uniform acceleration only. For a deceleration, substitute a as a NEGATIVE number. | u and v in m/s, a in m/s², s in m. Use when NO time is given or asked for. The final step is a square root. | Acceleration and the Velocity–Time Graph |
| F = m × a | F is the RESULTANT force in newtons (N), m is mass in kilograms (kg), a is acceleration in metres per second squared (m/s²) | N, kg, m/s². Rearranged: a = F ÷ m and m = F ÷ a. One newton is the resultant force that gives a 1 kg mass an acceleration of 1 m/s². | Resultant Force, Friction and F = ma |
| W = m × g | W is weight in newtons (N), m is mass in kilograms (kg), g is gravitational field strength in newtons per kilogram (N/kg). On Earth g ≈ 10 N/kg unless a question states otherwise | N, kg, N/kg. Rearranged: m = W ÷ g and g = W ÷ m. | Weight and Terminal Velocity |
| stopping distance = thinking distance + braking distance | thinking distance is the distance travelled during the driver's reaction time; braking distance is the distance travelled while the braking force acts | All three in metres (m). Thinking distance = speed × reaction time, so m = m/s × s. | Stopping Distance |
| F = k × x | F is the force applied in newtons (N), k is the spring constant in newtons per metre (N/m), x is the EXTENSION in metres (m) — not the length | N, N/m, m. Rearranged: k = F ÷ x and x = F ÷ k. The equation holds only up to the limit of proportionality. | Hooke's Law and Elasticity |
| p = m × v | p is momentum in kilogram metres per second (kg m/s), m is mass in kilograms (kg), v is velocity in metres per second (m/s) | kg m/s. Rearranged: m = p ÷ v and v = p ÷ m. Momentum is a VECTOR — it takes the direction of the velocity. | Momentum |
| total momentum before = total momentum after | the sum of m × v for every object before the interaction equals the sum after, provided no external force acts on the system | kg m/s throughout. Velocities in opposite directions must be given opposite signs. | Conservation of Momentum |
| F = (mv − mu) ÷ t | F is the average force in newtons (N), mv is the final momentum and mu the initial momentum in kg m/s, t is the time taken in seconds (s) | N, kg m/s, s. This is Newton's second law in its general form: force is the rate of change of momentum. | Conservation of Momentum |
| moment = F × d | moment is in newton metres (N m), F is the force in newtons (N), d is the PERPENDICULAR distance from the pivot to the line of action of the force, in metres (m) | N m, N, m. Rearranged: F = moment ÷ d and d = moment ÷ F. A newton metre is not a joule, even though the units look the same. | Moments and Centre of Gravity |
Topic 2 · Electricity
| Equation | Where | Units | Lesson |
|---|---|---|---|
| Q = I × t | Q is charge in coulombs (C), I is current in amperes (A), t is time in SECONDS (s) | C, A, s. Rearranged: I = Q ÷ t and t = Q ÷ I. Convert minutes to seconds before substituting. | Charge and Current |
| V = I × R | V is voltage in volts (V), I is current in amperes (A), R is resistance in ohms (Ω) | V, A, Ω. Rearranged: I = V ÷ R and R = V ÷ I. An ohm is one volt per ampere. | Resistance and Ohm's Law |
| R_total = R₁ + R₂ (series) | R_total is the total resistance of two components in series, in ohms (Ω), and R₁ and R₂ are their individual resistances | Ω. In series the resistances ADD. In parallel the total resistance is LESS than either branch on its own. | Series and Parallel Circuits |
| E = Q × V | E is energy transferred in joules (J), Q is charge in coulombs (C), V is voltage in volts (V) | J, C, V. Rearranged: Q = E ÷ V and V = E ÷ Q. The last of those is the definition: a volt is a joule per coulomb. | Voltage as Energy per Charge |
| P = I × V | P is power in watts (W), I is current in amperes (A), V is voltage in volts (V) | W, A, V. Rearranged: I = P ÷ V and V = P ÷ I. A watt is a joule per second, and amperes × volts = coulombs per second × joules per coulomb = joules per second. | Electrical Power and Energy |
| E = I × V × t | E is energy transferred in joules (J), I is current in amperes (A), V is voltage in volts (V), t is time in SECONDS (s) | J, A, V, s. This is the same as E = P × t, and it comes from combining Q = I × t with E = Q × V. | Electrical Power and Energy |
Topic 3 · Waves
| Equation | Where | Units | Lesson |
|---|---|---|---|
| v = f × λ | v is wave speed in metres per second (m/s), f is frequency in hertz (Hz), λ is wavelength in metres (m) | m/s, Hz, m. Rearranged: f = v ÷ λ and λ = v ÷ f. | The Wave Equation |
| f = 1 ÷ T | f is frequency in hertz (Hz), T is the period in seconds (s) | Hz, s. Rearranged: T = 1 ÷ f. Frequency and period are reciprocals of each other. | The Wave Equation |
| n = sin i ÷ sin r | n is the refractive index (no units), i is the angle of incidence in the air, r is the angle of refraction in the material — both measured from the NORMAL | None; n is a ratio. Rearranged: sin r = sin i ÷ n and sin i = n × sin r. For light entering a material from air, n is always greater than 1. | Refraction and Refractive Index |
| sin c = 1 ÷ n | c is the critical angle in degrees, n is the refractive index of the denser medium | Degrees for c; n has no units. Rearranged: n = 1 ÷ sin c. A higher refractive index gives a SMALLER critical angle. | Total Internal Reflection |
Topic 4 · Energy resources and energy transfers
| Equation | Where | Units | Lesson |
|---|---|---|---|
| efficiency = (useful energy output ÷ total energy input) × 100% | both energies in joules (J); efficiency as a percentage | J and J, giving a percentage. Rearranged: useful = efficiency × total, and total = useful ÷ efficiency. Convert a percentage to a decimal before dividing. | Efficiency, Sankey Diagrams and Insulation |
| W = F × d | W is work done in joules (J), F is the force in newtons (N), d is the distance moved in the direction of the force, in metres (m) | J, N, m. Rearranged: F = W ÷ d and d = W ÷ F. One joule is the work done when a force of one newton moves an object one metre. | Work Done |
| GPE = m × g × h | GPE is gravitational potential energy in joules (J), m is mass in kilograms (kg), g is gravitational field strength in newtons per kilogram (N/kg), h is the height raised in metres (m) | J, kg, N/kg, m. On Earth take g as 10 N/kg unless told otherwise. Rearranged: h = GPE ÷ (m × g). | Gravitational Potential and Kinetic Energy |
| KE = ½ × m × v² | KE is kinetic energy in joules (J), m is mass in kilograms (kg), v is speed in metres per second (m/s) | J, kg, m/s. SQUARE THE SPEED FIRST. Rearranged: v = √(2 × KE ÷ m). | Gravitational Potential and Kinetic Energy |
| P = W ÷ t | P is power in watts (W), W is work done or energy transferred in joules (J), t is time in SECONDS (s) | W, J, s. Rearranged: W = P × t and t = W ÷ P. One watt is one joule per second. | Power |
Topic 5 · Solids, liquids and gases
| Equation | Where | Units | Lesson |
|---|---|---|---|
| density = mass ÷ volume | density in kilograms per cubic metre (kg/m³), mass in kilograms (kg), volume in cubic metres (m³) | kg/m³, kg, m³. Rearranged: mass = density × volume and volume = mass ÷ density. 1 g/cm³ = 1000 kg/m³. | Density |
| p = F ÷ A | p is pressure in pascals (Pa), F is the force in newtons (N), A is the area in square metres (m²) | Pa, N, m². Rearranged: F = p × A and A = F ÷ p. One pascal is one newton per square metre. | Pressure, and Pressure in Liquids |
| p = h × ρ × g | p is the pressure difference in pascals (Pa), h is the height difference in metres (m), ρ is the density of the liquid in kg/m³, g is gravitational field strength in N/kg | Pa, m, kg/m³, N/kg. This gives the pressure due to the LIQUID only — add atmospheric pressure for the total. | Pressure, and Pressure in Liquids |
| Q = m × c × ΔT | Q is the energy transferred in joules (J), m is mass in kilograms (kg), c is specific heat capacity in J/kg °C, ΔT is the CHANGE in temperature in °C | J, kg, J/kg °C, °C. Rearranged: c = Q ÷ (m × ΔT) and ΔT = Q ÷ (m × c). ΔT is a change, not a temperature. | Specific Heat Capacity |
| p₁ ÷ T₁ = p₂ ÷ T₂ | p₁ and p₂ are the pressures before and after, T₁ and T₂ the temperatures IN KELVIN, at constant volume | Both pressures in the same unit; both temperatures in KELVIN. Pressure is directly proportional to kelvin temperature. | The Gas Laws |
| p₁V₁ = p₂V₂ | p₁ and V₁ are the pressure and volume before, p₂ and V₂ after, at constant temperature | Both pressures in the same unit; both volumes in the same unit. Pressure is inversely proportional to volume. | The Gas Laws |
Topic 6 · Magnetism and electromagnetism
| Equation | Where | Units | Lesson |
|---|---|---|---|
| Vp ÷ Vs = Np ÷ Ns | Vp and Vs are the primary and secondary voltages in volts (V); Np and Ns are the numbers of turns on the primary and secondary coils | V and V; turns are a pure number. Ns greater than Np gives a STEP-UP transformer; Ns less than Np gives a STEP-DOWN transformer. | Transformers |
| Vp × Ip = Vs × Is | Vp and Vs are the primary and secondary voltages in volts (V); Ip and Is are the primary and secondary currents in amperes (A) | V × A = W. This holds for a 100% efficient transformer: input power equals output power, so raising the voltage lowers the current in the same proportion. | Transformers |
Topic 7 · Radioactivity and particles
| Equation | Where | Units | Lesson |
|---|---|---|---|
| number of neutrons = A − Z | A is the mass number (protons + neutrons), Z is the atomic number (protons) | All three are pure counts with no units. In nuclide notation A is written above Z, both before the element symbol. | Atomic Structure and Isotopes |
Topic 8 · Astrophysics
| Equation | Where | Units | Lesson |
|---|---|---|---|
| weight = mass × gravitational field strength | weight in newtons (N), mass in kilograms (kg), gravitational field strength g in newtons per kilogram (N/kg) | N, kg, N/kg. On Earth g ≈ 10 N/kg, on the Moon ≈ 1.6 N/kg, on Mars ≈ 3.7 N/kg, on Jupiter ≈ 25 N/kg. | The Universe and Gravity |
| orbital speed = 2πr ÷ T | orbital speed in metres per second (m/s), r is the orbital radius in metres (m) measured from the CENTRE of the body being orbited, T is the orbital period in seconds (s) | m/s, m, s. 2πr is the circumference of the orbit — the distance travelled in one complete revolution. | Orbits |
| change in wavelength ÷ reference wavelength = velocity of galaxy ÷ speed of light | change in wavelength is the observed wavelength minus the laboratory value; reference wavelength is the laboratory value; velocity of the galaxy and the speed of light are both in metres per second (m/s) | The two wavelengths may be in any unit provided both are the same, because the ratio cancels them. Speed of light = 300 000 000 m/s. | Red-Shift |
From the equation to the mark
Each lesson linked above explains where the equation comes from, shows it worked, and then asks you to prove it, teach it and defend it — against Newton, Faraday or Joule, inside Incandio.
- Every Physics lesson — Physics on Incandio, topic by topic.
- Physics key terms — every definition to learn word for word.
- Physics required practicals — method, variables and errors for every one.
- The 4PH1 specification · Incandio Science