This is the complete AQA A-Level Physics equation toolkit, organised by topic so you can revise the whole course from one page. Remember that AQA hands you a data and formulae booklet in the exam itself, so this sheet is not about memorising symbols for their own sake – it is about learning what each equation means, which quantities it links together, and when to reach for it. In the exam, the marks go to students who recognise the situation and pick the right equation first time.
Key Constants
Acceleration due to gravity, g = 9.81 m s-2 · Speed of light, c = 3.00 × 108 m s-1 · Planck constant, h = 6.63 × 10-34 J s · Elementary charge, e = 1.60 × 10-19 C · Permittivity of free space, ε0 = 8.85 × 10-12 F m-1 · Gravitational constant, G = 6.67 × 10-11 N m2 kg-2 · Boltzmann constant, k = 1.38 × 10-23 J K-1 · Gas constant, R = 8.31 J K-1 mol-1
| Equation | What it is / When to use it |
|---|
| v = u + at | Final velocity for motion with constant acceleration. One of the SUVAT equations – use when time is involved and displacement is not. |
| s = ut + 0.5at2 | Displacement from initial velocity, acceleration and time. The workhorse SUVAT equation for projectiles and free fall. |
| v2 = u2 + 2as | Links speeds and displacement with no time involved. Ideal for braking distances and drops where only the height is known. |
| s = vt – 0.5at2 | Displacement written using the final velocity instead of the initial velocity – handy when u is the unknown. |
| s = ((u + v) / 2) × t | Displacement equals average velocity multiplied by time. Only valid for constant acceleration. |
| F = ma | Newton’s second law: resultant force equals mass multiplied by acceleration. Always use the resultant (unbalanced) force. |
| p = mv | Linear momentum. A vector, measured in kg m s-1; direction matters in collisions. |
| FΔt = Δ(mv) | Impulse of a force equals the change in momentum. Use for impacts, collisions and estimating forces from contact times. |
| W = Fs cos θ | Work done by a constant force, where θ is the angle between the force and the displacement. Only the component along the motion does work. |
| P = ΔW / Δt | Power is the rate of doing work (or transferring energy), in watts. |
| P = Fv | Power of a force moving at constant velocity – the key equation for vehicles travelling at top speed, where driving force balances drag. |
| Ek = 0.5mv2 | Kinetic energy of a moving mass. Note the squared speed: doubling v quadruples the energy. |
| ΔEp = mgΔh | Change in gravitational potential energy near the Earth’s surface, where g is treated as constant. |
| Efficiency = useful energy (or power) output / total energy (or power) input | Multiply by 100 to quote as a percentage. Use in energy-transfer and machine questions. |
| Moment = F × perpendicular distance from the pivot | Turning effect of a force, in N m. For a body in equilibrium the clockwise and anticlockwise moments about any point balance. |
| Torque of a couple = F × perpendicular distance between the two forces | A couple is two equal, opposite, parallel forces. Its torque is the same about every point. |
| Equation | What it is / When to use it |
|---|
| ρ = m / V | Density equals mass divided by volume, in kg m-3. |
| F = kx | Hooke’s law: extension x is proportional to the applied force, up to the limit of proportionality. k is the spring (force) constant in N m-1. |
| Elastic potential energy = 0.5kx2 = 0.5Fx | Energy stored in a stretched spring or wire – equal to the area under the force-extension graph. |
| Stress = F / A | Tensile stress, the force per unit cross-sectional area, in Pa (N m-2). Compare stresses, not forces, when specimens differ in thickness. |
| Strain = ΔL / L | Tensile strain: extension divided by the original length. It is a ratio, so it has no unit. |
| Young modulus, E = stress / strain = FL / (AΔL) | A measure of the stiffness of a material, independent of the specimen’s size. Larger E means a stiffer material. |
| Equation | What it is / When to use it |
|---|
| v = fλ | Wave speed equals frequency multiplied by wavelength. Applies to every type of wave. |
| f = 1 / T | Frequency is the reciprocal of the period (time for one complete oscillation or wave). |
| d sin θ = nλ | Diffraction grating equation: d is the slit spacing (1 / lines per metre), n is the order of the maximum, and θ is the angle to that maximum. Use to measure wavelengths precisely. |
| n = c / v | Refractive index of a material: speed of light in a vacuum divided by the speed of light in the material. |
| n1 sin θ1 = n2 sin θ2 | Snell’s law at a boundary between two media. Angles are measured from the normal; light bends towards the normal entering a denser medium. |
| sin θc = 1 / n | Critical angle for total internal reflection when light travels from a material of refractive index n into air. Above θc the light reflects inside the material. |
| w = λD / s | Double-slit fringe spacing w, where D is the distance from slits to screen and s is the slit separation. Rearranges to λ = ws / D for measuring the wavelength of light. |
| Intensity ∝ (amplitude)2 | For any wave, intensity is proportional to the square of the amplitude. Doubling the amplitude gives four times the intensity – also explains polarisation and superposition questions. |
| Equation | What it is / When to use it |
|---|
| V = W / Q | Potential difference is the work done (energy transferred) per unit charge between two points. |
| Q = It | Charge passed equals current multiplied by time. The starting point for most current electricity questions. |
| V = IR | Ohm’s law form: pd across a component equals current through it multiplied by its resistance. Only ohmic conductors have constant R. |
| R = ρL / A | Resistance of a uniform conductor: proportional to length L, inversely proportional to cross-sectional area A. ρ is the resistivity of the material in Ω m. |
| Resistors in series: R = R1 + R2 + … · In parallel: 1/R = 1/R1 + 1/R2 + … | Combine series and parallel sections one step at a time. Parallel combinations always come out smaller than the smallest resistor. |
| P = VI | Electrical power transferred by a component: pd across it multiplied by the current through it. |
| P = I2R = V2 / R | Power written using resistance – pick the form containing the two quantities you know. I2R is the form for heating losses in cables. |
| ε = I(R + r) | EMF of a cell or supply driving current through an external resistance R and its own internal resistance r. Terminal pd is V = ε – Ir, so pd drops when a large current is drawn. |
| Vout = Vin × R2 / (R1 + R2) | Potential divider: the output pd is the fraction R2 / (R1 + R2) of the input. The basis of sensor circuits with thermistors and LDRs. |
| I = nAvq | Current in terms of drift velocity v of the charge carriers, where n is the number of carriers per unit volume, A the cross-sectional area and q the charge on each carrier. Explains why drift speeds are tiny even though lamps light instantly. |
| Equation | What it is / When to use it |
|---|
| ω = 2π / T = 2πf | Angular speed in rad s-1: the angle swept out per second. Convert revolutions per minute into rad s-1 before using it. |
| v = ωr | Linear (tangential) speed of an object moving in a circle of radius r. |
| a = v2 / r = ω2r | Centripetal acceleration, directed towards the centre of the circle even when the speed is constant. |
| F = mv2 / r = mω2r | Resultant force needed to keep a mass moving in a circle. It is not an extra force – it must be provided by tension, friction, gravity or another real force. |
| a = -ω2x | The defining equation of simple harmonic motion: acceleration is proportional to displacement from equilibrium and always directed back towards it (the minus sign). |
| x = A cos(ωt) | Displacement in SHM when timing starts at maximum displacement (amplitude A). Use sin instead if timing starts at the equilibrium position. |
| v = ±ω√(A2 – x2) | Speed at any displacement x in SHM. Speed is greatest at the centre and zero at the extremes. |
| vmax = ωA and amax = ω2A | Maximum speed (at equilibrium) and maximum acceleration (at the extremes) of an oscillator. |
| T = 2π√(l / g) | Period of a simple pendulum of length l. Valid for small-angle oscillations; the period does not depend on the mass or the amplitude. |
| T = 2π√(m / k) | Period of a mass on a spring with spring constant k. Heavier masses and weaker springs oscillate more slowly. |
| Total energy = 0.5mω2A2 | Total energy in SHM is constant (when undamped) and proportional to the amplitude squared. |
| Ek = 0.5mω2(A2 – x2) and Ep = 0.5mω2x2 | Kinetic and potential energy at displacement x. Energy continually swaps between the two, with Ek maximum at the centre and Ep maximum at the extremes. |
| Equation | What it is / When to use it |
|---|
| F = Gm1m2 / r2 | Newton’s law of gravitation: the attractive force between two point masses. r is the separation of their centres. |
| g = GM / r2 | Gravitational field strength at a distance r from a planet of mass M. Also equals the acceleration of a mass in free fall at that point. |
| V = -GM / r | Gravitational potential. It is negative because it is defined as zero at infinity and work must be done to move a mass out to infinity against gravity. |
| T2 ∝ r3 | Kepler’s third law: for planets or satellites orbiting the same body, the square of the orbital period is proportional to the cube of the orbital radius. |
| v = √(GM / r) | Orbital speed for a circular orbit, found by setting the gravitational force equal to the centripetal force. Lower orbits are faster. |
| Escape velocity = √(2GM / r) | Minimum launch speed needed to escape a planet’s gravity completely, from equating kinetic energy to the change in potential energy to infinity. |
| F = Q1Q2 / (4πε0r2) | Coulomb’s law: the force between two point charges. Positive (repulsive) for like charges, negative (attractive) for opposite charges. |
| E = Q / (4πε0r2) | Electric field strength at distance r from a point charge Q. Direction is away from a positive charge, towards a negative one. |
| V = Q / (4πε0r) | Electric potential at distance r from a point charge. Unlike gravitational potential it is positive for a positive charge, and it is a scalar, so potentials from several charges simply add. |
| E = V / d | Field strength between parallel plates (a uniform field): pd divided by plate separation. Also gives the force per unit charge anywhere between the plates. |
| ΔW = QΔV | Work done moving a charge Q through a potential difference ΔV – for example, the energy gained by an electron accelerated through a pd (1 eV = 1.60 × 10-19 J). |
| C = Q / V | Capacitance equals the charge stored on one plate per unit pd across the capacitor, measured in farads. |
| E = 0.5QV = 0.5CV2 = Q2 / 2C | Energy stored by a capacitor – equal to the area under the charge-pd graph. Use whichever form matches the quantities given. |
| Capacitors in series: 1/C = 1/C1 + 1/C2 + … | Series capacitors combine like parallel resistors; every capacitor in the chain carries the same charge. |
| Capacitors in parallel: C = C1 + C2 + … | Parallel capacitors combine like series resistors; every capacitor has the same pd across it. |
| Time constant = RC | The time for the charge, pd or current of a discharging capacitor to fall to 1/e (about 37%) of its initial value. After about 5RC the capacitor is effectively discharged. |
| Q = Q0e-t/RC | Exponential decay of charge on a capacitor discharging through a resistor. Current and pd follow the same pattern: I = I0e-t/RC and V = V0e-t/RC. |
| Equation | What it is / When to use it |
|---|
| Q = mcΔθ | Energy needed to change the temperature of a mass m, where c is the specific heat capacity and Δθ the temperature change. The starting point for heating and cooling calculations. |
| Q = mL | Energy for a change of state at constant temperature, where L is the specific latent heat (of fusion or of vaporisation – check which one the question means). |
| pV = nRT | Ideal gas equation using n, the number of moles, and temperature in kelvin. The single equation that covers almost every gas calculation. |
| pV = NkT | Ideal gas equation using N, the number of molecules, and the Boltzmann constant k = R / NA. Use this form for molecular-level questions. |
| p = (1/3)ρ<c2> | Kinetic theory result: pressure from molecular collisions, where <c2> is the mean square speed of the molecules and ρ the gas density. |
| Average molecular kinetic energy = 1.5kT | Mean translational kinetic energy of one molecule is (3/2)kT – so the absolute temperature is a direct measure of average molecular energy. Double the kelvin temperature and you double the mean energy. |
| Boyle’s law: pV = constant | For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. |
| Charles’s law: V / T = constant | For a fixed mass of gas at constant pressure, volume is proportional to the absolute (kelvin) temperature. |
| Pressure law: p / T = constant | For a fixed mass of gas at constant volume, pressure is proportional to the absolute (kelvin) temperature. Never use Celsius in any of the gas laws. |
| Equation | What it is / When to use it |
|---|
| F = BIl sin θ | Force on a current-carrying conductor in a magnetic field (the motor effect). Maximum when the conductor is perpendicular to the field; θ is the angle between conductor and field. |
| F = BQv sin θ | Force on a single moving charge in a magnetic field. The force is always perpendicular to both the velocity and the field, so it changes direction but never speed. |
| Φ = BA cos θ | Magnetic flux through an area A, where θ is the angle between the field and the normal to the area. Flux is maximum when the field passes straight through the area. |
| Flux linkage = NΦ | Total flux linked by a coil of N turns – the quantity that matters for induction is the rate of change of flux linkage. |
| ε = -NΔΦ / Δt | Faraday’s law: the induced EMF equals the rate of change of flux linkage. The minus sign is Lenz’s law – the induced effect opposes the change producing it. |
| Vs / Vp = Ns / Np | Transformer equation for an ideal transformer: the pd ratio equals the turns ratio. Step-up transformers have more secondary turns; remember current steps the opposite way so power is conserved. |
| r = mv / (BQ) | Radius of the circular path of a charge moving perpendicular to a uniform magnetic field, found from BQv = mv2 / r. Used in mass spectrometers and particle detectors. |
| Motor effect → Fleming’s left-hand rule; Generator effect → Fleming’s right-hand rule | Hand rules for directions: left hand when a current experiences a force (motors), right hand when motion induces an EMF (generators). First finger = field, second finger = current, thumb = motion/force. |
| Equation | What it is / When to use it |
|---|
| E = hf | Energy of a single photon: Planck constant multiplied by frequency. Light energy comes in these packets (quanta). |
| E = hc / λ | Photon energy from wavelength – often the quickest route when the question gives λ in nanometres. Shorter wavelength means a more energetic photon. |
| hf = Φ + Ek(max) | Einstein’s photoelectric equation: photon energy equals the work function Φ (energy needed to free the electron) plus the maximum kinetic energy of the emitted photoelectron. Below the threshold frequency f0 = Φ / h, no electrons are emitted however bright the light. |
| λ = h / (mv) = h / p | de Broglie wavelength of a moving particle. Diffraction effects appear when this wavelength is similar to the size of the gap or structure the particle meets – the basis of electron diffraction. |
| ΔE = hf | Energy of the photon emitted or absorbed when an electron jumps between energy levels: the photon carries exactly the difference between the two levels. |
| N = N0e-λt | Radioactive decay law: the number of undecayed nuclei falls exponentially. λ here is the decay constant (probability of decay per unit time), not a wavelength. |
| A = λN | Activity (decays per second, in becquerel) equals the decay constant multiplied by the number of undecayed nuclei. Activity follows the same exponential decay: A = A0e-λt. |
| t1/2 = ln 2 / λ | Half-life: the time for the number of nuclei (or the activity) to halve. A larger decay constant means a shorter half-life. |
| E = mc2 | Mass-energy equivalence. In nuclear reactions the binding energy released equals the mass defect (loss of mass) multiplied by c2. |
| Binding energy per nucleon = total binding energy / number of nucleons | The best measure of how stable a nucleus is. The curve peaks near iron-56, which is why energy is released by fission of very heavy nuclei and by fusion of very light ones – both move nuclei towards the peak. |
| R = R0A1/3 | Nuclear radius for mass number A, with R0 ≈ 1.4 × 10-15 m. Because R grows only with the cube root of A, nuclear density is roughly the same for all nuclei. |
This page is an original revision aid written for QuaidianPoint students. It is not affiliated with, or endorsed by, AQA.
