ExaminerPrep · Formula handout · IB Physics SL & HL
Equations Not in the Data Booklet
For IB Diploma Physics SL and HL (syllabus first assessed 2025)
examinerprep.comEvery equation below is one you must know or be able to derive yourself, because it is not printed in the data booklet you get in Papers 1 and 2.
How to use this sheet
Learn these until you can write them from memory, and know where each one comes from: most are two lines of algebra away from a booklet equation, and a derivation is worth knowing in case the question asks you to show it.
- SL+HL = everyone needs it. HL = Additional Higher Level only.
- Derived = not printed, but follows from a booklet equation. Practise the derivation once.
- Exam tip and Common error boxes flag where marks are usually gained or lost.
- Equations are magnitudes unless a sign is shown. Use SI units throughout unless told otherwise.
- The data booklet can be revised between sessions. Check this sheet against the current version before your exams.
Tools: uncertainties, maths and graphs
Uncertainties SL+HL
The booklet gives the propagation rules (sums, products/quotients, powers). These are not given:
Fractional and percentage uncertainty
Uncertainty from repeated readings (half the range)
Multiplying by an exact constant
Uncertainty in a gradient (from the steepest and shallowest lines through all error bars)
Percentage difference from an accepted value
Exam tip
Quote the absolute uncertainty to 1 significant figure (2 is acceptable if the first digit is 1), then round the value to the same decimal place.
Maths not in the booklet SL+HL
The booklet gives the volume of a sphere but not its surface area. You need it for stars (E.5) and for radiation from spheres (B.1).
Small-angle approximation (θ in radians, roughly θ < 0.1 rad; behind s = λD/d and θ = λ/b)
Arc length and angle
Linearising for graphs
Graph relationships SL+HL
| Graph | Gradient gives | Area under it gives |
|---|---|---|
| displacement–time | velocity | — |
| velocity–time | acceleration | displacement |
| acceleration–time | — | change in velocity |
| force–time | rate of change of momentum | impulse (Δp) |
| force–extension | spring constant k | work done / elastic energy |
| pressure–volume | — | work done by or on the gas |
| power–time | — | energy transferred |
| current–time | — | charge |
Common error
Reading the gradient of a curve from one point. Draw a tangent at the point asked for and use a large triangle.
A. Space, time and motion
A.1 Kinematics SL+HL
Definitions of average velocity and acceleration (the booklet gives only the four suvat equations)
Projectile components (launch speed u at angle θ above the horizontal)
Derived Level ground, no air resistance: time of flight, maximum height, range
Exam tip
These three only hold for launch and landing at the same height. In any other case, apply suvat separately to the horizontal and vertical motion.
A.2 Forces and momentum SL+HL
Equilibrium (Newton’s first law)
Conservation of momentum (isolated system)
Elastic collision: kinetic energy is also conserved. Explosion from rest: total momentum after is zero.
Weight components on a slope (angle θ to the horizontal)
Derived Centripetal force (from F = ma and a = v2/r)
Common error
Drawing a separate “centripetal force” on a free-body diagram. It is the resultant of the real forces (tension, gravity, friction, normal force).
Normal force in a lift (upward acceleration a positive)
Derived Terminal velocity of a sphere (weight = drag + buoyancy, using Stokes’ law)
A.3 Work, energy and power SL+HL
Conservation of energy (no dissipative forces)
Work–energy theorem
Power as rate of energy transfer
Exam tip
With friction, energy lost = friction force × distance along the path, not the vertical height.
A.4 Rigid body mechanics HL
Rolling without slipping
Total kinetic energy of a rolling object
Derived Rolling down a height h from rest
Rotational work and power
Rotational equilibrium (both conditions together)
Conservation of angular momentum (no external torque) and angular momentum of a point mass
Common error
Assuming rotational kinetic energy is conserved when I changes. Angular momentum is conserved; kinetic energy usually is not.
A.5 Galilean and special relativity HL
Inverse Lorentz transformations (from S′ back to S)
Interval forms (use these for two events)
Derived Relativity of simultaneity (events simultaneous in S, Δt = 0)
Exam tip
Proper time Δt0 is measured by the observer who sees both events at the same place; proper length L0 is measured in the frame where the object is at rest. Identify them before using the booklet equations.
B. The particulate nature of matter
B.1 Thermal energy transfers SL+HL
Heating with a known power (e.g. an electric heater, P = IV)
Mixing: energy lost by the hot body = energy gained by the cold body (no losses)
Derived Power radiated per unit area by a black body
Exam tip
A temperature change is the same in K and °C, but σT4 and Wien’s law need absolute temperature in K.
B.2 Greenhouse effect SL+HL
Intensity
Mean incoming solar intensity on the whole Earth (disc area πR2 intercepts, sphere area 4πR2 shares)
Derived Energy balance for an equilibrium planet (albedo α, emissivity e)
Common error
Forgetting the factor 4, or using α instead of (1 − α) for the absorbed fraction.
B.3 Gas laws SL+HL
Amount of substance from mass (M = molar mass in kg mol−1)
Derived Single-change gas laws (fixed amount of ideal gas)
Link between the constants
Derived rms speed of gas molecules (from p = ⅓ρv2 and pV = nRT)
Common error
Using grams per mole for M. Convert to kg mol−1 first.
B.4 Thermodynamics HL
Sign convention with Q = ΔU + W: W is work done by the gas (positive on expansion).
Special processes
| Process | Condition | First law becomes |
|---|---|---|
| Isovolumetric (isochoric) | W = 0 | Q = ΔU |
| Isobaric | p constant | W = pΔV |
| Isothermal | ΔU = 0 | Q = W, and pV = constant |
| Adiabatic | Q = 0 | W = −ΔU |
| Complete cycle | ΔU = 0 | Qnet = Wnet = enclosed area on p–V |
Derived Adiabatic change for a monatomic ideal gas, in terms of T
Heat engines: energy in, work out and energy rejected
Second law (isolated system)
Exam tip
No real engine can beat the Carnot efficiency between the same two temperatures. Use it as a check on your answer.
B.5 Current and circuits SL+HL
Kirchhoff’s laws
Potential divider
Derived Terminal potential difference (lost volts = Ir)
Charge and energy
Exam tip
Treat an ideal ammeter as zero resistance and an ideal voltmeter as infinite resistance unless the question says otherwise.
C. Wave behaviour
C.1 Simple harmonic motion SL+HL
Angular frequency
Derived ω for the two standard oscillators
Maximum speed and acceleration
Phase difference from a time difference
HL Derived Kinetic energy at displacement x (the booklet gives ET and Ep only)
Exam tip
The pendulum period is independent of mass and (for small angles) of amplitude. The spring period is independent of g.
C.2 Wave model SL+HL
Phase difference between two points on a wave
Intensity and amplitude
Inverse-square law for a point source
Common error
Thinking that doubling the amplitude doubles the intensity. It quadruples it.
C.3 Wave phenomena SL+HL
Absolute refractive index
Critical angle (light going from medium n1 into a less dense medium n2)
HL Grating spacing and highest order visible (N lines per metre)
HL Single slit: width of the central maximum (screen at distance D)
Common error
Forgetting to convert lines per mm into lines per metre before finding d.
C.4 Standing waves and resonance SL+HL
The booklet gives no equations for this topic.
String fixed at both ends, or pipe open at both ends (n = 1, 2, 3, …)
Pipe closed at one end (odd harmonics only, n = 1, 2, 3, …)
Spacings
Exam tip
Sketch the pattern first (nodes at fixed or closed ends, antinodes at open ends) and read λ off the sketch. This avoids errors in numbering harmonics.
C.5 Doppler effect
SL+HL Redshift for light (v ≪ c)
SL+HL Derived Reflection from a moving object (radar, ultrasound; v ≪ wave speed c)
HL Source and observer both moving (upper signs when they approach each other)
Common error
Getting the sign wrong. Check your answer: approaching means a higher received frequency.
D. Fields
D.1 Gravitational fields
SL+HL Orbital radius from the planet’s centre
SL+HL Derived Circular orbit (gravity provides the centripetal force)
SL+HL Derived Kepler’s third law
HL Derived Energies of a satellite in circular orbit
HL Derived Energy needed to move to a higher circular orbit
Common error
Using the height above the surface as r. Always measure r from the centre of the planet.
Exam tip
A geostationary satellite has T = 24 h and orbits above the equator.
D.2 Electric and magnetic fields
SL+HL Derived Field of a point charge (from F = kq1q2/r2 and E = F/q)
SL+HL Quantisation of charge and the electronvolt
SL+HL Derived Magnetic field of a long straight wire (from the force per unit length between two wires)
Exam tip
Field lines meet equipotentials at right angles, and no work is done moving a charge along an equipotential.
D.3 Motion in electromagnetic fields SL+HL
Force on a charge in an electric field
Acceleration through a potential difference V (from rest)
Derived Circular motion in a uniform magnetic field (qvB = mv2/r)
Derived Velocity selector (crossed fields, undeflected particle: qE = qvB)
Exam tip
The magnetic force is always perpendicular to the velocity, so it does no work and the speed stays constant. Between parallel plates, treat the motion like a projectile: constant velocity along the plates, constant acceleration across them.
D.4 Induction HL
Flux linkage and induced current
Coil of N turns, area A, rotating at ω in a uniform field B
Exam tip
Doubling the rotation speed doubles both the peak emf and the frequency of the output.
Common error
Dropping the minus sign without explanation. State Lenz’s law: the induced current opposes the change in flux that causes it.
E. Nuclear and quantum physics
E.1 Structure of the atom
SL+HL Photon energy from wavelength (hc is given as a constant)
SL+HL Photon emitted or absorbed in a transition
SL+HL Derived Distance of closest approach (head-on alpha scattering, all Ek becomes Ep)
HL Derived Hydrogen transition wavelength (from E = −13.6/n2 eV)
HL Derived Nuclear density is about the same for all nuclei (from R = R0A1/3)
Common error
Leaving ΔE in eV when using it with h in J s. Convert, or use hc = 1.24 × 10−6 eV m.
E.2 Quantum physics HL
Threshold frequency and stopping potential
Momentum of a photon
Derived de Broglie wavelength from kinetic energy (non-relativistic; second form for a charge accelerated through V)
Exam tip
Intensity changes the number of photoelectrons, not their maximum kinetic energy. Frequency changes Emax.
E.3 Radioactive decay
SL+HL Mass defect and binding energy
SL+HL Binding energy per nucleon
SL+HL Unit shortcut (mass in u, energy in MeV)
SL+HL Remaining fraction after n half-lives (n = t / T½)
In every decay or reaction equation, nucleon number A and charge (proton) number Z are each conserved.
HL Mass and count rate decay the same way
HL Linear form for graphs (gradient = −λ)
Common error
Using atomic mass instead of nuclear mass without accounting for the electrons. Check which one the question gives.
E.4 Fission SL+HL
Energy released in a reaction
Power output of a reactor or power station
E.5 Fusion and stars SL+HL
Derived Comparing two stars (from L = σAT4 with A = 4πR2)
Derived Radius of a star
Derived Distance from apparent brightness
Exam tip
In ratio questions the constants cancel. Write the ratio first and substitute last.
Prepared by Evan Kotronis · ExaminerPrep · examinerprep.com
Want help putting this into practice?
Book a free consultation: we look at where your child stands and what would help most.