IB Physics Formula Booklet Guide: Equations by Theme

This IB physics formula booklet guide explains the equations of the IB Diploma physics course theme by theme, using the inverse square law for brightness, $b = \frac{L}{4\pi d^2}$ , as an example of how one short line links energy, waves and astrophysics. The IB supplies its own physics data booklet for the exams; this page is a separate study aid that says what each equation means, when it applies and which unit each symbol takes.

The current course is organised into five themes: space, time and motion; the particulate nature of matter; wave behaviour; fields; and nuclear and quantum physics. Some subtopics are for Higher Level only, so check your syllabus to see which apply to you. IB symbols are close to the ones Indian students use: s for displacement, u and v for initial and final velocity. Other course guides are on the formula sheets hub.

Quick facts

What this is
A study guide, not the IB data booklet
Themes
A space, time, motion; B matter; C waves; D fields; E nuclear and quantum
Symbols
s, u, v, a, t for motion
First law
Q = ΔU + W, with W done by the gas
Levels
SL and HL, with extra HL subtopics
Example equation
$b = \frac{L}{4\pi d^2}$

Theme A: space, time and motion

Kinematics, forces, energy and momentum
Equation	In words	Unit	Topic page
$s = \frac{(u + v)t}{2}$	displacement is average velocity times time	m	Displacement topic
$v = u + at,\ s = ut + \frac{1}{2}at^2$	uniform acceleration	m/s, m	Motion topic
$F = ma = \frac{\Delta p}{\Delta t}$	resultant force and momentum change	N	Force topic
$E_k = \frac{p^2}{2m}$	kinetic energy written with momentum	J	Kinetic energy topic
$\Delta E_p = mg\,\Delta h$	change in gravitational potential energy	J	Potential energy topic
$P = Fv$	power delivered by a force at speed v	W	Work and energy topic
$\tau = Fr\sin\theta,\ L = I\omega$	torque and angular momentum (HL)	N m, kg m²/s	Torque topic

The relativity subtopic uses $\gamma = (1 - v^2/c^2)^{-1/2}$ for time dilation and length contraction; see the relativity formula page.

Theme B: the particulate nature of matter

Thermal physics, gases and circuits
Equation	In words	Unit	Topic page
$Q = mc\,\Delta T,\ Q = mL$	warming a sample, then melting or boiling it	J	Heat topic
$L = \sigma AT^4$	luminosity of a black body (Stefan Boltzmann)	W	Heat transfer topic
$pV = nRT = Nk_BT$	ideal gas equation	J	Thermodynamics topic
$\bar{E}_k = 1.5\,k_BT$	average translational energy per particle	J	Energy topic
$Q = \Delta U + W$	energy balance for a gas that does work W (HL)	J	First law topic
$V = IR,\ P = VI$	circuit basics	V, W	Ohm's law topic
$\varepsilon = I(R + r)$	cell with internal resistance	V	EMF topic

Example 1: brightness of a star

A star of luminosity 3.8 × 10²⁶ W is 1.5 × 10¹¹ m away. Find its apparent brightness.

$b = \frac{3.8 \times 10^{26}}{4\pi(1.5 \times 10^{11})^2} = \frac{3.8 \times 10^{26}}{2.83 \times 10^{23}} = 1.3 \times 10^{3}\ \text{W/m}^2$ .

Answer: about 1.3 × 10³ W/m², roughly the intensity of sunlight above the atmosphere of our planet.

Theme C: wave behaviour

Oscillations and waves
Equation	In words	Unit	Topic page
$T = \frac{1}{f}$	period and frequency	s	Period topic
$a = -\omega^2 x$	defining condition for simple harmonic motion	m/s²	Amplitude topic
$v = f\lambda$	wave equation	m/s	Wave velocity topic
$n_1\sin\theta_1 = n_2\sin\theta_2$	bending of light at a boundary	no unit	Refraction topic
$s = \frac{\lambda D}{d}$	fringe spacing for two slits	m	Wavelength topic
$\frac{\Delta f}{f} \approx \frac{v}{c}$	Doppler shift for light at low speed	no unit	Frequency topic

IB writes s for fringe spacing. Do not confuse it with displacement in theme A.

Theme D: fields

Gravitational, electric and magnetic fields
Equation	In words	Unit	Topic page
$F = G\frac{m_1m_2}{r^2},\ g = \frac{GM}{r^2}$	gravitational force and field strength	N, N/kg	Gravitation topic
$v = \sqrt{\frac{GM}{r}}$	how fast a satellite circles at radius r	m/s	Orbital velocity topic
$F = k\frac{q_1q_2}{r^2},\ E = \frac{F}{q}$	electric force and field	N, N/C	Electric field topic
$F = qvB\sin\theta,\ F = BIL\sin\theta$	magnetic force on a charge and on a wire	N	Magnetic force topic
$\Phi = BA\cos\theta,\ \varepsilon = -N\frac{\Delta\Phi}{\Delta t}$	flux and induced emf (HL)	Wb, V	Magnetic flux topic

Example 2: a satellite in low orbit

A satellite circles 600 km above the ground. Find its orbital speed and period. Take M = 5.97 × 10²⁴ kg for the Earth, whose radius is 6.37 × 10⁶ m.

Orbit radius: r = 6.37 × 10⁶ + 6.0 × 10⁵ = 6.97 × 10⁶ m.

$v = \sqrt{\frac{(6.674 \times 10^{-11})(5.97 \times 10^{24})}{6.97 \times 10^{6}}} = \sqrt{5.72 \times 10^{7}} = 7.56 \times 10^{3}\ \text{m/s}$ .

$T = \frac{2\pi r}{v} = \frac{2\pi(6.97 \times 10^6)}{7.56 \times 10^3} = 5.79 \times 10^{3}\ \text{s}$ , about 97 minutes.

Theme E: nuclear and quantum physics

Atoms, nuclei and photons
Equation	In words	Unit	Topic page
$E = hf$	photon energy	J	Photons topic
$E_{max} = hf - \Phi$	photoelectric effect (HL)	J	Work function topic
$\lambda = \frac{h}{p}$	de Broglie wavelength (HL)	m	Matter waves topic
$E = mc^2$	mass defect and binding energy	J	Mass energy topic
$N = N_0e^{-\lambda t},\ T_{1/2} = \frac{\ln 2}{\lambda}$	radioactive decay (decay law at HL)	s	Nuclear physics topic

The stars subtopic ties back to theme B: luminosity from $L = \sigma AT^4$ and peak wavelength from Wien's law, $\lambda_{max}T = 2.9 \times 10^{-3}\ \text{m K}$ .

Using the IB physics formula booklet in practice

Know where each line lives. In timed papers you lose minutes searching. Practise with the official booklet from the start of the course.
Learn what is not listed. Definitions, such as what a field strength or a half life means, and unit conversions are rarely given.
Watch the symbols. s, Φ and λ each have more than one meaning in different themes.
Show working in the internal assessment. Uncertainty propagation follows the same rules as error analysis in other courses.

To compare with other courses, see the AP Physics 1 formula sheet or the Class 12 physics sheet.

Frequently asked questions

Is this the official IB physics data booklet?

No. It is a study guide written for this site. The IB provides its own data booklet for exams, so download the current version and practise with it.

What is in the physics formula booklet IB students use?

In general it contains fundamental constants, unit prefixes and the equations of each theme, grouped by topic. It does not explain the equations or list every definition.

Do SL and HL students use the same formula booklet?

Usually one booklet covers both, with HL only equations marked or grouped separately. Check the version for your exam session.

How is IB physics different from AP physics?

IB is a two year course organised into themes with SL and HL options, while AP splits physics into separate courses. Much of the core physics and many equations are the same.