Physics Data Booklet - IB Formula Reference | RevisionDojo

IB Physics Data Booklet

RevisionDojo's IB Physics SL and HL Data Booklet is designed to give IB students a clear, exam-ready reference to every essential physics formula, constant, and equation you’ll need. Unlike generic physics resources, our booklet is directly aligned with the official IB Physics syllabus, ensuring that you practice with the exact data and formulas you'll have access to during your exams.

Whether you're revising mechanics, thermal physics, waves, fields, or quantum theory, our clean layout and topic-by-topic structure make it easy to locate the right information under exam pressure. For students aiming to maximize efficiency, this resource is the perfect companion to our IB Physics notes, question bank, and past papers, giving you a complete toolkit for IB Physics success.

Data Booklet

Mathematical equations

Uncertainties

If: $y=a \pm b$	then: $\Delta y=\Delta a+\Delta b$
If: $y=\frac{a b}{c}$	then: $\frac{\Delta y}{y}=\frac{\Delta a}{a}+\frac{\Delta b}{b}+\frac{\Delta c}{c}$
If: $y=a^{n}$	then: $\frac{\Delta y}{y}=\left\\|n \frac{\Delta a}{a}\right\\|$

Fundamental constants

Quantity	Symbol	Approximate value
Acceleration of free fall	$g$	$9.8 \mathrm{~ms}^{-2}$ (Earth's surface)
Gravitational constant	G	$6.67 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$
Avogadro constant	$N_{\text {A }}$	$6.02 \times 10^{23} \mathrm{~mol}^{-1}$
Gas constant	$R$	8.31 $\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$
Boltzmann constant	$k_{\mathrm{B}}$	$1.38 \times 10^{-23} \mathrm{JK}^{-1}$
Stefan-Boltzmann constant	$\sigma$	$5.67 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}$
Coulomb constant	k	$8.99 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}$
Permittivity of free space	$\varepsilon_{0}$	$8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}$
Permeability of free space	$\mu_{0}$	$4 \pi \times 10^{-7} \mathrm{TmA}^{-1}$
Speed of light in vacuum	c	$3.00 \times 10^{8} \mathrm{~ms}^{-1}$
Planck constant	$h$	$6.63 \times 10^{-34} \mathrm{Js}$
Elementary charge	e	$1.60 \times 10^{-19} \mathrm{C}$
Electron rest mass	$m_{\mathrm{e}}$	$9.110 \times 10^{-31} \mathrm{~kg}=0.000549 \mathrm{u}=0.511 \mathrm{MeV} \mathrm{c}^{-2}$
Proton rest mass	$m_{p}$	$1.673 \times 10^{-27} \mathrm{~kg}=1.007276 \mathrm{u}=938 \mathrm{MeV} \mathrm{c}^{-2}$
Neutron rest mass	$m_{n}$	$1.675 \times 10^{-27} \mathrm{~kg}=1.008665 \mathrm{u}=940 \mathrm{MeV} \mathrm{c}^{-2}$
(Unified) atomic mass unit	u	$1.661 \times 10^{-27} \mathrm{~kg}=931.5 \mathrm{MeVc}^{-2}$
Solar constant	$S$	$1.36 \times 10^{3} \mathrm{~W} \mathrm{~m}^{-2}$
Fermi radius	$R_{0}$	$1.20 \times 10^{-15} \mathrm{~m}$

Metric (SI) multipliers

Prefix	Abbreviation	Value
$\text{peta}$	$P$	$10^{15}$
$\text{tera}$	$T$	$10^{12}$
$\text{giga}$	$G$	$10^{9}$
$\text{mega}$	$M$	$10^{6}$
$\text{kilo}$	$k$	$10^{3}$
$\text{hecto}$	$h$	$10^{2}$
$\text{deca}$	$da$	$10^{1}$
$\text{deci}$	$d$	$10^{-1}$
$\text{centi}$	$C$	$10^{-2}$
$\text{milli}$	$m$	$10^{-3}$
$\text{micro}$	$μ$	$10^{-6}$
$\text{nano}$	$n$	$10^{-9}$
$\text{pico}$	$p$	$10^{-12}$
$\text{femto}$	$f$	$10^{-15}$

Unit conversions

1 radian $(\mathrm{rad}) \equiv \frac{180^{\circ}}{\pi}$
Temperature $(\mathrm{K})=$ temperature $\left({ }^{\circ} \mathrm{C}\right)+273$
1 light year $(\mathrm{ly})=9.46 \times 10^{15} \mathrm{~m}$
1 parsec $(\mathrm{pc})=3.26 \mathrm{ly}$
1 astronomical unit $(\mathrm{AU})=1.50 \times 10^{11} \mathrm{~m}$
1 kilowatt-hour $(\mathrm{kWh})=3.60 \times 10^{6} \mathrm{~J}$
$h c=1.99 \times 10^{-25} \mathrm{Jm}=1.24 \times 10^{-6} \mathrm{eVm}$

Electrical circuit symbols

Cell

Voltmeter

Variable resistor

Potentiometer

Heating element

Battery

Ammeter

Light-dependent resistor (LDR)

Lamp

Motor

Switch

Resistor

Thermistor

Light emitting diode (LED)

Earth (ground)

Electromagnetic spectrum

A. Space, time and motion


Standard level and higher level
A. 1 Kinematics	$\begin{aligned} & s=\frac{u+v}{2} t \\ & v=u+a t \\ & s=u t+\frac{1}{2} a t^{2} \\ & v^{2}=u^{2}+2 a s \end{aligned}$
A. 2 Forces and momentum	$\begin{aligned} & F_{\mathrm{f}} \leq \mu_{\mathrm{s}} F_{\mathrm{N}} \\ & F_{\mathrm{f}}=\mu_{\mathrm{d}} F_{\mathrm{N}} \\ & F_{\mathrm{H}}=-k x \\ & F_{\mathrm{d}}=6 \pi \eta r v \\ & F_{\mathrm{b}}=\rho V g \\ & F_{\mathrm{g}}=m g \\ & p=m v \\ & J=F \Delta t \\ & F=m a=\frac{\Delta p}{\Delta t} \\ & a=\frac{v^{2}}{r}=\omega^{2} r=\frac{4 \pi^{2} r}{T^{2}} \\ & v=\frac{2 \pi r}{T}=\omega r \end{aligned}$
A. 3 Work, energy and power	$\begin{aligned} & W=F s \cos \theta \\ & E_{\mathrm{k}}=\frac{1}{2} m v^{2}=\frac{p^{2}}{2 m} \\ & \Delta E_{\mathrm{p}}=m g \Delta h \\ & E_{\mathrm{H}}=\frac{1}{2} k \Delta x^{2} \\ & P=\frac{\Delta W}{\Delta t}=F V \\ & \eta=\frac{\text { useful work out }}{\text { total work in }}=\frac{\text { useful power out }}{\text { total power in }} \end{aligned}$
Additional higher level
A. 4 Rigid body mechanics	$\begin{aligned} & \tau=F r \sin \theta \\ & \Delta \theta=\frac{\omega_{\mathrm{f}}+\omega_{\mathrm{i}}}{2} t \\ & \omega_{\mathrm{f}}=\omega_{\mathrm{i}}+\alpha t \\ & \Delta \theta=\omega_{\mathrm{i}} t+\frac{1}{2} \alpha t^{2} \\ & \omega_{\mathrm{f}}^{2}=\omega_{\mathrm{i}}^{2}+2 \alpha \Delta \theta \\ & I=\Sigma m r^{2} \\ & \tau=I \alpha \\ & L=I \omega \\ & \Delta L=\tau \Delta t \\ & \Delta L=\Delta(I \omega) \\ & E_{k}=\frac{1}{2} I \omega^{2}=\frac{L^{2}}{2 I} \end{aligned}$
A. 5 Galilean and special relativity	$\begin{aligned} & x^{\prime}=x-v t \\ & t^{\prime}=t \\ & u^{\prime}=u-v \\ & x^{\prime}=\gamma(x-v t) \text { where } \gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}} \\ & t^{\prime}=\gamma\left(t-\frac{v x}{c^{2}}\right) \\ & u^{\prime}=\frac{u-v}{1-\frac{u v}{c^{2}}} \\ & (\Delta s)^{2}=(c \Delta t)^{2}-\Delta x^{2} \\ & \Delta t=\gamma \Delta t_{0} \\ & L=\frac{L_{0}}{\gamma} \\ & \tan \theta=\frac{v}{c} \end{aligned}$

B. The particulate nature of matter


Standard level and higher level
B. 1 Thermal energy transfers	$\begin{aligned} & \rho=\frac{m}{V} \\ & \overline{E_{\mathrm{k}}}=\frac{3}{2} k_{\mathrm{B}} T \\ & Q=m c \Delta T \\ & Q=m L \\ & \frac{\Delta Q}{\Delta t}=k A \frac{\Delta T}{\Delta x} \\ & L=\sigma A T^{4} \\ & b=\frac{L}{4 \pi d^{2}} \\ & \lambda_{\max } T=2.9 \times 10^{-3} \mathrm{mK} \end{aligned}$
B. 2 Greenhouse effect	$\begin{aligned} & \text { emissivity }=\frac{\text { power radiated per unit area }}{\sigma T^{4}} \\ & \text { albedo }=\frac{\text { total scattered power }}{\text { total incident power }} \end{aligned}$
B. 3 Gas laws	$\begin{aligned} & P=\frac{F}{A} \\ & n=\frac{N}{N_{\mathrm{A}}} \\ & \frac{P V}{T}=\text { constant } \\ & P V=n R T=N k_{\mathrm{B}} T \\ & P=\frac{1}{3} \rho V^{2} \\ & U=\frac{3}{2} n R T=\frac{3}{2} N k_{\mathrm{B}} T \end{aligned}$
B. 5 Current and circuits	$\begin{aligned} & I=\frac{\Delta q}{\Delta t} \\ & V=\frac{W}{q} \\ & R=\frac{V}{I} \\ & \rho=\frac{R A}{L} \\ & P=I V=I^{2} R=\frac{V^{2}}{R} \end{aligned}$
	Series circuits
	$\begin{gathered} I=I_{1}=I_{2}=\ldots \\ V=V_{1}+V_{2}+\ldots \\ R_{s}=R_{1}+R_{2}+\ldots \end{gathered}$
	$\varepsilon=I(R+r)$
Additional higher level
B. 4 Thermodynamics	$\begin{aligned} & Q=\Delta U+W \\ & W=P \Delta V \\ & \Delta U=\frac{3}{2} n R \Delta T=\frac{3}{2} N \\ & \Delta S=\frac{\Delta Q}{T} \\ & S=k_{\mathrm{B}} \ln \Omega \\ & P V^{\frac{5}{3}}=\text { constant } \\ & \eta=\frac{\text { useful work }}{\text { input energy }} \\ & \eta_{\text {Carnot }}=1-\frac{T_{\mathrm{c}}}{T_{\mathrm{h}}} \end{aligned}$

C. Wave behaviour


Standard level and higher level
C. 1 Simple harmonic motion	$\begin{aligned} a & =-\omega^{2} x \\ T & =\frac{1}{f}=\frac{2 \pi}{\omega} \\ T & =2 \pi \sqrt{\frac{m}{k}} \\ T & =2 \pi \sqrt{\frac{l}{g}} \end{aligned}$
C. 2 Wave model	$v=f \lambda=\frac{\lambda}{T}$
C. 3 Wave phenomena	$\frac{n_{1}}{n_{2}}=\frac{\sin \theta_{2}}{\sin \theta_{1}}=\frac{v_{2}}{v_{1}}$ Constructive interference: path difference $=n \lambda$ Destructive interference: path difference $=\left(n+\frac{1}{2}\right) \lambda$ $s=\frac{\lambda D}{d}$
C. 5 Doppler effect	$\frac{\Delta f}{f}=\frac{\Delta \lambda}{\lambda} \approx \frac{v}{c}$
Additional higher level
C. 1 Simple harmonic motion	$\begin{aligned} & x=x_{0} \sin (\omega t+\phi) \\ & v=\omega x_{0} \cos (\omega t+\phi) \\ & v= \pm \omega \sqrt{x_{0}^{2}-x^{2}} \\ & E_{\mathrm{T}}=\frac{1}{2} m \omega^{2} x_{0}^{2} \\ & E_{\mathrm{p}}=\frac{1}{2} m \omega^{2} x^{2} \end{aligned}$
C. 3 Wave phenomena	$\begin{aligned} & \theta=\frac{\lambda}{b} \\ & n \lambda=d \sin \theta \end{aligned}$
C. 5 Doppler effect	Moving source: $f^{\prime}=f\left(\frac{v}{v \pm u_{s}}\right)$ Moving observer: $f^{\prime}=f\left(\frac{v \pm u_{0}}{v}\right)$

D. Fields


Standard level and higher level
D.1 Gravitational fields	$\begin{aligned} & F=G \frac{m_{1} m_{2}}{r^{2}} \\ & g=\frac{F}{m}=G \frac{M}{r^{2}} \end{aligned}$
D.2 Electric and magnetic fields	$\begin{aligned} & F=k \frac{q_{1} q_{2}}{r^{2}} \text { where } k=\frac{1}{4 \pi \varepsilon_{0}} \\ & E=\frac{F}{q} \\ & E=\frac{V}{d} \end{aligned}$
D.3 Motion in electromagnetic fields	$\begin{aligned} & F=q v B \sin \theta \\ & F=B I L \sin \theta \\ & \frac{F}{L}=\mu_{0} \frac{I_{1} I_{2}}{2 \pi r} \end{aligned}$
Additional higher level
D.1 Gravitational fields	$\begin{aligned} & E_{\mathrm{p}}=-G \frac{m_{1} m_{2}}{r} \\ & V_{\mathrm{g}}=-G \frac{M}{r} \\ & g=-\frac{\Delta V_{\mathrm{g}}}{\Delta r} \\ & W=m \Delta V_{\mathrm{g}} \\ & v_{\text {esc }}=\sqrt{\frac{2 G M}{r}} \\ & v_{\text {orbital }}=\sqrt{\frac{G M}{r}} \end{aligned}$
D.2 Electric and magnetic fields	$\begin{aligned} & E_{\mathrm{p}}=k \frac{q_{1} q_{2}}{r} \\ & V_{\mathrm{e}}=\frac{k Q}{r} \\ & E=-\frac{\Delta V_{\mathrm{e}}}{\Delta r} \\ & W=q \Delta V_{\mathrm{e}} \end{aligned}$
D.4 Induction	$\Phi=B A \cos \theta$
	$\varepsilon=-N \frac{\Delta \Phi}{\Delta t}$
	$\varepsilon=B v L$

E. Nuclear and quantum physics


Standard level and higher level
E. 1 Structure of the atom	$E=h f$
E. 3 Radioactive decay	$E=m c^{2}$
E. 5 Fusion and stars	$\mathrm{d}(\text { parsec })=\frac{1}{\mathrm{p}(\text { arc-second })}$
Additional higher level
E. 1 Structure of the atom	$\begin{aligned} & R=R_{0} A^{\frac{1}{3}} \\ & E=-\frac{13.6}{n^{2}} \mathrm{eV} \\ & m v r=\frac{n h}{2 \pi} \end{aligned}$
E. 2 Quantum physics	$\begin{aligned} & E_{\max }=h f-\Phi \\ & \lambda=\frac{h}{p} \\ & \lambda_{\mathrm{f}}-\lambda_{i}=\Delta \lambda=\frac{h}{m_{\mathrm{e}} c}(1-\cos \theta) \end{aligned}$
E. 3 Radioactive decay	$\begin{aligned} & N=N_{0} e^{-\lambda t} \\ & A=\lambda N=\lambda N_{0} e^{-\lambda t} \\ & T_{\frac{1}{2}}=\frac{\ln 2}{\lambda} \end{aligned}$