IB Physics data booklet, explained

Every equation for themes A to E, plus the constants, unit tables, circuit symbols and electromagnetic spectrum, word for word and in the order the IB prints them. Press Explain beside an entry to see what it means and how to use it, with worked examples for the formulas.

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Booklet
Physics data booklet, first assessment 2025, version 1.2
Syllabus
Physics, first assessment 2025
Levels
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Physics data booklet

First assessment 2025, Version 1.2

Reproduced from the IB Physics data booklet, First assessment 2025, Version 1.2. Explanations are ours.

Contents

  1. Mathematical equationssheet 3
  2. Uncertaintiessheet 4
  3. Fundamental constantssheet 5
  4. Metric (SI) multiplierssheet 6
  5. Unit conversionssheet 7
  6. Electrical circuit symbolssheet 8
  7. Electromagnetic spectrumsheet 9
  8. ASpace, time and motionsheet 10
  9. BThe particulate nature of mattersheet 11
  10. CWave behavioursheet 12
  11. DFieldssheet 13
  12. ENuclear and quantum physicssheet 14

Mathematical equations

Area of a triangle
A=12(bh)A = \frac{1}{2}(bh)
where bb is the base, hh is the height
Area of a circle
A=πr2A = \pi r^2
where rr is the radius
Circumference of a circle
C=2πrC = 2\pi r
Volume of a cuboid
V=lwhV = lwh
where ll is the length, ww is the width, hh is the height
Volume of a cylinder
V=πr2hV = \pi r^2 h
Volume of a prism
V=AhV = Ah
where AA is the area of cross-section
Volume of a sphere
V=43πr3V = \frac{4}{3}\pi r^3
Area of the curved surface of a cylinder
A=2πrhA = 2\pi rh
θAAVAH
Vectors
AH=Acos⁡θA_{\mathrm{H}} = A\cos\theta
AV=Asin⁡θA_{\mathrm{V}} = A\sin\theta
Trigonometric relationships
tan⁡θ=sin⁡θcos⁡θ\tan\theta = \frac{\sin\theta}{\cos\theta}
sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1

Uncertainties

If: y=a±by = a \pm b
then:
Δy=Δa+Δb\Delta y = \Delta a + \Delta b
If: y=abcy = \frac{ab}{c}
then:
Δyy=Δaa+Δbb+Δcc\frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}
If: y=any = a^n
then:
Δyy=∣nΔaa∣\frac{\Delta y}{y} = \left|n\frac{\Delta a}{a}\right|

Fundamental constants

QuantitySymbolApproximate value
Acceleration of free fall
gg
9.8 m s−2 (Earth’s surface)9.8\ \mathrm{m\,s^{-2}}\ \text{(Earth’s surface)}
Gravitational constant
GG
6.67×10−11 N m2 kg−26.67\times10^{-11}\ \mathrm{N\,m^{2}\,kg^{-2}}
Avogadro constant
NAN_{\mathrm{A}}
6.02×1023 mol−16.02\times10^{23}\ \mathrm{mol^{-1}}
Gas constant
RR
8.31 J K−1 mol−18.31\ \mathrm{J\,K^{-1}\,mol^{-1}}
Boltzmann constant
kBk_{\mathrm{B}}
1.38×10−23 J K−11.38\times10^{-23}\ \mathrm{J\,K^{-1}}
Stefan–Boltzmann constant
σ\sigma
5.67×10−8 W m−2 K−45.67\times10^{-8}\ \mathrm{W\,m^{-2}\,K^{-4}}
Coulomb constant
kk
8.99×109 N m2 C−28.99\times10^{9}\ \mathrm{N\,m^{2}\,C^{-2}}
Permittivity of free space
ε0\varepsilon_0
8.85×10−12 C2 N−1 m−28.85\times10^{-12}\ \mathrm{C^{2}\,N^{-1}\,m^{-2}}
Permeability of free space
μ0\mu_0
4π×10−7 T m A−14\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}
Speed of light in vacuum
cc
3.00×108 m s−13.00\times10^{8}\ \mathrm{m\,s^{-1}}
Planck constant
hh
6.63×10−34 J s6.63\times10^{-34}\ \mathrm{J\,s}
Elementary charge
ee
1.60×10−19 C1.60\times10^{-19}\ \mathrm{C}
Electron rest mass
mem_{\mathrm{e}}
9.110×10−31 kg=0.000549 u=0.511 MeV c−29.110\times10^{-31}\ \mathrm{kg} = 0.000549\ \mathrm{u} = 0.511\ \mathrm{MeV\,c^{-2}}
Proton rest mass
mpm_{\mathrm{p}}
1.673×10−27 kg=1.007276 u=938 MeV c−21.673\times10^{-27}\ \mathrm{kg} = 1.007276\ \mathrm{u} = 938\ \mathrm{MeV\,c^{-2}}
Neutron rest mass
mnm_{\mathrm{n}}
1.675×10−27 kg=1.008665 u=940 MeV c−21.675\times10^{-27}\ \mathrm{kg} = 1.008665\ \mathrm{u} = 940\ \mathrm{MeV\,c^{-2}}
(Unified) atomic mass unit
u\mathrm{u}
1.661×10−27 kg=931.5 MeV c−21.661\times10^{-27}\ \mathrm{kg} = 931.5\ \mathrm{MeV\,c^{-2}}
Solar constant
SS
1.36×103 W m−21.36\times10^{3}\ \mathrm{W\,m^{-2}}
Fermi radius
R0R_0
1.20×10−15 m1.20\times10^{-15}\ \mathrm{m}

Metric (SI) multipliers

PrefixAbbreviationValue
petaP101510^{15}
teraT101210^{12}
gigaG10910^{9}
megaM10610^{6}
kilok10310^{3}
hectoh10210^{2}
decada10110^{1}
decid10−110^{-1}
centic10−210^{-2}
millim10−310^{-3}
microμ10−610^{-6}
nanon10−910^{-9}
picop10−1210^{-12}
femtof10−1510^{-15}

Unit conversions

1 radian (rad) ≡180∘π\equiv \frac{180^{\circ}}{\pi}
Temperature (K) == temperature (°C) +273+ 273
1 light year (ly) =9.46×1015 m= 9.46\times10^{15}\ \mathrm{m}
1 parsec (pc) =3.26 ly= 3.26\ \mathrm{ly}
1 astronomical unit (AU) =1.50×1011 m= 1.50\times10^{11}\ \mathrm{m}
1 kilowatt-hour (kWh) =3.60×106 J= 3.60\times10^{6}\ \mathrm{J}
hc=1.99×10−25 J m=1.24×10−6 eV mhc = 1.99\times10^{-25}\ \mathrm{J\,m} = 1.24\times10^{-6}\ \mathrm{eV\,m}

Electrical circuit symbols

Cell
Battery
Switch
Voltmeter
Ammeter
Resistor
Variable resistor
Light-dependent resistor (LDR)
Thermistor
Potentiometer
Lamp
Light emitting diode (LED)
Heating element
Motor
Earth (ground)

Electromagnetic spectrum

energy10−1610−1410−1210−1010−810−610−410−2100102104106108wavelength / mγ raysX-raysUVIRmicrowavesradio wavesVIBGYOR400700wavelength / nm

Wavelength / m from 10−1610^{-16} to 10810^{8}, with energy increasing towards shorter wavelengths. The visible band, V I B G Y O R, is expanded below it on a wavelength / nm scale from 400400 to 700700.

ASpace, time and motion

Standard level and higher level

A.1
Kinematics
s=u+v2ts = \frac{u + v}{2}t
v=u+atv = u + at
s=ut+12at2s = ut + \frac{1}{2}at^2
v2=u2+2asv^2 = u^2 + 2as
A.2
Forces and momentum
Ff≤μsFNF_{\mathrm{f}} \le \mu_{\mathrm{s}} F_{\mathrm{N}}
Ff=μdFNF_{\mathrm{f}} = \mu_{\mathrm{d}} F_{\mathrm{N}}
FH=−kxF_{\mathrm{H}} = -kx
Fd=6πηrvF_{\mathrm{d}} = 6\pi\eta rv
Fb=ρVgF_{\mathrm{b}} = \rho Vg
Fg=mgF_{\mathrm{g}} = mg
p=mvp = mv
J=FΔtJ = F\Delta t
F=ma=ΔpΔtF = ma = \frac{\Delta p}{\Delta t}
a=v2r=ω2r=4π2rT2a = \frac{v^2}{r} = \omega^2 r = \frac{4\pi^2 r}{T^2}
v=2πrT=ωrv = \frac{2\pi r}{T} = \omega r
A.3
Work, energy and power
W=Fscos⁡θW = Fs\cos\theta
Ek=12mv2=p22mE_{\mathrm{k}} = \frac{1}{2}mv^2 = \frac{p^2}{2m}
ΔEp=mgΔh\Delta E_{\mathrm{p}} = mg\Delta h
EH=12kΔx2E_{\mathrm{H}} = \frac{1}{2}k\Delta x^2
P=ΔWΔt=FvP = \frac{\Delta W}{\Delta t} = Fv
η=useful work outtotal work in=useful power outtotal power in\eta = \frac{\text{useful work out}}{\text{total work in}} = \frac{\text{useful power out}}{\text{total power in}}

Additional higher level

A.4
Rigid body mechanics
τ=Frsin⁡θ\tau = Fr\sin\theta
Δθ=ωf+ωi2t\Delta\theta = \frac{\omega_{\mathrm{f}} + \omega_{\mathrm{i}}}{2}t
ωf=ωi+αt\omega_{\mathrm{f}} = \omega_{\mathrm{i}} + \alpha t
Δθ=ωit+12αt2\Delta\theta = \omega_{\mathrm{i}}t + \frac{1}{2}\alpha t^2
ωf2=ωi2+2αΔθ\omega_{\mathrm{f}}^2 = \omega_{\mathrm{i}}^2 + 2\alpha\Delta\theta
I=Σmr2I = \Sigma mr^2
τ=Iα\tau = I\alpha
L=IωL = I\omega
ΔL=τΔt\Delta L = \tau\Delta t
ΔL=Δ(Iω)\Delta L = \Delta(I\omega)
Ek=12Iω2=L22IE_k = \frac{1}{2}I\omega^2 = \frac{L^2}{2I}
A.5
Galilean and special relativity
x′=x−vtx' = x - vt
t′=tt' = t
u′=u−vu' = u - v
x′=γ(x−vt)x' = \gamma(x - vt)
where γ=11−v2c2\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}
t′=γ(t−vxc2)t' = \gamma\left(t - \frac{vx}{c^2}\right)
u′=u−v1−uvc2u' = \frac{u - v}{1 - \frac{uv}{c^2}}
(Δs)2=(cΔt)2−Δx2(\Delta s)^2 = (c\Delta t)^2 - \Delta x^2
Δt=γΔt0\Delta t = \gamma\Delta t_0
L=L0γL = \frac{L_0}{\gamma}
tan⁡θ=vc\tan\theta = \frac{v}{c}

BThe particulate nature of matter

Standard level and higher level

B.1
Thermal energy transfers
ρ=mV\rho = \frac{m}{V}
Ek‾=32kBT\overline{E_{\mathrm{k}}} = \frac{3}{2}k_{\mathrm{B}}T
Q=mcΔTQ = mc\Delta T
Q=mLQ = mL
ΔQΔt=−kAΔTΔx\frac{\Delta Q}{\Delta t} = -kA\frac{\Delta T}{\Delta x}
L=σAT4L = \sigma AT^{4}
b=L4πd2b = \frac{L}{4\pi d^{2}}
λmaxT=2.9×10−3 m K\lambda_{\mathrm{max}}T = 2.9\times10^{-3}\ \mathrm{m\,K}
B.2
Greenhouse effect
emissivity=power radiated per unit areaσT4\text{emissivity} = \frac{\text{power radiated per unit area}}{\sigma T^{4}}
albedo=total scattered powertotal incident power\text{albedo} = \frac{\text{total scattered power}}{\text{total incident power}}
B.3
Gas laws
P=FAP = \frac{F}{A}
n=NNAn = \frac{N}{N_{\mathrm{A}}}
PVT=constant\frac{PV}{T} = \text{constant}
PV=nRT=NkBTPV = nRT = Nk_{\mathrm{B}}T
P=13ρv2P = \frac{1}{3}\rho v^{2}
U=32nRT=32NkBTU = \frac{3}{2}nRT = \frac{3}{2}Nk_{\mathrm{B}}T
B.5
Current and circuits
I=ΔqΔtI = \frac{\Delta q}{\Delta t}
V=WqV = \frac{W}{q}
R=VIR = \frac{V}{I}
ρ=RAL\rho = \frac{RA}{L}
P=IV=I2R=V2RP = IV = I^{2}R = \frac{V^{2}}{R}
I=I1=I2=…I = I_1 = I_2 = \ldots
Series circuits
V=V1+V2+…V = V_1 + V_2 + \ldots
Series circuits
Rs=R1+R2+…R_s = R_1 + R_2 + \ldots
Series circuits
I=I1+I2+…I = I_1 + I_2 + \ldots
Parallel circuits
V=V1=V2=…V = V_1 = V_2 = \ldots
Parallel circuits
1Rp=1R1+1R2+…\frac{1}{R_{\mathrm{p}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots
Parallel circuits
ε=I(R+r)\varepsilon = I(R + r)

Additional higher level

B.4
Thermodynamics
Q=ΔU+WQ = \Delta U + W
W=PΔVW = P\Delta V
ΔU=32nRΔT=32NkBΔT\Delta U = \frac{3}{2}nR\Delta T = \frac{3}{2}Nk_B\Delta T
ΔS=ΔQT\Delta S = \frac{\Delta Q}{T}
S=kBln⁡ΩS = k_{\mathrm{B}}\ln\Omega
PV53=constantPV^{\frac{5}{3}} = \text{constant}
η=useful workinput energy\eta = \frac{\text{useful work}}{\text{input energy}}
ηCarnot=1−TcTh\eta_{\mathrm{Carnot}} = 1 - \frac{T_{\mathrm{c}}}{T_{\mathrm{h}}}

CWave behaviour

Standard level and higher level

C.1
Simple harmonic motion
a=−ω2xa = -\omega^2 x
T=1f=2πωT = \frac{1}{f} = \frac{2\pi}{\omega}
T=2πmkT = 2\pi\sqrt{\frac{m}{k}}
T=2πlgT = 2\pi\sqrt{\frac{l}{g}}
C.2
Wave model
v=fλ=λTv = f\lambda = \frac{\lambda}{T}
C.3
Wave phenomena
n1n2=sin⁡θ2sin⁡θ1=v2v1\frac{n_1}{n_2} = \frac{\sin\theta_2}{\sin\theta_1} = \frac{v_2}{v_1}
Constructive interference: path difference=nλ\text{Constructive interference: path difference} = n\lambda
Destructive interference: path difference=(n+12)λ\text{Destructive interference: path difference} = (n + \frac{1}{2})\lambda
s=λDds = \frac{\lambda D}{d}
C.5
Doppler effect
Δff=Δλλ≈vc\frac{\Delta f}{f} = \frac{\Delta\lambda}{\lambda} \approx \frac{v}{c}

Additional higher level

C.1
Simple harmonic motion
x=x0sin⁡(ωt+ϕ)x = x_0 \sin(\omega t + \phi)
v=ωx0cos⁡(ωt+ϕ)v = \omega x_0 \cos(\omega t + \phi)
v=±ωx02−x2v = \pm\omega\sqrt{x_0^{2} - x^{2}}
ET=12mω2x02E_{\mathrm{T}} = \frac{1}{2}m\omega^2 x_0^2
Ep=12mω2x2E_{\mathrm{p}} = \frac{1}{2}m\omega^2 x^2
C.3
Wave phenomena
θ=λb\theta = \frac{\lambda}{b}
nλ=dsin⁡θn\lambda = d\sin\theta
C.5
Doppler effect
Moving source: f′=f(vv±us)\text{Moving source: } f' = f\left(\frac{v}{v \pm u_{\mathrm{s}}}\right)
Moving observer: f′=f(v±uov)\text{Moving observer: } f' = f\left(\frac{v \pm u_{\mathrm{o}}}{v}\right)

DFields

Standard level and higher level

D.1
Gravitational fields
F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}
g=Fm=GMr2g = \frac{F}{m} = G\frac{M}{r^2}
D.2
Electric and magnetic fields
F=kq1q2r2F = k\frac{q_1 q_2}{r^2}
where k=14πε0k = \frac{1}{4\pi\varepsilon_0}
E=FqE = \frac{F}{q}
E=VdE = \frac{V}{d}
D.3
Motion in electromagnetic fields
F=qvBsin⁡θF = qvB\sin\theta
F=BILsin⁡θF = BIL\sin\theta
FL=μ0I1I22πr\frac{F}{L} = \mu_0\frac{I_1 I_2}{2\pi r}

Additional higher level

D.1
Gravitational fields
Ep=−Gm1m2rE_{\mathrm{p}} = -G\frac{m_1 m_2}{r}
Vg=−GMrV_{\mathrm{g}} = -G\frac{M}{r}
g=−ΔVgΔrg = -\frac{\Delta V_{\mathrm{g}}}{\Delta r}
W=mΔVgW = m\Delta V_{\mathrm{g}}
vesc=2GMrv_{\mathrm{esc}} = \sqrt{\frac{2GM}{r}}
vorbital=GMrv_{\mathrm{orbital}} = \sqrt{\frac{GM}{r}}
D.2
Electric and magnetic fields
Ep=kq1q2rE_{\mathrm{p}} = k\frac{q_1 q_2}{r}
Ve=kQrV_{\mathrm{e}} = \frac{kQ}{r}
E=−ΔVeΔrE = -\frac{\Delta V_{\mathrm{e}}}{\Delta r}
W=qΔVeW = q\Delta V_{\mathrm{e}}
D.4
Induction
Φ=BAcos⁡θ\Phi = BA\cos\theta
ε=−NΔΦΔt\varepsilon = -N\frac{\Delta\Phi}{\Delta t}
ε=BvL\varepsilon = BvL

ENuclear and quantum physics

Standard level and higher level

E.1
Structure of the atom
E=hfE = hf
E.3
Radioactive decay
E=mc2E = mc^2
E.5
Fusion and stars
d(parsec)=1p(arc-second)\text{d(parsec)} = \frac{1}{\text{p(arc-second)}}

Additional higher level

E.1
Structure of the atom
R=R0A13R = R_0 A^{\frac{1}{3}}
E=−13.6n2 eVE = -\frac{13.6}{n^2}\,\mathrm{eV}
mvr=nh2πmvr = \frac{nh}{2\pi}
E.2
Quantum physics
Emax=hf−ΦE_{\mathrm{max}} = hf - \Phi
λ=hp\lambda = \frac{h}{p}
λf−λi=Δλ=hmec(1−cos⁡θ)\lambda_{\mathrm{f}} - \lambda_i = \Delta\lambda = \frac{h}{m_{\mathrm{e}}c}(1 - \cos\theta)
E.3
Radioactive decay
N=N0e−λtN = N_0 e^{-\lambda t}
A=λN=λN0e−λtA = \lambda N = \lambda N_0 e^{-\lambda t}
T12=ln⁡2λT_{\frac{1}{2}} = \frac{\ln 2}{\lambda}

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