Physics data booklet Data booklet —

Study edition

Physics
data booklet

The physics reference tables, annotated page for page: the constants, the conversions, the circuit symbols and every equation, on the page you already know.

Course
Physics, standard level and higher level

First examination
2025

Themes
A Space, time and motion · B The particulate nature of matter · C Wave behaviour · D Fields · E Nuclear and quantum physics

How to use it
Every table, section label and page break sits where the original puts it, so the page you revise from here is the page you turn to there.

Printing
A4, scale 100%, background graphics on. One sheet prints as one page, 17 in all.

Annotated study edition — always sit the exam with the official booklet your school issues.

Physics data booklet Version 1.0 · re-creation

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Physics data booklet Data booklet —

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Physics data booklet Data booklet —

Index

— Introduction prose 1 — Mathematical equations 1 page 2 — Uncertainties · Fundamental constants 1 page 3 — Metric (SI) multipliers · Unit conversions 1 page 4 — Electrical circuit symbols · Electromagnetic spectrum 1 page 5 A Space, time and motion 2 pages 6–7 B The particulate nature of matter 2 pages 8–9 C Wave behaviour 2 pages 10–11 D Fields 2 pages 12–13 E Nuclear and quantum physics page 13 13

Reading the tables. The left column carries the section label the course uses — A.1, B.4, E.2 and so on. The middle column names the section. The right column holds its equations, one to a line.

Magnitudes only. Every equation in this booklet relates the magnitudes of the quantities involved. No vector notation is used anywhere, so F = ma is a statement about sizes, not directions.

Physics data booklet Contents

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Physics data booklet Introduction 1

1

Introduction

This booklet collects the reference material a Physics course keeps coming back to: the electrical circuit symbols, the mathematics the course expects you to apply, the physical constants and unit conversions, and the equations that belong to each theme and topic.

Keep it open while you work rather than reaching for it only in an examination. The course guide points at these same equations from the “Understandings” sections, which keeps the emphasis where it belongs: on reading a situation and choosing the right relationship, instead of memorising symbols, constants and formulas.

The content is in two parts. The first part is used throughout the course — symbols, mathematics, constants and conversions. The second part gathers the equations for the individual themes and topics. Throughout, every equation is written for the magnitude of the quantity only; vector notation is not used.

In an examination you must have a clean copy of the official booklet. Schools obtain it and make sure that every student has one. Use this page-for-page re-creation to rehearse, and the official copy on the day.

Where the sections sit. Pages 2 to 5 hold the mathematics, the constants and conversions, and the symbols and spectrum. Pages 6 to 13 then run through themes A to E, each section marked standard level and higher level or additional higher level.

Standard level and higher level. Sections marked additional higher level are examined at HL only. They sit in their own block below the shared material, exactly as they do in the printed booklet.

Physics data booklet 1

06

Physics data booklet Mathematical equations 2

2

Mathematical equations

Area of a triangle

A = \frac{1}{2} (b h) where b is the base, h is the height

Area of a circle

A = π r^{2} where r is the radius

Circumference of a circle

C = 2 π r

Volume of a cuboid

V = l w h where l is the length, w is the width, h is the height

Volume of a cylinder

V = π r^{2} h

Volume of a prism

V = A h where A is the area of cross-section

Volume of a sphere

V = \frac{4}{3} π r^{3}

Area of the curved surface of a cylinder

A = 2 π r h

Vectors

A_{H} = A \cos θ

A_{V} = A \sin θ

Trigonometric relationships

\tan θ = \frac{\sin θ}{\cos θ}

\sin^{2} θ + \cos^{2} θ = 1

Physics data booklet 2

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Physics data booklet Data and constants 3

3

Uncertainties

If:

y = a \pm b

then: Δ y = Δ a + Δ b

If:

y = \frac{a b}{c}

then: \frac{Δ y}{y} = \frac{Δ a}{a} + \frac{Δ b}{b} + \frac{Δ c}{c}

If:

y = a^{n}

then: \frac{Δ y}{y} = | n \frac{Δ a}{a} |

3

Fundamental constants

Quantity	Symbol	Approximate value
Acceleration of free fall	$g$	$9.8 {m s}^{- 2}$ (Earth's surface)
Gravitational constant	$G$	$6.67 \times 1 0^{- 11} {N m}^{2} {kg}^{- 2}$
Avogadro constant	$N_{A}$	$6.02 \times 1 0^{23} {mol}^{- 1}$
Gas constant	$R$	$8.31 {J K}^{- 1} {mol}^{- 1}$
Boltzmann constant	$k_{B}$	$1.38 \times 1 0^{- 23} {J K}^{- 1}$
Stefan–Boltzmann constant	$σ$	$5.67 \times 1 0^{- 8} {W m}^{- 2} K^{- 4}$
Coulomb constant	$k$	$8.99 \times 1 0^{9} {N m}^{2} C^{- 2}$
Permittivity of free space	$ε_{0}$	$8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$
Permeability of free space	$μ_{0}$	$4 π \times 1 0^{- 7} {T m A}^{- 1}$
Speed of light in vacuum	$c$	$3.00 \times 1 0^{8} {m s}^{- 1}$
Planck constant	$h$	$6.63 \times 1 0^{- 34} J s$
Elementary charge	$e$	$1.60 \times 1 0^{- 19} C$
Electron rest mass	$m_{e}$	$9.110 \times 1 0^{- 31} kg = 0.000549 u = 0.511 {MeV c}^{- 2}$
Proton rest mass	$m_{p}$	$1.673 \times 1 0^{- 27} kg = 1.007276 u = 938 {MeV c}^{- 2}$
Neutron rest mass	$m_{n}$	$1.675 \times 1 0^{- 27} kg = 1.008665 u = 940 {MeV c}^{- 2}$
(Unified) atomic mass unit	$u$	$1.661 \times 1 0^{- 27} kg = 931.5 {MeV c}^{- 2}$
Solar constant	$S$	$1.36 \times 1 0^{3} {W m}^{- 2}$
Fermi radius	$R_{0}$	$1.20 \times 1 0^{- 15} m$

Physics data booklet 3

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Physics data booklet Data and conversions 4

4

Metric (SI) multipliers

Prefix	Abbreviation	Value
peta	P	$1 0^{15}$
tera	T	$1 0^{12}$
giga	G	$1 0^{9}$
mega	M	$1 0^{6}$
kilo	k	$1 0^{3}$
hecto	h	$1 0^{2}$
deca	da	$1 0^{1}$
deci	d	$1 0^{- 1}$
centi	c	$1 0^{- 2}$
milli	m	$1 0^{- 3}$
micro	μ	$1 0^{- 6}$
nano	n	$1 0^{- 9}$
pico	p	$1 0^{- 12}$
femto	f	$1 0^{- 15}$

4

Unit conversions

Angle

1 radian (rad) = \frac{180 °}{π}

Temperature

temperature (K) = temperature (°C) + 273

Distance

1 light year (ly) = 9.46 \times 1 0^{15} m

Distance

1 parsec (pc) = 3.26 ly

Distance

1 astronomical unit (AU) = 1.50 \times 1 0^{11} m

Energy

1 kilowatt-hour (kWh) = 3.60 \times 1 0^{6} J

Photon energy × wavelength

h c = 1.99 \times 1 0^{- 25} J m = 1.24 \times 1 0^{- 6} eV m

Physics data booklet 4

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Physics data booklet Symbols and spectrum 5

5

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)

5

Electromagnetic spectrum

Physics data booklet 5

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Physics data booklet Theme A · Space, time and motion 6

A

Space, time and motion

SL · HL

Standard level and higher level

A.1

Kinematics

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

A.2

Forces and momentum

F_{f} \leq μ_{s} F_{N}

F_{f} = μ_{d} F_{N}

F_{H} = - k x

F_{d} = 6 π η r v

F_{b} = ρ V g

F_{g} = m g

p = m v

J = F Δ t

F = m a = \frac{Δ p}{Δ t}

a = \frac{v^{2}}{r} = ω^{2} r = \frac{4 π^{2} r}{T^{2}}

v = \frac{2 π r}{T} = ω r

A.3

Work, energy and power

W = F s \cos θ

E_{k} = \frac{1}{2} m v^{2} = \frac{p^{2}}{2 m}

Δ E_{p} = m g Δ h

E_{H} = \frac{1}{2} k Δ x^{2}

P = \frac{Δ W}{Δ t} = F v

η = \frac{useful work out}{total work in} = \frac{useful power out}{total power in}

Physics data booklet 6

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Physics data booklet Theme A · Space, time and motion 7

AHL

Additional higher level

A.4

Rigid body mechanics

τ = F r \sin θ

Δ θ = \frac{ω_{i} + ω_{f}}{2} t

ω_{f} = ω_{i} + α t

Δ θ = ω_{i} t + \frac{1}{2} α t^{2}

ω_{f}^{2} = ω_{i}^{2} + 2 α Δ θ

I = Σ m r^{2}

τ = I α

L = I ω

Δ L = τ Δ t

Δ L = Δ (I ω)

E_{k} = \frac{1}{2} I ω^{2} = \frac{L^{2}}{2 I}

A.5

Galilean and special relativity

x^{'} = x - v t

t^{'} = t

u^{'} = u - v

x^{'} = γ (x - v t) where γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}

t^{'} = γ (t - \frac{v x}{c^{2}})

u^{'} = \frac{u - v}{1 - \frac{u v}{c^{2}}}

(Δ s)^{2} = (c Δ t)^{2} - Δ x^{2}

Δ t = γ Δ t_{0}

L = \frac{L_{0}}{γ}

\tan θ = \frac{v}{c}

Physics data booklet 7

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Physics data booklet Theme B · The particulate nature of matter 8

B

The particulate nature of matter

SL · HL

Standard level and higher level

B.1

Thermal energy transfers

ρ = \frac{m}{V}

{\bar{E}}_{k} = \frac{3}{2} k_{B} T

Q = m c Δ T

Q = m L

\frac{Δ Q}{Δ t} = - k A \frac{Δ T}{Δ x}

L = σ A T^{4}

b = \frac{L}{4 π d^{2}}

λ_{max} T = 2.9 \times 1 0^{- 3} m K

B.2

Greenhouse effect

emissivity = \frac{power radiated per unit area}{σ T^{4}}

albedo = \frac{total scattered power}{total incident power}

B.3

Gas laws

P = \frac{F}{A}

n = \frac{N}{N_{A}}

\frac{P V}{T} = constant

P V = n R T = N k_{B} T

P = \frac{1}{3} ρ v^{2}

U = \frac{3}{2} n R T = \frac{3}{2} N k_{B} T

Physics data booklet 8

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Physics data booklet Theme B · The particulate nature of matter 9

B.5

Current and circuits

I = \frac{Δ q}{Δ t}

V = \frac{W}{q}

R = \frac{V}{I}

ρ = \frac{R A}{L}

P = I V = I^{2} R = \frac{V^{2}}{R}

Series circuits	Parallel circuits
$I = I_{1} = I_{2} = \dots$	$I = I_{1} + I_{2} + \dots$
$V = V_{1} + V_{2} + \dots$	$V = V_{1} = V_{2} = \dots$
$R_{s} = R_{1} + R_{2} + \dots$	$\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \dots$

ε = I (R + r)

AHL

Additional higher level

B.4

Thermodynamics

Q = Δ U + W

W = P Δ V

Δ U = \frac{3}{2} n R Δ T = \frac{3}{2} N k_{B} Δ T

Δ S = \frac{Δ Q}{T}

S = k_{B} \ln Ω

P V^{\frac{5}{3}} = constant

η = \frac{useful work}{input energy}

η_{Carnot} = 1 - \frac{T_{c}}{T_{h}}

Physics data booklet 9

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Physics data booklet Theme C · Wave behaviour 10

C

Wave behaviour

SL · HL

Standard level and higher level

C.1

Simple harmonic motion

a = - ω^{2} x

T = \frac{1}{f} = \frac{2 π}{ω}

T = 2 π \sqrt{\frac{m}{k}}

T = 2 π \sqrt{\frac{l}{g}}

C.2

Wave model

v = f λ = \frac{λ}{T}

C.3

Wave phenomena

\frac{n_{1}}{n_{2}} = \frac{\sin θ_{2}}{\sin θ_{1}} = \frac{v_{2}}{v_{1}}

Constructive interference: path difference = n λ

Destructive interference: path difference = (n + \frac{1}{2}) λ

s = \frac{λ D}{d}

C.5

Doppler effect

\frac{Δ f}{f} = \frac{Δ λ}{λ} \approx \frac{v}{c}

AHL

Additional higher level

C.1

Simple harmonic motion

x = x_{0} \sin (ω t + φ)

v = ω x_{0} \cos (ω t + φ)

v = \pm ω \sqrt{x_{0}^{2} - x^{2}}

E_{T} = \frac{1}{2} m ω^{2} x_{0}^{2}

E_{p} = \frac{1}{2} m ω^{2} x^{2}

Physics data booklet 10

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Physics data booklet Theme C · Wave behaviour 11

AHL

Additional higher level (continued)

C.3

Wave phenomena

θ = \frac{λ}{b}

n λ = d \sin θ

C.5

Doppler effect

Moving source: f^{'} = f (\frac{v}{v \pm u_{s}})

Moving observer: f^{'} = f (\frac{v \pm u_{o}}{v})

Why this page is short. Only two higher level sections run past the previous page: the diffraction results of C.3, and the moving source and moving observer forms of the Doppler effect in C.5. Everything else in theme C is already on page 10.

Physics data booklet 11

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Physics data booklet Theme D · Fields 12

D

Fields

SL · HL

Standard level and higher level

D.1

Gravitational fields

F = G \frac{m_{1} m_{2}}{r^{2}}

g = \frac{F}{m} = G \frac{M}{r^{2}}

D.2

Electric and magnetic fields

F = k \frac{q_{1} q_{2}}{r^{2}} where k = \frac{1}{4 π ε_{0}}

E = \frac{F}{q}

E = \frac{V}{d}

D.3

Motion in electromagnetic fields

F = q v B \sin θ

F = B I L \sin θ

\frac{F}{L} = μ_{0} \frac{I_{1} I_{2}}{2 π r}

AHL

Additional higher level

D.1

Gravitational fields

E_{p} = - G \frac{m_{1} m_{2}}{r}

V_{g} = - G \frac{M}{r}

g = - \frac{Δ V_{g}}{Δ r}

W = m Δ V_{g}

v_{esc} = \sqrt{\frac{2 G M}{r}}

v_{orbital} = \sqrt{\frac{G M}{r}}

D.2

Electric and magnetic fields

E_{p} = k \frac{q_{1} q_{2}}{r}

V_{e} = \frac{k Q}{r}

E = - \frac{Δ V_{e}}{Δ r}

W = q Δ V_{e}

Physics data booklet 12

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Physics data booklet Themes D–E 13

D.4

Induction

Φ = B A \cos θ

ε = - N \frac{Δ Φ}{Δ t}

ε = B v L

E

Nuclear and quantum physics

SL · HL

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

d (parsec) = \frac{1}{p (arc-second)}

AHL

Additional higher level

E.1

Structure of the atom

R = R_{0} A^{\frac{1}{3}}

E = - \frac{13.6}{n^{2}} eV

m v r = \frac{n h}{2 π}

E.2

Quantum physics

E_{max} = h f - Φ

λ = \frac{h}{p}

λ_{f} - λ_{i} = Δ λ = \frac{h}{m_{e} c} (1 - \cos θ)

E.3

Radioactive decay

N = N_{0} e^{- λ t}

A = λ N = λ N_{0} e^{- λ t}

T_{\frac{1}{2}} = \frac{\ln 2}{λ}

Physics data booklet 13

Physicsdata booklet

Contents

Introduction

Mathematical equations

Uncertainties

Fundamental constants

Metric (SI) multipliers

Unit conversions

Electrical circuit symbols

Electromagnetic spectrum

Space, time and motion

Standard level and higher level

Additional higher level

The particulate nature of matter

Standard level and higher level

Additional higher level

Wave behaviour

Standard level and higher level

Additional higher level

Additional higher level (continued)

Fields

Standard level and higher level

Additional higher level

Nuclear and quantum physics

Standard level and higher level

Additional higher level

Physics
data booklet