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QCE Physics formula and data book: every equation, every constant

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Formula sheet

The card below opens today's Year 12 Physics paper with the book in a drawer. The contents follow, grouped as the QCAA prints them but in our own layout. The QCAA's book is version 1.3 of the 2025 Physics syllabus materials and is licensed under Creative Commons, so check any value against the QCAA Physics page before you rely on it.

Formula sheet

Year 12 Physics

Open formula sheet

Processing of data

\Delta\overline{x}=\pm\frac{\left(x_{max}-x_{min}\right)}{2}absolute uncertainty of the mean
\text{percentage uncertainty (\%)}=\frac{\text{absolute uncertainty}}{\text{measurement}}\times100\%percentage uncertainty
\text{percentage error (\%)}=\left|\frac{\text{measured value}-\text{true value}}{\text{true value}}\right|\times100\%percentage error

Heating processes

T_K=T_C+273temperature conversion
\Delta U=Q+Wfirst law of thermodynamics
Q=mc\Delta Theat for a temperature change
\eta=\frac{\text{energy output}}{\text{energy input}}\times\frac{100}{1}\%efficiency
Q=mLheat for a change of state

Ionising radiation and nuclear reactions

N=N_0\left(\frac{1}{2}\right)^nradioactive decay after n half-lives
\Delta E=\Delta mc^2mass-energy equivalence

Special relativity

t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}time dilation
p_v=\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}}relativistic momentum
L=L_0\sqrt{1-\frac{v^2}{c^2}}length contraction
\Delta E=\Delta mc^2energy change

Electrical circuits

I=\frac{q}{t}current
P=I^2Rpower from current and resistance
V=\frac{W}{q}potential difference
V_t=V_1+V_2+\ldots V_nseries potential difference
P=\frac{W}{t}power from work and time
R_t=R_1+R_2+\ldots R_nseries resistance
V=IROhm's law
I_t=I_1+I_2+\ldots I_nparallel current
P=VIpower from potential difference and current
\frac{1}{R_t}=\frac{1}{R_1}+\frac{1}{R_2}+\ldots\frac{1}{R_n}parallel resistance

Electromagnetism

F=\frac{1}{4\pi\varepsilon_0}\frac{Qq}{r^2}=\frac{kQq}{r^2}Coulomb's law
F=qvB\sin\thetaforce on a moving charge
E=\frac{F}{q}=\frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}=\frac{kq}{r^2}electric field
\phi=BA\cos\thetamagnetic flux
V=\frac{\Delta U}{q}electric potential
emf=-\frac{N\Delta\left(BA_{\perp}\right)}{\Delta t}induced emf from area change
B=\frac{\mu_0I}{2\pi r}field around a long straight wire
emf=-N\frac{\Delta\phi}{\Delta t}induced emf from flux change
B=\mu_0nIfield inside a solenoid
I_pV_p=I_sV_stransformer power
F=BIL\sin\thetaforce on a conductor
\frac{V_p}{V_s}=\frac{N_p}{N_s}transformer ratio

Linear motion and force

v=u+atfinal velocity
W=\Delta Ework and energy
s=ut+\frac{1}{2}at^2displacement
W=Fswork done by a force
v^2=u^2+2asvelocity and displacement
E_k=\frac{1}{2}mv^2kinetic energy
a=\frac{F_{net}}{m}acceleration
\Delta E_p=mg\Delta hchange in gravitational potential energy
p=mvmomentum
\sum\frac{1}{2}mv^2_{before}=\sum\frac{1}{2}mv^2_{after}elastic collision
\sum mv_{before}=\sum mv_{after}conservation of momentum

Gravity and motion

v_y=u_y+gtvertical velocity
v=\frac{2\pi r}{T}orbital speed
s_y=u_yt+\frac{1}{2}gt^2vertical displacement
a_c=\frac{v^2}{r}centripetal acceleration
v_y^2=u_y^2+2gs_yvertical velocity and displacement
F_c=F_{net}=\frac{mv^2}{r}centripetal force
v_x=u_xhorizontal velocity
F=\frac{GMm}{r^2}law of universal gravitation
s_x=u_xthorizontal displacement
g=\frac{F}{m}=\frac{GM}{r^2}gravitational field strength
F_g=mgweight
\frac{T_a^2}{r_a^3}=\frac{T_b^2}{r_b^3}=\frac{4\pi^2}{GM}Kepler's third law

Waves

v=f\lambdawave speed
L=n\frac{\lambda}{2}standing wave, open at both ends
f=\frac{1}{T}frequency and period
L=(2n-1)\frac{\lambda}{4}standing wave, closed at one end
\frac{\sin i}{\sin r}=\frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}=\frac{n_2}{n_1}refraction
I\propto\frac{1}{r^2}inverse square law

Quantum theory

\lambda_{max}=\frac{b}{T}Wien's law
n\lambda=2\pi rstanding electron waves
E=hf=\frac{hc}{\lambda}photon energy
mvr=\frac{nh}{2\pi}angular momentum in the Bohr model
E_k=hf-Wphotoelectric effect
\lambda=\frac{h}{p}de Broglie wavelength
W=hf_0work function
\frac{1}{\lambda}=R\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)Rydberg formula

The Standard Model

B=n_b-n_{\overline{b}}baryon number from baryons
L=n_l-n_{\overline{l}}lepton number
B=\frac{1}{3}\left(n_q-n_{\overline{q}}\right)baryon number from quarks

Physical constants

QuantitySymbolValueUnit
specific heat capacity of iceci2.05×10³J kg⁻¹ K⁻¹
specific heat capacity of watercw4.18×10³J kg⁻¹ K⁻¹
specific heat capacity of steamcs2.00×10³J kg⁻¹ K⁻¹
latent heat of fusion for waterLf3.34×10⁵J kg⁻¹
latent heat of vaporisation for waterLv2.26×10⁶J kg⁻¹
electron volt1 eV1.60×10⁻¹⁹J
speed of light in a vacuumc3×10⁸m s⁻¹
atomic mass unit1 amu1.66×10⁻²⁷kg
mass of an alpha particlem_alpha6.6446572×10⁻²⁷kg
mass of an electronme9.1093835×10⁻³¹kg
mass of a neutronmn1.6749275×10⁻²⁷kg
mass of a protonmp1.6726219×10⁻²⁷kg
charge on an electrone-1.6×10⁻¹⁹C
Coulomb's constantk9×10⁹N m² C⁻²
magnetic permeability of free spaceμ04π×10⁻⁷T m A⁻¹
mean acceleration due to gravity on Earthg9.8m s⁻²
gravitational constantG6.67×10⁻¹¹N m² kg⁻²
mass of the EarthMEarth5.97×10²⁴kg
mass of the MoonMMoon7.35×10²²kg
mass of the SunMSun1.99×10³⁰kg
speed of sound in air at 25 °Cvs346m s⁻¹
Wien's displacement constantb2.898×10⁻³m K
Planck's constanth6.626×10⁻³⁴J s
Rydberg's constantR1.097×10⁷m⁻¹

When you get the book

Physics has a combination-response external examination worth 50% of your final result. The syllabus describes two written papers, and the QCAA states the conditions for each:

PaperPerusal timeWorking timeCalculatorBook
Paper 15 minutes90 minutesQCAA-approved graphics or scientific calculatorQCAA Physics formula and data book
Paper 25 minutes90 minutesQCAA-approved graphics or scientific calculatorQCAA Physics formula and data book

Each paper has a mix of question types on Units 3 and 4, from multiple choice to paragraph responses, and may show unseen graphs, tables or diagrams. See our QCE Physics guide for the course.

What is not in the Physics formula and data book

  • Definitions of the symbols. The book does not say that u is initial velocity, N is the number of turns or L is a length, so learn them.
  • Units for each equation. There are none beside the equations, only beside the constants.
  • Gravitational potential energy in orbit and escape velocity. Neither is listed.
  • Photon momentum and Compton scattering. The book has λ = h/p but no p = E/c line.
  • Lens and mirror formulas. Waves cover refraction and standing waves only.
  • Rearranged forms. Every line is written once.
  • Vector component rules. The projectile lines separate x and y but give no sine or cosine resolution of a launch velocity.

How to use the book in the exam

  1. Read the 5 minutes of perusal time for the question styles, not the book: you will find the equations faster once you know which ones the paper needs.
  2. Take every constant from the data pages. The book uses g = 9.8 m s⁻² and c = 3 × 10⁸ m s⁻¹ as printed, and your answer should do the same.
  3. Convert units before you substitute: eV to J, grams to kilograms, nanometres to metres.
  4. Write the number of significant figures the data justify, and include the unit.

Example 1: melting ice, then warming it

How much energy turns 0.50 kg of ice at 0 °C into water at 20 °C? Use the latent heat of fusion first, then the heat-capacity line with the specific heat capacity of water from the book:

Q=mL_f+mc_w\Delta T=0.50\times3.34\times10^{5}+0.50\times4.18\times10^{3}\times20=2.09\times10^{5}\ \text{J}

That is 167,000 J to melt the ice plus 41,800 J to warm the water. The melting needs four times as much energy as the warming. The Specific Heat Capacity Calculator handles the second step.

Example 2: time dilation

A spacecraft moves at 0.80c. A clock aboard it records 3.0 s between two events. The time measured by an observer at rest is given by the time-dilation line:

t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{3.0}{\sqrt{1-0.64}}=\frac{3.0}{0.60}=5.0\ \text{s}

Here t₀ is the time the clock on the spacecraft itself records, because that clock is present at both events. Mixing up t and t₀ is the commonest relativity error.

Example 3: photon energy

Green light has a wavelength of 500 nm. The photon energy line E = hc/λ gives:

E=\frac{hc}{\lambda}=\frac{6.626\times10^{-34}\times3\times10^{8}}{500\times10^{-9}}=3.98\times10^{-19}\ \text{J}

Dividing by 1.60 × 10⁻¹⁹ J per electron volt gives 2.48 eV. Practise this in the Light and Energy course.

Practise with the book open

Our Year 12 Physics daily paper is a short timed paper of 8 questions worth 25 to 35 marks. It is not a QCAA paper. Use it as a short mock with the book open and a calculator. Year 11 Physics covers the earlier units, and our HSC physics formula sheet guide shows how New South Wales differs.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. They show which line of the sheet each question wanted. We do not publish official answers, past paper answers or leaked papers.

Common questions

Do you get a formula sheet in QCE Physics?
Yes. The QCAA provides the Physics formula and data book in both external papers, according to the syllabus conditions.
Can I use a graphics calculator in QCE Physics?
Yes. The syllabus allows a QCAA-approved graphics or scientific calculator in both papers.
How long is each QCE Physics paper?
5 minutes of perusal time and 90 minutes of working time.
What constants does the book give?
Heat capacities, latent heats, the electron volt, c, particle masses, electron charge, Coulomb's constant, μ₀, g, G, masses of the Earth, Moon and Sun, the speed of sound, and the Wien, Planck and Rydberg constants.
Is the book the same each year?
It carries a version number: the one used here is version 1.3 for the 2025 syllabus.

Revision cards

Say the answer first, then flip the card to check it.

Where to go next

  • Solve it

    Specific Heat Capacity Calculator

    Work out heating energy and specific and latent heat

    Open the tool
  • Learn it

    Laws of Motion

    Newton's laws, momentum, and the forces that shape our world

    Start the course
  • Test it

    Year 12 Physics

    A new exam-style paper every day, with instant marking and a mark scheme

    Start today's paper
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