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NCEA Level 3 Physics formula sheet (resource booklet)

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Formula sheet

The card below opens today's Level 3 Physics paper with the sheet in the drawer, so you practise the way you will sit the exam. The contents follow, grouped by standard in our own layout. NZQA prints the three standards as one block of formulae over two pages. This is the 2025 booklet, the latest NZQA has published. NZQA's 2026 specification lists the same three standards, so expect the same layout, but read the booklet in front of you in the exam.

Formula sheet

NCEA Level 3 Physics

Open formula sheet

Wave systems (91523)

d\sin\theta=n\lambdaDiffraction grating: slit spacing d, angle θ to the nth maximum
n\lambda=\frac{dx}{L}Two-slit pattern: slit spacing d, fringe distance x, screen distance L
f'=f\frac{v_W}{v_W\pm v_S}Doppler effect: observed frequency f′ from a moving source
v=f\lambdaWave speed
f=\frac{1}{T}Frequency and period

Mechanical systems (91524): linear motion, momentum and energy

F=maNewton's second law
p=mvMomentum
\Delta p=F\Delta tImpulse
\Delta E_p=mg\Delta hChange in gravitational potential energy
W=FdWork done
E_{\text{K(LIN)}}=\frac{1}{2}mv^2Linear kinetic energy
x_{\text{COM}}=\frac{m_1x_1+m_2x_2}{m_1+m_2}Centre of mass of two masses
F_g=\frac{GMm}{r^2}Gravitational force
F_c=\frac{mv^2}{r}Centripetal force

Mechanical systems (91524): rotation

d=r\thetaArc length
v=r\omegaSpeed on a circle
a=r\alphaTangential acceleration
\omega=\frac{\Delta\theta}{\Delta t}Angular velocity
\alpha=\frac{\Delta\omega}{\Delta t}Angular acceleration
\omega=2\pi fAngular velocity and frequency
f=\frac{1}{T}Frequency and period
E_{\text{K(ROT)}}=\frac{1}{2}I\omega^2Rotational kinetic energy
\omega_f=\omega_i+\alpha tFinal angular velocity
\theta=\frac{\omega_f+\omega_i}{2}tAngle turned, from the average angular velocity
\omega_f^2=\omega_i^2+2\alpha\thetaFinal angular velocity, without time
\theta=\omega_it+\frac{1}{2}\alpha t^2Angle turned, from the initial angular velocity
\theta=\omega_ft-\frac{1}{2}\alpha t^2Angle turned, from the final angular velocity
\tau=I\alphaTorque and angular acceleration
\tau=FrTorque from a force
L=mvrAngular momentum of a point mass
L=I\omegaAngular momentum

Mechanical systems (91524): oscillations

F=-kyHooke's law
E_p=\frac{1}{2}ky^2Elastic potential energy
T=2\pi\sqrt{\frac{l}{g}}Period of a pendulum
T=2\pi\sqrt{\frac{m}{k}}Period of a mass on a spring
y=A\sin\omega tDisplacement, starting from the centre
v=A\omega\cos\omega tVelocity, starting from the centre
a=-A\omega^2\sin\omega tAcceleration, starting from the centre
a=-\omega^2yAcceleration and displacement
y=A\cos\omega tDisplacement, starting from the maximum
v=-A\omega\sin\omega tVelocity, starting from the maximum
a=-A\omega^2\cos\omega tAcceleration, starting from the maximum

Electrical systems (91526): fields, capacitors and resistors

V=EdUniform electric field
\Delta E=VqEnergy change of a charge
E=\frac{1}{2}QVEnergy stored in a capacitor
Q=CVCharge on a capacitor
C=\frac{\varepsilon_0\varepsilon_rA}{d}Parallel plate capacitor
C_T=C_1+C_2+\ldotsCapacitors in parallel
\frac{1}{C_T}=\frac{1}{C_1}+\frac{1}{C_2}+\ldotsCapacitors in series
\tau=RCTime constant of an RC circuit
R_T=R_1+R_2+\ldotsResistors in series
\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\ldotsResistors in parallel
V=IROhm's law
P=VIPower

Electrical systems (91526): induction and alternating current

\phi=BAMagnetic flux
\varepsilon=-\frac{\Delta\phi}{\Delta t}Induced emf from changing flux
\varepsilon=-L\frac{\Delta I}{\Delta t}Induced emf in an inductor
\frac{N_p}{N_s}=\frac{V_p}{V_s}Transformer
E=\frac{1}{2}LI^2Energy stored in an inductor
\tau=\frac{L}{R}Time constant of an LR circuit
I=I_{\text{MAX}}\sin\omega tAlternating current
V=V_{\text{MAX}}\sin\omega tAlternating voltage
I_{\text{MAX}}=\sqrt{2}I_{\text{rms}}Peak and rms current
V_{\text{MAX}}=\sqrt{2}V_{\text{rms}}Peak and rms voltage
X_C=\frac{1}{\omega C}Capacitive reactance
X_L=\omega LInductive reactance
V=IZImpedance
f_0=\frac{1}{2\pi\sqrt{LC}}Resonant frequency
\omega=2\pi fAngular frequency
f=\frac{1}{T}Frequency and period

Useful data

The booklet ends with five constants:

QuantitySymbolValue
speed of lightc3.00 × 10⁸ m s⁻¹
charge on an electronq−1.60 × 10⁻¹⁹ C
acceleration due to gravity on Earthg9.81 m s⁻²
permittivity of free spaceε₀8.85 × 10⁻¹² F m⁻¹
universal gravitational constantG6.67 × 10⁻¹¹ N m² kg⁻²

What is not on the sheet

  • Linear equations of motion. The Level 3 sheet has the rotational versions, such as final angular velocity = initial angular velocity + αt, but not v = u + at or its relatives. The Level 2 sheet gives them, and NZQA does not repeat them at Level 3, so learn them.
  • Force laws for charges and currents. F = Eq, F = BIL and F = Bqv are not on it. NZQA does print them on the Scholarship Physics sheet, which makes their absence here easy to miss.
  • What the symbols mean and their units. The booklet gives bare formulae. Torque is τ, and so is a time constant, so you have to know which one a question wants.
  • Which formula to use, and how to rearrange it. Every formula is printed with one quantity alone on the left.
  • The physics itself. Marks for explaining resonance, superposition, why momentum is conserved or how a transformer works come from understanding, not from the sheet.

NZQA's 2026 specification adds that the acceleration due to gravity will be given as 9.81 m s⁻², that candidates need an approved calculator, a ruler and a protractor, and that a "show that" question needs unrounded values written down.

How to use the sheet in the exam

  1. Write down what the question gives, with units, and what it asks for.
  2. Find the standard's block on the sheet, then the line that holds exactly those quantities.
  3. Convert everything to SI before you substitute: nanometres to metres, millimetres to metres, revolutions to radians.
  4. Rearrange first, then substitute, and keep unrounded values until the last line.

Wave systems: two-slit fringes

Light of wavelength 600 nm passes through two slits 0.20 mm apart. The screen is 2.0 m from the slits. How far from the central bright fringe is the first bright fringe? The question gives a wavelength, a slit spacing and a screen distance, and asks for a fringe distance, so the line is the two-slit line, nλ = dx/L. Make x the subject:

x=\frac{n\lambda L}{d}=\frac{1\times600\times10^{-9}\times2.0}{0.20\times10^{-3}}=6.0\times10^{-3}\ \text{m}

That is 6.0 mm. The usual slip is to leave 600 nm and 0.20 mm in their own units, which gives an answer a factor of 1000 out.

Mechanical systems: a flywheel

A flywheel starts from rest and speeds up at 2.5 rad s⁻² for 8.0 s. Its moment of inertia is 0.40 kg m². How many radians does it turn through, and what is its rotational kinetic energy at the end? It starts from rest, so the initial angular velocity is 0. Use the angle line that has no final speed in it, then the final angular velocity line, then the energy line:

\theta=\omega_it+\frac{1}{2}\alpha t^2=0+\frac{1}{2}\times2.5\times8.0^2=80\ \text{rad}
\omega_f=\omega_i+\alpha t=0+2.5\times8.0=20\ \text{rad s}^{-1}\qquad E_{\text{K(ROT)}}=\frac{1}{2}I\omega^2=\frac{1}{2}\times0.40\times20^2=80\ \text{J}

Both come out at 80, in radians and joules. Do not let that fool you into thinking they are the same quantity. Practise choosing the line in our Laws of Motion course, then press Mark to check your answer there:

Choose the equation of motion that solves each problem.

Press Mark to have your answer marked in the Laws of Motion course.

The Level 3 sheet and the others

Each level has its own sheet. The Level 2 Physics sheet is a single sheet of 40 or so lines that includes linear motion and the lens equation. The Scholarship Physics sheet is the Level 3 content plus linear motion, the force laws for charges and currents, and modern physics: the photoelectric effect, mass-energy equivalence and the hydrogen energy levels. For how the three Level 3 standards work, see the NCEA Level 3 Physics guide.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. Sit the paper with the sheet open beside you, mark it, and the worked answers show which formula each question wanted. We do not publish official or past paper answers. Every question on the daily paper is our own.

Use the sheet with today's paper

Uni-Sine publishes a free daily paper on the NCEA Level 3 Physics track. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full NCEA exam, and it is not written by NZQA. Open the sheet from the paper itself, answer as if the clock is running, and mark it. The point is to find the right line quickly, because NZQA gives you formulae but never the choice of formula.

Common mistakes with the Level 3 Physics sheet

  • Assuming a formula is there. Check the booklet before the exam for the lines you rely on. Linear motion is the one that catches people.
  • Mixing up the two taus. Torque is τ = Iα or τ = Fr. The time constants are τ = RC and τ = L/R.
  • Using degrees for angular quantities. ω, α and θ in these formulae are in radians.
  • Rounding early. NZQA asks for unrounded values in "show that" questions.
  • Using the wrong g. Level 3 uses 9.81 m s⁻², and Level 2 uses 9.8.

Common questions

Do you get a formula sheet in NCEA Level 3 Physics?
Yes. NZQA supplies a Resource Booklet with the exam. It holds the formulae for 91523, 91524 and 91526 and five constants, and you may keep it after the exam.
When is the 2026 Level 3 Physics exam?
Thursday 12 November 2026, in the afternoon session, which starts at 2.00 pm. NZQA sessions last 3 hours and you should arrive at least 20 minutes early.
Is linear motion on the Level 3 Physics formula sheet?
No. The 2025 booklet has the rotational equations but not v = u + at or its relatives, so you need to know those.
What value of g does Level 3 Physics use?
NZQA's 2026 specification says g will be given as 9.81 m s⁻², and the booklet lists it as a constant.
Is the booklet different each year?
NZQA publishes one for each exam. The 2025 booklet is the latest published. Read the booklet you are given in the exam.

Revision cards

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

Where to go next

  • Solve it

    Pendulum and SHM Simulator

    Swing a pendulum and graph its displacement, velocity and acceleration

    Open the tool
  • Learn it

    Laws of Motion

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

    Start the course
  • Test it

    NCEA Level 3 Physics

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

    Start today's paper
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