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Higher Physics formula sheet: the SQA relationships sheet and data sheet

Published 12 Nov 20266 min read

Higher Physics

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Formula sheet

The card below opens today's Higher Physics paper with the relationships sheet in the drawer. The contents follow in our own layout, grouped by topic. The sheet printed one continuous list in 2026, headed Paper 2, and it was the same as the 2025 sheet. Check it against the 2026 sheet before you rely on this page.

Formula sheet

Higher Physics

Open formula sheet

Equations of motion

d=vtdistance = speed × time

s=vtdisplacement = velocity × time

v=u+atfinal velocity

s=ut+\frac{1}{2}at^2displacement from initial velocity

v^2=u^2+2asvelocity from displacement

s=\frac{1}{2}(u+v)tdisplacement from average velocity

Forces, energy and momentum

W=mgweight

F=maforce

E_w=Fdwork done

E_p=mghgravitational potential energy

E_k=\frac{1}{2}mv^2kinetic energy

P=\frac{E}{t}power

p=mvmomentum

Ft=mv-muimpulse

F=\frac{Gm_1m_2}{r^2}gravitational force between two masses

Special relativity

t^{\prime}=\frac{t}{\sqrt{1-\left(\frac{v}{c}\right)^2}}time dilation

l^{\prime}=l\sqrt{1-\left(\frac{v}{c}\right)^2}length contraction

The expanding universe

f_o=f_s\left(\frac{v}{v\pm v_s}\right)Doppler effect for a moving source

z=\frac{\lambda_{\text{observed}}-\lambda_{\text{rest}}}{\lambda_{\text{rest}}}redshift from wavelengths

z=\frac{v}{c}redshift from speed

v=H_0dHubble's law

Photons and energy

E=mc^2mass-energy equivalence

E=hfphoton energy

E_k=hf-hf_0photoelectric effect

E_2-E_1=hfenergy level transition

Waves and optics

T=\frac{1}{f}period

v=f\lambdawave speed

d\sin\theta=m\lambdagrating equation

n=\frac{\sin\theta_1}{\sin\theta_2}refractive index

\frac{\sin\theta_1}{\sin\theta_2}=\frac{\lambda_1}{\lambda_2}=\frac{v_1}{v_2}refraction in terms of wavelength and speed

\sin\theta_c=\frac{1}{n}critical angle

I=\frac{k}{d^2}intensity and distance

I=\frac{P}{A}intensity and power

I_1d_1^2=I_2d_2^2inverse square law between two points

\text{path difference}=m\lambda\ \text{or}\ \left(m+\frac{1}{2}\right)\lambdapath difference for a maximum or minimum, m = 0, 1, 2 and so on

Electricity

V_{rms}=\frac{V_{peak}}{\sqrt{2}}root mean square voltage

I_{rms}=\frac{I_{peak}}{\sqrt{2}}root mean square current

Q=Itcharge

V=IRvoltage

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

R_T=R_1+R_2+\cdotsresistors in series

\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\cdotsresistors in parallel

E=V+Ire.m.f. and internal resistance

V_1=\frac{R_1}{R_1+R_2}V_svoltage across one resistor in a potential divider

\frac{V_1}{V_2}=\frac{R_1}{R_2}voltage ratio in a potential divider

C=\frac{Q}{V}capacitance

E=\frac{1}{2}QV=\frac{1}{2}CV^2=\frac{1}{2}\frac{Q^2}{C}energy stored in a capacitor

W=QVwork done moving a charge

Uncertainties

\frac{\text{max value}-\text{min value}}{\text{number of values}}random uncertainty

\Delta R=\frac{R_{max}-R_{min}}{n}the same, for a quantity R

Additional relationships

C=2\pi rcircumference of a circle

A=\pi r^2area of a circle

A=4\pi r^2area of a sphere

V=\frac{4}{3}\pi r^3volume of a sphere

\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}sine

\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}cosine

\tan\theta=\frac{\text{opposite}}{\text{adjacent}}tangent

\sin^2\theta+\cos^2\theta=1the link between sine and cosine

The last page of the sheet lists the electron arrangements of the elements. In the equations, a prime on t or l marks the moving frame in special relativity, and the subscript s in the Doppler equation is the source.

The data sheet

The course specification says a data sheet and a relationships sheet are provided. The data sheet is printed in the question paper. It gives constants such as the speed of light and Planck's constant, and values such as the refractive indices of materials, so check it before you decide that a value is missing.

What is not on the Higher Physics relationships sheet

Symbols and units. Nothing names the letters or gives the unit. You must know that p is momentum and that z has no unit.
Which equation to use. There are three ways to write power in electricity alone and several ways to write the speed of a wave. The sheet does not tell you.
Constants and data. These are on the data sheet.
Rules for circuits. The current rules for series and parallel circuits, and the voltage rules, are not printed.
Rearranging, and checking units. Each equation has one subject, so you do the algebra.
Definitions and explanations. The sheet has equations, not the physics. The marks for explaining the Doppler effect, the photoelectric effect or why a grating gives maxima are yours to earn.

How the paper uses the sheets

Higher Physics changes for 2027. The course specification, valid from session 2026 to 2027, gives a single question paper of 130 marks and 2 hours 30 minutes, in two sections: 20 marks of multiple choice and 110 of written answers. The data sheet and relationships sheet are provided. The assignment is 20 marks, scaled to 33. In 2026 there were two papers and the sheet was headed Paper 2, so check the 2027 sheet when it is published. In the 2027 timetable the exam is on Tuesday 4 May from 09:00 to 11:30 (Exam Timetable 2027, version 02). Our Higher Physics guide covers the course and the grades.

Using the sheets under exam pressure

List what you are given, with units, and what you are asked for.
Find the equation that holds exactly those quantities, and look at the data sheet for any constant.
Rearrange first, then substitute, and keep the working.
Give the answer to the right number of significant figures, with its unit.

Critical angle

Light travels in glass of refractive index 1.50 towards a boundary with air. Find the critical angle. From sin θc = 1/n,

\theta_c=\sin^{-1}\left(\frac{1}{1.50}\right)=41.8^\circ

Check it in the Refraction Calculator. Practise the related equations in the Light and Energy course, then press Mark.

Press Mark to have your answer marked in the Light & Energy course.

Time dilation

A spacecraft moves at 0.80c. A clock on board measures an interval of 6.0 µs. How long does an observer on Earth measure? The factor under the root is 1 − 0.80² = 0.36, so its root is 0.60:

t^{\prime}=\frac{t}{\sqrt{1-(v/c)^2}}=\frac{6.0}{0.60}=10\ \mu\text{s}

The time measured on Earth is longer, so the answer must be bigger than 6.0 µs. That is a quick check on the direction of the effect.

Internal resistance

A cell with e.m.f. 6.0 V and internal resistance 0.50 Ω supplies a current of 2.0 A. The terminal potential difference is the lost volts taken from the e.m.f.:

V=E-Ir=6.0-2.0\times0.50=5.0\ \text{V}

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 line each question wanted. We do not publish official or past paper answers.

Use the sheet with today's paper

Uni-Sine publishes a free daily paper for Higher Physics. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full SQA paper and not set by SQA. Many schools set a longer prelim in winter: see our prelims guide. Open the sheet, set a timer, and write the line you use at the start of each answer.

Common mistakes

Taking the wrong root in relativity. The factor is 1 − (v/c)², then the square root of it, and the moving clock shows the longer time.
Mixing up sign in the Doppler equation. The ± is − when the source approaches, which raises the observed frequency.
Leaving a ½ out of the capacitor energy. The three forms all start with ½.
Using n the wrong way up. n = sin θ1 ÷ sin θ2, with θ1 in the less dense medium.
Forgetting to look for the constant. Speed of light, h and the masses are on the data sheet.
Skipping units on random uncertainty. It has the same unit as the quantity.

Common questions

Do you get a formula sheet in SQA Higher Physics?

Yes. SQA provides a relationships sheet and a data sheet with the question paper.

What is on the Higher Physics relationships sheet?

Equations for motion, forces and energy, special relativity, the expanding universe, photons, waves and optics, electricity, capacitors and uncertainties, plus the circle, sphere and trigonometry relationships.

What is on the Higher Physics data sheet?

Constants and data for materials. It is printed in the question paper, separately from the relationships sheet.

Does the sheet give units or symbol names?

No. It gives the equations only.

Is the Higher Physics relationships sheet the same every year?

The 2026 sheet was the same as the 2025 sheet. The course has one question paper from 2027, so check the 2027 sheet when it comes out.

When is the Higher Physics exam in 2027?

Tuesday 4 May 2027, from 09:00 to 11:30.

Revision cards

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

Where to go next

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