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AQA GCSE Physics equation sheet (8463): every equation and how to use it

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Formula sheet

The card below opens today's Physics paper with this sheet in the drawer, so you practise the way you will sit the exam. The contents follow, grouped by topic in our own layout. AQA prints one continuous list, so check against the 2027 Physics Equations Sheet before you rely on anything here.

Formula sheet

GCSE Physics Foundation

Open formula sheet

Energy

E_k=\frac{1}{2}mv^2kinetic energy = ½ × mass × speed²
E_e=\frac{1}{2}ke^2elastic potential energy = ½ × spring constant × extension²
E_p=mghgravitational potential energy = mass × gravitational field strength × height
\Delta E=mc\Delta\thetachange in thermal energy = mass × specific heat capacity × temperature change
P=\frac{E}{t}power = energy transferred ÷ time
P=\frac{W}{t}power = work done ÷ time
\text{efficiency}=\frac{\text{useful output energy transfer}}{\text{total input energy transfer}}efficiency = useful output energy transfer ÷ total input energy transfer
\text{efficiency}=\frac{\text{useful power output}}{\text{total power input}}efficiency = useful power output ÷ total power input

Electricity

Q=Itcharge flow = current × time
V=IRpotential difference = current × resistance
P=VIpower = potential difference × current
P=I^2Rpower = current² × resistance
E=Ptenergy transferred = power × time
E=QVenergy transferred = charge flow × potential difference

Particle model of matter

\rho=\frac{m}{V}density = mass ÷ volume
E=mLthermal energy for a change of state = mass × specific latent heat
pV=\text{constant}for a gas, pressure × volume = constant

Forces and motion

W=mgweight = mass × gravitational field strength
W=Fswork done = force × distance along the line of action of the force
F=keforce on a spring = spring constant × extension
M=Fdmoment of a force = force × distance normal to the direction of the force
p=\frac{F}{A}pressure = force normal to a surface ÷ area of that surface
p=h\rho gpressure due to a column of liquid = height × density × gravitational field strength (Higher Tier only)
s=vtdistance travelled = speed × time
a=\frac{\Delta v}{t}acceleration = change in velocity ÷ time taken
v^2-u^2=2asfinal velocity² − initial velocity² = 2 × acceleration × distance
F=maresultant force = mass × acceleration
p=mvmomentum = mass × velocity (Higher Tier only)
F=\frac{m\Delta v}{\Delta t}force = change in momentum ÷ time taken (Higher Tier only)

Waves

T=\frac{1}{f}period = 1 ÷ frequency
v=f\lambdawave speed = frequency × wavelength
\text{magnification}=\frac{\text{image height}}{\text{object height}}magnification = image height ÷ object height

Magnetism and electromagnetism

F=BIlforce on a conductor at right angles to a magnetic field = magnetic flux density × current × length (Higher Tier only)
\frac{V_p}{V_s}=\frac{n_p}{n_s}potential difference across primary ÷ across secondary = turns on primary ÷ turns on secondary (Higher Tier only)
V_pI_p=V_sI_sprimary potential difference × primary current = secondary potential difference × secondary current (Higher Tier only)

What the letters stand for

The sheet does not name the symbols or give units. These are the ones the equations above use:

QuantitySymbolUnit
massmkilogram (kg)
speed, velocityv, umetre per second (m/s)
accelerationametre per second squared (m/s²)
force, weightF, Wnewton (N)
distance, extension, height, lengths, e, h, lmetre (m)
time, periodt, Tsecond (s)
energy, work doneE, Wjoule (J)
powerPwatt (W)
chargeQcoulomb (C)
currentIampere (A)
potential differenceVvolt (V)
resistanceRohm (Ω)
densityρkilogram per cubic metre (kg/m³)
pressureppascal (Pa)
momentumpkilogram metre per second (kg m/s)
spring constantknewton per metre (N/m)
specific heat capacitycjoule per kilogram degree Celsius (J/kg °C)
specific latent heatLjoule per kilogram (J/kg)
frequencyfhertz (Hz)
magnetic flux densityBtesla (T)

What is not on the equation sheet

  • Values. There are no constants or data on it: no gravitational field strength, no specific heat capacities, no specific latent heats. Any value you need has to come from the question, so read the question for it.
  • Units. The sheet shows none, and the specification expects equations to be used with standard SI units. Convert centimetres to metres, minutes to seconds and kilojoules to joules before you substitute.
  • Which equation to use. Power alone appears four times, as P = E/t, P = W/t, P = VI and P = I²R. The sheet will not tell you which one fits. Pick the line that holds the quantities the question gives you and the one it asks for.
  • Symbols for three equations. Efficiency, in both versions, and magnification are printed in words only. Write them out in words in your working.
  • Rearranging. Every equation is printed with one quantity on its own. If you need another, you rearrange it yourself.
  • Atomic structure and space physics. Nothing on the sheet belongs to Topic 4 or Topic 8, so those marks come from knowing the ideas, and from reading the data a question gives you.
  • Circuit rules. The sheet does not carry the rules for series and parallel circuits: the current is the same everywhere in a series circuit, and the potential differences across components add up to the supply.

Will the sheet change in 2027 and 2028?

For 2027 AQA says the sheets are unchanged from 2026, and the 2027 Physics sheet is headed "for use in June 2027 only". From 2028, for the life of the current GCSEs, Ofqual has told the boards to publish the sheets by 1 September the year before and to keep them consistent. It has also told them not to set questions that can be answered just by copying from the sheet. AQA says this applies to the standard-demand questions that currently ask you to write down the equation that links the quantities. Read AQA's announcement of 1 September 2026 for the detail.

How to use the equation sheet in the exam

  1. List what the question gives, with units, and what it asks for.
  2. Find the line on the sheet that holds exactly those quantities.
  3. Convert any units so they are all SI.
  4. Rearrange before you substitute, then write the numbers in.
  5. Check the size and the unit of your answer. Does it make sense?

Practise choosing the equation 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.

Both tiers: heating water

A kettle heats 0.80 kg of water from 20 °C to 65 °C. The question gives the specific heat capacity of water as 4200 J/kg °C. How much thermal energy does the water gain?

The question gives mass, specific heat capacity and two temperatures, and asks for energy, so the line to use is change in thermal energy = mass × specific heat capacity × temperature change.

\Delta E=mc\Delta\theta=0.80\times4200\times(65-20)=0.80\times4200\times45=151200\ \text{J}

That is 151 kJ, or 151,000 J to 3 significant figures. The common slip is to use 65 as the temperature change: Δθ is the change, 65 − 20 = 45 °C. Check it in the Specific Heat Capacity Calculator.

Both tiers: a stretched spring

A spring has a spring constant of 40 N/m and is stretched by 12 cm. How much energy does it store?

The sheet says elastic potential energy = ½ × spring constant × extension². Convert the extension first: 12 cm is 0.12 m.

E_e=\frac{1}{2}ke^2=\frac{1}{2}\times40\times0.12^2=0.288\ \text{J}

Using 12 instead of 0.12 gives 2,880 J, which is 10,000 times too big. The extension is squared, so a factor of 100 in the unit becomes a factor of 10,000 in the answer. Try it in the Hooke's Law Calculator.

Higher Tier: a transformer

A transformer steps 230 V down to 11.5 V. Its primary coil has 2000 turns. (a) How many turns does the secondary coil have? (b) The primary current is 0.40 A. What is the secondary current if no energy is lost?

(a) Use the turns ratio line, marked HT on the sheet:

\frac{V_p}{V_s}=\frac{n_p}{n_s}\quad\text{so}\quad\frac{230}{11.5}=\frac{2000}{n_s}\quad\text{and}\quad n_s=\frac{2000\times11.5}{230}=100

(b) With no energy lost, the power in equals the power out, which is the other transformer line:

V_pI_p=V_sI_s\quad\text{so}\quad230\times0.40=11.5\times I_s\quad\text{and}\quad I_s=\frac{92}{11.5}=8.0\ \text{A}

The voltage fell by a factor of 20 and the current rose by a factor of 20, so the power is the same. A step-down transformer trades voltage for current.

The AQA sheet and the other boards

Each board publishes its own sheet for its own papers, so use the one for the board on your exam paper. The Department for Education and Ofqual decision that you need not memorise the physics equations covers exams in 2025, 2026 and 2027, as AQA's announcement says. For Edexcel and OCR, the exam dates and the 2026 grade boundaries, see our GCSE 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 equation 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 GCSE Physics Foundation and GCSE Physics Higher. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full AQA paper, and it is not written by AQA. Open the sheet, set a timer and write the equation you use at the top of each answer. After marking, look at any question where you did not use the sheet, or used the wrong line.

Common mistakes with the equation sheet

  • Forgetting to square. Kinetic energy squares the speed, and elastic potential energy squares the extension.
  • Not converting units. Centimetres, grams, minutes and kilowatt hours all need converting to SI first.
  • Using the final temperature as the change. Use the difference.
  • Mixing up the two p equations. One is pressure and one is momentum.
  • Taking g from memory. Use the value the question gives.
  • Worrying about the HT lines on Foundation. If you sit the Foundation tier, you can ignore the six marked HT.

Common questions

Do you get an equation sheet in AQA GCSE Physics?
Yes. AQA says the Physics equations sheet is included with Physics (8463) papers 1 and 2, with the physics papers in Combined Science: Trilogy (8464) and with all four Combined Science: Synergy (8465) papers.
Is the 2027 AQA physics equation sheet different?
No. AQA says the sheets for 2027 are unchanged from 2026.
Do I need to memorise the GCSE Physics equations?
Not for exams in 2025, 2026 and 2027: the Department for Education and Ofqual decided that you do not have to, and the sheet is in the paper. Knowing the common ones still saves time, because the sheet does not say which to use.
Which equations on the AQA sheet are Higher Tier only?
Six: pressure due to a column of liquid (p = hρg), momentum (p = mv), force and change in momentum (F = mΔv/Δt), force on a conductor in a magnetic field (F = BIl), and the two transformer equations.
Does the AQA equation sheet give constants or units?
No. It lists equations only. Values such as gravitational field strength come from the question, and you must work in SI units.
Will there be an equation sheet after 2027?
Yes. Ofqual has set conditions for 2028 onwards that keep the sheets for the life of the current GCSEs, with a clean copy in every paper.

Revision cards

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

Where to go next

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    Specific Heat Capacity Calculator

    Work out heating energy and specific and latent heat

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  • Learn it

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  • Test it

    GCSE Physics Foundation

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