GCSE Physics equations, explained

By The STEM-Tutor team · Updated October 2026

Knowing the GCSE Physics equations is only half the job. You also need the units and when each equation applies. Here they are, by topic.

Do you need to memorise them?

For GCSE Physics and Combined Science exams in 2025, 2026 and 2027, an equations sheet is provided in the exam, including the equations students previously had to recall. Arrangements for later years may differ, so check what your board provides for your exam year. Either way, you need to know what every symbol means, which equation fits each situation, and how to rearrange it.

Forces and motion

• weight = mass × gravitational field strength (W = mg): N, kg, N/kg
• resultant force = mass × acceleration (F = ma): N, kg, m/s²
• speed = distance ÷ time (v = s/t): m/s, m, s
• acceleration = change in velocity ÷ time (a = Δv/t)
• work done = force × distance (W = Fs): J, N, m
• momentum = mass × velocity (p = mv): kg m/s
• force = spring constant × extension (F = ke)
• moment = force × distance (M = Fd): N m
• pressure = force ÷ area (p = F/A): Pa

Energy

• kinetic energy = ½ × mass × speed² (E_k = ½mv²)
• gravitational potential energy = mass × g × height (E_p = mgh)
• elastic potential energy = ½ × spring constant × extension² (E_e = ½ke²)
• power = energy transferred ÷ time (P = E/t): W
• efficiency = useful output ÷ total input
• change in thermal energy = mass × specific heat capacity × temperature change (ΔE = mcΔθ)

Electricity

• charge = current × time (Q = It): C, A, s
• potential difference = current × resistance (V = IR): V, A, Ω
• power = potential difference × current (P = VI)
• power = current² × resistance (P = I²R)
• energy transferred = power × time (E = Pt)
• energy transferred = charge × potential difference (E = QV)

Matter and waves

• density = mass ÷ volume (ρ = m/V): kg/m³
• wave speed = frequency × wavelength (v = fλ): m/s, Hz, m

Tips for exam questions

1. Write the equation first, then substitute.
2. Convert to standard units: grams to kilograms, kilometres to metres, minutes to seconds.
3. Rearrange before substituting if you find it easier.
4. Give the unit with your answer.

See our GCSE Physics topics list for where each equation fits.

How to rearrange equations confidently

Many physics marks depend on rearranging an equation before you substitute numbers. The rule is simple: do the same to both sides. To make m the subject of W = mg, divide both sides by g to get m = W/g. For equations with a square, such as E_k = ½mv², do the inverse operations in reverse order: multiply by 2, divide by m, then take the square root, giving v = √(2E_k/m). Formula triangles work for simple equations, but learning to rearrange properly helps with harder ones.

Worked examples

Example 1: speed

A train travels 150 km in 2 hours. Find its average speed in m/s.

• 150 km = 150 000 m and 2 hours = 7200 s.
• v = s/t = 150 000/7200 ≈ 20.8 m/s. Converting units first is half the question.

Example 2: density

A block has mass 540 g and volume 200 cm³. Find its density in kg/m³.

• ρ = m/V = 540/200 = 2.7 g/cm³.
• 1 g/cm³ = 1000 kg/m³, so the density is 2700 kg/m³ (aluminium).

Example 3: rearranging kinetic energy

A 0.2 kg ball has 10 J of kinetic energy. Find its speed.

• v = √(2E_k/m) = √(20/0.2) = √100 = 10 m/s.

Example 4: wave speed

A wave has frequency 200 Hz and wavelength 1.7 m. Find its speed.

• v = fλ = 200 × 1.7 = 340 m/s, the speed of sound in air.

Example 5: pressure

A 600 N person stands on an area of 0.04 m². Find the pressure.

• p = F/A = 600/0.04 = 15 000 Pa.

Example 6: transformers (Higher, physics only)

A transformer has 100 turns on the primary coil and 2000 on the secondary. The input is 12 V. Find the output voltage.

• V_s/V_p = N_s/N_p, so V_s = 12 × 2000/100 = 240 V. It is a step-up transformer.

Example 7: specific latent heat

How much energy is needed to melt 0.5 kg of ice at 0 °C? (L = 334 000 J/kg)

• E = mL = 0.5 × 334 000 = 167 000 J. The temperature does not change while it melts.

Units and prefixes

Always convert to standard units before substituting: metres, kilograms, seconds, amps, volts and joules. Learn the common prefixes: kilo (k) means 1000, mega (M) means 1 000 000, milli (m) means 1/1000 and micro (μ) means 1/1 000 000. So 3 kW is 3000 W, 250 mA is 0.25 A and 2 MJ is 2 000 000 J. Many lost marks come from units rather than physics, so build this habit early.

Common mistakes

• Substituting before converting units, such as using grams or minutes.
• Forgetting to square the speed in E_k or to take the square root at the end.
• Writing an answer without a unit.
• Confusing the symbols, such as using s for speed instead of displacement.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Which equations are given on the equation sheet?

For GCSE exams in 2025, 2026 and 2027, an equations sheet is provided with the Physics and Combined Science papers, including the equations students previously had to recall. Check the arrangements for your exam year, and learn the equations anyway, because using it fluently saves time.

Should I use formula triangles?

They are fine for three-term equations like V = IR, but they do not work for equations with squares or more terms. Learn to rearrange properly too.

Key takeaways

• Convert to standard units before substituting.
• Rearrange using inverse operations, doing the same to both sides.
• Always include units in your answer.
• Know where every equation is on the sheet, and learn the common ones by heart.
• Practise with real exam questions, not just equations alone.

Where to go next

Use the equations in each topic.

• GCSE Physics forces
• GCSE Physics energy
• GCSE Physics electricity

A five-step method for every calculation

1. Write down the values given, with units.
2. Convert any units that are not standard.
3. Write the equation in symbols.
4. Rearrange, then substitute the numbers.
5. Write the answer with a unit and sensible rounding.

Following these steps every time makes your working easy to mark, earns method marks even after a slip, and helps you spot your own mistakes when you check. With practice, the steps become automatic.