GCSE Physics Equations: Complete UK Formula Sheet With Worked Examples

Overview

Physics equations are not simply a list to memorise. In an exam, you must identify the physical quantities in a question, select a suitable relationship, convert the values into compatible units, substitute accurately, and give the answer in a sensible form. A correct formula with an incorrect unit conversion can still produce a wrong answer.

The equations below cover common GCSE topics. Some exam boards provide an equation sheet, while other equations or definitions may still need to be recalled. The exact presentation and required equations can vary between specifications and between foundation and higher content. For a board-specific comparison, see our guide to AQA, Edexcel, and OCR Physics.

Forces and motion

• Speed = distance ÷ time: v = s ÷ t. Speed is measured in metres per second (m/s), distance in metres (m), and time in seconds (s).
• Acceleration = change in velocity ÷ time: a = (v - u) ÷ t. Here, u is initial velocity and v is final velocity.
• Force = mass × acceleration: F = ma. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in m/s².
• Weight = mass × gravitational field strength: W = mg. Weight is measured in newtons and gravitational field strength in N/kg.
• Momentum = mass × velocity: p = mv. Momentum is measured in kg m/s.

Energy, work, and power

• Work done = force × distance: W = Fs, where the distance is measured in the direction of the force.
• Power = energy transferred ÷ time: P = E ÷ t. Power is measured in watts (W).
• Kinetic energy: Ek = ½mv².
• Gravitational potential energy: Ep = mgh, where h is the change in height.
• Elastic potential energy: Ee = ½ke², where k is spring constant and e is extension.

Electricity

• Charge = current × time: Q = It. Charge is measured in coulombs (C), current in amperes (A), and time in seconds.
• Potential difference = energy transferred ÷ charge: V = E ÷ Q.
• Power = potential difference × current: P = VI.
• Energy transferred = power × time: E = Pt.
• Resistance = potential difference ÷ current: R = V ÷ I.

Density, pressure, and waves

• Density = mass ÷ volume: ρ = m ÷ V. Use kg/m³ unless the question clearly uses another unit.
• Pressure = force ÷ area: p = F ÷ A. Pressure is measured in pascals (Pa).
• Pressure in a liquid: p = hρg, where appropriate to your specification.
• Wave speed = frequency × wavelength: v = fλ. Frequency is measured in hertz (Hz) and wavelength in metres.
• Magnification = image height ÷ object height: M = image height ÷ object height.

Equations are only part of GCSE physics revision. You also need definitions, graphs, practical methods, required precautions, and explanations of patterns. Our guide to substituting, rearranging, and checking units can be used alongside this formula sheet.

How to estimate

Use the same calculation routine for almost every GCSE physics equation. It reduces avoidable errors and gives you a clear method to show in a worked solution.

1. Identify the quantities. Underline the numbers and label what each one represents. For example, distinguish mass from weight and distance from displacement.
2. Write the equation before substituting. This demonstrates your method and makes rearrangement easier to check.
3. Rearrange if necessary. If the unknown is not already on its own, change the equation first.
4. Convert units. Change grams to kilograms, centimetres to metres, minutes to seconds, and millimetres to metres when required by the equation.
5. Substitute with brackets. This is particularly useful for negative values, powers, and numbers in standard form.
6. Check the magnitude and unit. Ask whether the result is physically plausible. A mass of 500 g should be entered as 0.500 kg when kilograms are required.
7. Round at the end. Keep extra digits during the calculation, then give the final result to a sensible number of significant figures.

For rearranging, imagine the equation as a balance. In F = ma, divide both sides by m to obtain a = F ÷ m, or divide by a to obtain m = F ÷ a. A formula triangle can help with simple relationships, but writing the algebra is safer for equations containing squares, fractions, or several terms.

Use your calculator’s brackets and powers carefully. For example, kinetic energy requires the velocity to be squared before multiplying by mass and one-half. It is not the same as (½m v)². If a value is given in standard form, enter the exponent using the calculator’s dedicated power-of-ten key where possible.

Inputs and assumptions

Before calculating, make a short input checklist:

• Unit system: use SI units unless instructed otherwise. Common conversions include 1 km = 1,000 m, 1 g = 0.001 kg, and 1 minute = 60 s.
• Direction: velocity, acceleration, force, and momentum can involve direction. Use signs consistently when a question describes opposite directions.
• Local gravitational field strength: use the value stated in the question. If none is given, follow your exam board’s convention or the value on the permitted equation sheet.
• Measured quantities: do not report more precision than the data supports. A measurement recorded to the nearest millimetre does not justify a long decimal answer.
• Graph values: read scales carefully and include units on axes. A gradient may have a compound unit, so do not label it automatically as m/s.
• Board requirements: check your current AQA, Edexcel, or OCR specification and exam materials. The presence of an equation on one board’s sheet does not guarantee identical treatment on another.

Where a question gives a value in centimetres cubed, remember that volume conversion is cubed too. For example, converting a length from centimetres to metres changes a volume by a factor of one million, not one hundred. This is a common source of density errors.

Worked examples

Example 1: acceleration

A cyclist increases velocity from 4 m/s to 10 m/s in 3 s. Calculate the acceleration.

Start with a = (v - u) ÷ t.

a = (10 - 4) ÷ 3 = 2 m/s²

The acceleration is 2 m/s². The subtraction matters because acceleration depends on the change in velocity, not simply the final velocity.

Example 2: kinetic energy

A 2.0 kg object travels at 5.0 m/s. Calculate its kinetic energy.

Ek = ½mv²

Ek = ½ × 2.0 × 5.0² = 25 J

The velocity is squared before the other operations are completed. The answer is 25 J.

Example 3: electrical energy

A component operates at 12 V with a current of 0.50 A for 60 s. Find the energy transferred.

First calculate power: P = VI = 12 × 0.50 = 6.0 W.

Then use E = Pt: E = 6.0 × 60 = 360 J.

The energy transferred is 360 J. You could also combine the relationships as E = VIt, provided the units remain consistent.

Example 4: density and conversion

An object has a mass of 0.60 kg and a volume of 200 cm³. Calculate its density in kg/m³.

Convert the volume first: 200 cm³ = 200 × 10-6 m³ = 0.000200 m³.

ρ = m ÷ V = 0.60 ÷ 0.000200 = 3,000 kg/m³.

The density is 3,000 kg/m³. Entering 200 as though it were 200 m³ would produce a meaningless result.

For longer written responses, show the relationship, substitutions, units, and conclusion. When an explanation is required as well as a calculation, use the calculation as evidence rather than stopping at the numerical answer. See how to answer GCSE Physics 6-mark questions for a structured approach to extended responses.

When to recalculate

Revisit this GCSE physics formula sheet whenever your school changes specification focus, your exam board publishes a new equation sheet, or you begin a new topic. Before the final revision period, compare the equations here with your board’s current official materials rather than relying on an older printed list.

Use this progress checklist each time you revise:

1. Tick the equations you can identify from a worded question.
2. Circle any equation you can use only when the unknown is already isolated.
3. Practise rearranging the circled equations without a formula triangle.
4. Complete one unit-conversion question for each major topic.
5. Attempt mixed physics exam questions without looking at the topic heading.
6. Review every lost mark: formula choice, rearrangement, conversion, arithmetic, unit, rounding, or explanation.

Return to the guide after each set of past-paper questions and update your checklist. The aim is not to memorise equations in isolation; it is to recognise the physical situation, choose a defensible model, calculate carefully, and communicate the result with a unit. For additional support with SI units and prefixes, use our quick-check guide to physics units and conversions.