Pressure and volume of a gas: pV = constant
For a fixed mass of gas at a constant temperature, pressure × volume = constant. In symbols, p V = constant, or p₁V₁ = p₂V₂ for a before and after. Pressure p is in pascals (Pa) and volume V is in cubic metres (m³). It is in the separate GCSE Physics courses of all three boards, and the exam sheet prints it.
Equation
p1 V1 = p2 V2
| Symbol | Quantity | Unit |
|---|---|---|
p1 | initial pressure | Pa |
V1 | initial volume | m³ |
p2 | final pressure | Pa |
V2 | final volume | m³ |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Given on the sheet | p V = constant |
| AQA Combined Science (8464) | Not in this specification | |
| Edexcel Physics (1PH0) | Given on the sheet | P1 V1 = P2 V2 |
| Edexcel Combined Science (1SC0) | Not in this specification | |
| OCR Gateway Physics A (J249) | Given on the sheet | p V = constant |
| OCR Twenty First Century Physics B (J259) | Given on the sheet | p V = constant |
Calculator: p1 V1 = p2 V2
Squash a gas and its pressure rises
Gas particles fly about and hit the walls of their container. Each hit is a small push, and all the pushes together make the pressure.
Squeeze the gas into half the space and the particles hit the walls twice as often. The pressure doubles. Let the gas spread into twice the space and the pressure halves. Pressure and volume move in opposite directions, and their product stays the same.
Put your finger over the end of a bike pump and push the handle. The air inside gets harder to squash as its volume shrinks. The push you feel on the handle is the pressure going up.
Conditions and board forms
Two things must stay fixed: the amount of gas and its temperature. If the gas warms up or leaks, the equation no longer applies.
- AQA Physics (8463): p V = constant.
- Edexcel Physics (1PH0): P₁V₁ = P₂V₂, with a capital P for pressure.
- OCR Gateway (J249) and OCR Twenty First Century (J259): p V = constant.
No board marks it as Higher tier. It is physics-only content: AQA Combined Science Trilogy (8464) and Edexcel Combined Science (1SC0) leave it out. The specifications place it with the equations you select and apply, and each exam from 2025 gives you a printed sheet with it. See the Edexcel equation list or the OCR Twenty First Century list.
Working with before and after
Most questions give a starting pressure and volume, then change one of them. Write p₁V₁ = p₂V₂ and put in the three values you know.
Volume units cancel, so cm³ on both sides works fine as long as you use the same unit twice. The same is true for kPa. Give the answer in the unit the question asks for.
Pressure also comes up with solids and liquids. For a force on an area, see the pressure equation. For the pressure under water, see the liquid pressure equation.
Worked examples
p
- Change the pressure to pascals: 100 kPa = 100 000 Pa
- p₂ = p₁V₁ ÷ V₂
- p₂ = 100 000 × 60 ÷ 20
- p₂ = 300 000 Pa
300 000 Pa
V
- Both pressures are in kPa, so the units cancel
- V₂ = p₁V₁ ÷ p₂
- V₂ = 100 × 4 ÷ 25
- V₂ = 16 m³
16 m³
Common mistakes
- Dividing the wrong way. If the volume gets smaller, the pressure must get bigger, so check your answer goes the right way.
- Using it when the temperature changes. Warming a gas raises its pressure on its own, so this equation no longer holds.
- Mixing kPa on one side with Pa on the other. Use one unit on both sides of p₁V₁ = p₂V₂.
- Adding pressure and volume. It is their product that stays constant, so multiply them.
Rearrange p₁V₁ = p₂V₂ for any one value in the Equation Rearranger.
Questions people ask
Is this Boyle's law?
Yes. Many textbooks call it Boyle's law, after the scientist Robert Boyle. The name and the equation describe the same relationship.
Why does a balloon grow as it rises?
The air pressure outside falls with height. The gas inside pushes out until its pressure matches, so its volume grows. If the temperature stayed the same, pV = constant would tell you by how much.