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Boyle’s law calculator
Thermal physics and gases
For a fixed mass of gas at constant temperature, pressure times volume stays constant.
p1 V1 = p2 V2
This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equationp1 V1 = p2 V2
- Rearrange to make p2 the subjectp2 = p1 V1 / V2
- Substitute the valuesp2 = (1 × 105) × (6 × 10−4) ÷ (2.5 × 10−4)
- Calculatep2 = 2.4 × 105 Pa
- Give the answer to 3 significant figuresp2 = 2.40 × 105 Pa
Worked example
Find p2, the final pressure. Given: initial pressure p1 = 1.00 × 10⁵ Pa; initial volume V1 = 6.00 × 10⁻⁴ m³; final volume V2 = 2.50 × 10⁻⁴ m³.
- Write the equationp1 V1 = p2 V2
- Rearrange to make p2 the subjectp2 = p1 V1 / V2
- Substitute the valuesp2 = (1 × 105) × (6 × 10−4) ÷ (2.5 × 10−4)
- Calculatep2 = 2.4 × 105 Pa
- Give the answer to 3 significant figuresp2 = 2.40 × 105 Pa
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| p1 | Initial pressure | Pa |
| V1 | Initial volume | m³ |
| p2 | Final pressure | Pa |
| V2 | Final volume | m³ |
Boyle’s law: rearranged
- To find initial pressure: p1 = p2 V2 / V1
- To find initial volume: V1 = p2 V2 / p1
- To find final pressure: p2 = p1 V1 / V2
- To find final volume: V2 = p1 V1 / p2
Exam tip
Use the same pressure unit and the same volume unit on both sides. Both pressures must be absolute pressures.
Common questions
What is the formula for boyle’s law?
The equation is p1 V1 = p2 V2, where p1 is the initial pressure (Pa); V1 is the initial volume (m³); p2 is the final pressure (Pa); V2 is the final volume (m³).
What units should I use for boyle’s law?
In SI units: initial pressure in Pa, initial volume in m³, final pressure in Pa, final volume in m³. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange p1 V1 = p2 V2?
Rearranging gives these forms: to find initial pressure: p1 = p2 V2 / V1. to find initial volume: V1 = p2 V2 / p1. to find final pressure: p2 = p1 V1 / V2. to find final volume: V2 = p1 V1 / p2.
Practise boyle’s law questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
More thermal physics and gases equations: Specific heat capacity, Specific latent heat, Ideal gas equation, Gas equation with molecules, Mean kinetic energy of a gas atom, Stefan–Boltzmann law, Wien’s law. See the full list on the physics equation calculator page.