What this calculator does
Boyle's law says that at constant temperature, squeezing a gas into half the volume doubles its pressure. The product of pressure and volume stays constant, which is why it is often written simply as p₁V₁ = p₂V₂.
It was one of the first quantitative gas laws established, and it is the special case of the ideal gas law with temperature and the amount of gas both held fixed.
The formula
Multiply the initial pressure by the initial volume, then divide by the final volume to get the final pressure. The relationship works equally in either direction.
| Term | Meaning |
|---|---|
| Isothermal | At constant temperature, which is the condition Boyle's law requires. |
| Inverse proportion | Pressure and volume move in opposite directions so that their product stays fixed. |
| Ideal gas | A gas whose molecules take up no space and do not attract each other, which real gases approximate at ordinary conditions. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial pressure (p1) (kPa) | The initial pressure, in kilopascals. |
| Initial volume (V1) (L) | The initial volume, in litres. |
| Solve for | Whether to solve for the final pressure or the final volume. |
| Known final value (V2 if solving p2; p2 if solving V2) (L or kPa) | The known final value: the volume if solving for pressure, or the pressure if solving for volume. |
When to use it
Understanding a syringe or a pump
Compressing a sealed volume raises its pressure in exact inverse proportion, which is how a bicycle pump works.
Diving physiology
A lungful of air at depth expands on ascent, which is why divers are trained never to hold their breath while surfacing.
Checking a gas calculation
When only pressure and volume change, this is the quickest route to the answer without the full gas law.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does pressure rise as the gas is compressed?
The same quantity of gas compressed into decreasing volumes.
| Final volume | Final pressure (p2) | p1·V1 = p2·V2 |
|---|---|---|
| 2 L | 101.325 kPa | 202.65 kPa·L |
| 1 L | 202.650 kPa | 202.65 kPa·L |
| 0.5 L | 405.300 kPa | 202.65 kPa·L |
| 0.25 L | 810.600 kPa | 202.65 kPa·L |
Questions
Why must temperature be constant?
Because compressing a gas normally heats it, which raises pressure further. Boyle's law isolates the volume effect alone, so it applies to slow compression where heat has time to escape.
Why do divers not hold their breath on ascent?
Because air in the lungs expands as pressure falls. A lungful taken at 10 metres would double in volume by the surface, which can rupture lung tissue if the breath is held.
How does this relate to the ideal gas law?
It is the same relationship with temperature and amount held constant. PV = nRT reduces to PV = constant when n and T do not change.
Does it work for real gases?
Closely, at ordinary pressures and temperatures. Deviations appear at high pressure and low temperature, where molecular volume and attraction stop being negligible.
For the full relationship including temperature, see the ideal gas law calculator. For molecular speeds in that gas, see the RMS speed calculator.