Pressure Volume Calculator
Find a gas's new volume using Boyle's law.
Results update as you type.
How it works
Boyle's law describes how the volume of a fixed amount of gas responds to a change in pressure at constant temperature, and this pressure volume calculator applies it to find the new volume from an initial pressure, an initial volume, and a final pressure. Squeeze a gas harder and it shrinks; ease the pressure and it expands, always so that pressure and volume trade off in exact proportion. It is the principle behind a syringe, a bicycle pump, and the way your lungs draw air. This relationship matters in chemistry, medicine, diving, and engineering alike. Anaesthetists track gas volumes as pressures change, divers must understand how air in their lungs and equipment behaves at depth, and engineers designing pneumatic systems rely on it constantly. Because pressure and volume are inversely linked, the calculator lets you predict one from the other without repeatedly rearranging the equation by hand. The law works because, at a fixed temperature, squeezing a gas into a smaller space makes its molecules strike the walls more often, raising the pressure in exact inverse proportion to the volume. Students, divers, and lab technicians use a pressure volume calculator to model how gases behave under changing pressure and to solve Boyle's law problems quickly and reliably.
P₁ × V₁ = P₂ × V₂
Boyle's law states that pressure times volume stays constant for a fixed amount of gas at constant temperature, so the initial pressure times the initial volume equals the final pressure times the final volume. Rearranging gives the new volume as the initial pressure times the initial volume, divided by the final pressure. Pressure and volume are inversely proportional, because compressing a gas into less space makes its molecules collide with the walls more often.
Source:Standard physics (Boyle's law)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter initial pressure, initial volume and final pressure.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
New volume updates instantly as you type — no button to press.
Frequently asked questions
What units should I use for pressure and volume?
You can use any units you like for pressure and volume, as long as you are consistent, because Boyle's law depends only on ratios. If the two pressures are in atmospheres and the initial volume is in litres, the new volume comes out in litres. Common choices are atmospheres, pascals, or bar for pressure and litres or cubic metres for volume; just keep both pressures in the same unit.
Does temperature need to stay constant?
Yes. Boyle's law only holds when the temperature and the amount of gas stay fixed. If the temperature changes as well, you need the combined gas law or the ideal gas law, which account for temperature and moles too. In practice, keep the process slow enough for heat to equalise, or ensure the gas returns to the same temperature, so that pressure and volume trade off cleanly as the law assumes.
Why are pressure and volume inversely related?
At a constant temperature, the gas molecules move at the same average speed no matter the container size. Compressing the gas into a smaller volume packs the molecules closer, so they strike the walls more frequently and the pressure rises. Expanding the gas does the opposite. This trade-off keeps the product of pressure and volume constant, which is exactly what Boyle's law expresses in a single simple equation.
What does the example with 2, 3, and 6 show?
Starting with a pressure of 2 and a volume of 3, the product is 6. Raising the final pressure to 6 forces the volume down to 1, because 6 times 1 also equals 6, keeping the pressure-volume product constant. Tripling the pressure has cut the volume to a third, a clear illustration of the inverse relationship at the heart of Boyle's law.
Where does Boyle's law apply in real life?
Boyle's law appears wherever gases are compressed or expanded at steady temperature. It explains how a syringe draws fluid, how a bicycle pump forces air into a tyre, and how scuba divers must exhale as they rise so expanding lung air does not injure them. Weather balloons, pneumatic tools, and internal combustion engines all rely on the same predictable trade-off between a gas's pressure and its volume.