Boyle's law calculator

Squeeze a gas and it takes up less room, in exact proportion. This is the one gas law you cannot get wrong by using the wrong unit, which is precisely why it teaches nobody to check the others. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.

The unit cancels, and that is the whole character of it

Boyle's law is P₁V₁ = P₂V₂. Rearranged, the new volume is the old one times the ratio of the pressures — and a ratio of two pressures has no unit at all. As long as both are measured in the same thing, it cancels:

V₂ = V₁ × (P₁ ÷ P₂)

Pascals, atmospheres, psi, millimetres of mercury: every one gives the same answer. The selector on this page changes the labels and nothing else, which you can check by changing it.

That is a pleasant property and a bad teacher. Somebody who learns gases through Boyle's law never once has to think about units, and then meets Charles's law, where a temperature in Celsius gives nonsense, or the ideal gas law, where the constant itself changes with the units. Both of those are unforgiving in a way this one never is.

What has to stay constant

The temperature, and the amount of gas. Neither is usually true in practice: compressing a gas warms it, which is why a bicycle pump gets hot near the valve, and letting it expand cools it, which is how a refrigerator works. Boyle's law describes what happens once the heat has had time to leave again.

For a fast compression — a piston, a pump, a diesel engine — the gas has no time to lose that heat and the pressure rises faster than this page says. That is adiabatic compression, and it needs the heat capacity ratio of the particular gas: another measured constant per substance, and not something this page will invent.

Where it stops being true

At high enough pressure the molecules are close enough that their own volume matters, and the gas resists compression more than the law predicts. Push further and it condenses, at which point there is no gas law at all. Boyle's original experiments in 1662 used air in a J-shaped tube at a few atmospheres, which is comfortably inside the range where it holds.

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