Boyle's Law describes one of the most fundamental properties of gases: at constant temperature, pressure and volume are inversely proportional. Squeeze a gas into half the space and the pressure doubles. Release it into twice the volume and the pressure halves. The relationship is captured in the equation P1 times V1 equals P2 times V2, where the subscripts 1 and 2 refer to the initial and final states of the gas. This law was established by Robert Boyle in 1662 through careful experiments and remains one of the three classical gas laws, alongside Charles's Law (which relates volume and temperature) and Gay-Lussac's Law (which relates pressure and temperature). Together they combine into the Combined Gas Law. In practice, Boyle's Law applies well to air, nitrogen, oxygen, and other common gases at everyday pressures and temperatures. It underpins the design of syringes, pumps, pistons, diving equipment, and countless other pneumatic systems. This calculator lets you solve for any one of the four variables. Choose which variable you want to find, enter the other three, and the calculator returns the missing value. You can work in atmospheres, kilopascals, or pascals for pressure, and in litres or cubic metres for volume. Keep your units consistent within a calculation.
Calculate.co.nz is proud to be partnered with Premium Homes, a recognised leader in eco-friendly, sustainable, and energy-efficient homebuilding. With a dedicated team and award-winning experience, they create homes that prioritise health, comfort, and long-term performance. Their founders, Andrew and Kelly, set out to raise the standard of residential construction in New Zealand by combining practical building expertise with a clear commitment to doing things better for homeowners.
atm
L
atm
L
1 L
solved variable
P1 × V12
P2 × V22
Pressure ratio P2/P12
Volume ratio V2/V10.5
Boyle's Law assumes ideal gas behaviour at constant temperature. Real gases deviate at high pressures or near their condensation point.
How it works
Boyle's Law states P1 × V1 = P2 × V2 at constant temperature. Rearranging: V2 = P1V1/P2, P2 = P1V1/V2, V1 = P2V2/P1, P1 = P2V2/V1. You select which variable to solve for, enter the other three values, and the calculator applies the appropriate rearrangement. The product P × V is constant for an ideal gas at constant temperature (isothermal process), so P1V1 and P2V2 are shown for verification. Pressure ratio and volume ratio confirm the inverse relationship.
Worked example
A gas starts at P1 = 1 atm and V1 = 2 L. The pressure is increased to P2 = 2 atm at constant temperature. Rearranging Boyle's Law: V2 = P1 × V1 / P2 = 1 × 2 / 2 = 1 L. The product P1V1 = 2 and P2V2 = 2 × 1 = 2, confirming the law holds. Pressure ratio is 2, volume ratio is 0.50. These match the default values pre-filled above.
