Boyle's Law Calculator

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.

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Solve for

Initial pressure P1

atm

Initial volume V1

Final pressure P2

atm

Final volume V2

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.

Related calculators

Charles's Law Calculator: solve for volume or temperature at constant pressure.
Combined Gas Law Calculator: solve for P, V, or T when all three change.
Ideal Gas Law Calculator: use PV = nRT to find pressure, volume, moles, or temperature.
Pressure Converter: convert between atm, kPa, Pa, bar, and psi.

Frequently asked questions

What is Boyle's Law?

Boyle's Law states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. If you double the pressure on a gas, its volume halves. The mathematical relationship is P1 times V1 equals P2 times V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. It applies to ideal gases and is a good approximation for real gases at moderate pressures.

What conditions does Boyle's Law assume?

Boyle's Law assumes that the amount of gas (number of moles) is constant and that the temperature does not change. These are isothermal (constant-temperature) conditions. It also assumes ideal gas behaviour, meaning gas molecules have no volume and no intermolecular forces. For real gases, Boyle's Law is a good approximation at low to moderate pressures and temperatures well above the boiling point of the gas.

How do you solve for V2 using Boyle's Law?

Rearrange P1V1 = P2V2 to isolate V2: V2 = (P1 times V1) divided by P2. For example, if P1 = 1 atm, V1 = 2 L, and P2 = 2 atm, then V2 = (1 times 2) divided by 2 = 1 L. You can solve for any of the four variables by rearranging the equation: P1 = P2V2/V1, V1 = P2V2/P1, and P2 = P1V1/V2.