Boyle's Law Calculator
Boyle's Law describes the inverse relationship between the pressure and volume of a gas at constant temperature. Established by Robert Boyle in 1662, it states that P1 x V1 = P2 x V2 at constant temperature and moles of gas. This fundamental gas law is applied in scuba diving (pressure at depth), respiratory physiology (breathing mechanics), pneumatic engineering, and chemistry laboratories to calculate how gas volumes change when pressurized or expanded. Enter any three of the four variables and the calculator solves for the fourth. Use consistent units throughout: the result is independent of which pressure or volume unit you choose, as long as both initial and final quantities use the same unit.
Boyle's Law formula
P1 * V1 = P2 * V2 (constant T and n)
P2 = P1 * V1 / V2
V2 = P1 * V1 / P2
Units: any consistent pressure and volume units
Boyle's Law applications
- Scuba diving: at 10 m depth, pressure doubles and lungs would halve in volume if breath is held.
- Breathing: diaphragm expands chest volume, lowering pressure below atmospheric, pulling air in.
- Syringe: pulling the plunger increases volume, decreasing pressure and drawing in fluid.
- Pressure cookers: sealed volume; temperature and pressure both rise together.
Boyle's Law: frequently asked questions
What is Boyle's Law?
Boyle's Law states that at constant temperature, the pressure and volume of a fixed amount of gas are inversely proportional: P1 * V1 = P2 * V2. If you halve the volume of a gas at constant temperature, the pressure doubles. This was established by Robert Boyle in 1662.
What are the conditions for Boyle's Law?
Boyle's Law applies to ideal gases at constant temperature (isothermal process) and fixed amount of gas (constant n). In practice, it works well for real gases at low to moderate pressures. At very high pressures or temperatures near the boiling point, gas behavior deviates from ideal.
How is Boyle's Law used in practice?
Boyle's Law underlies the operation of syringes, bicycle pumps, scuba diving physiology (pressure at depth), air compressors, and pneumatic tools. For scuba divers, doubling depth increases pressure by one atmosphere, halving the volume of any air space in the body.
How does Boyle's Law relate to the ideal gas law?
Boyle's Law is a special case of the ideal gas law PV = nRT with T and n held constant. The full ideal gas law also describes how temperature and amount of gas affect pressure and volume. Combining Boyle's, Charles', and Gay-Lussac's laws gives the combined gas law.
What units can I use for Boyle's Law?
Any consistent pressure units work (Pa, kPa, atm, psi, mmHg) and any volume units (L, mL, m^3, ft^3), as long as both sides of the equation use the same units. The ratio P1*V1 = P2*V2 is dimensionless, so unit consistency is all that matters.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.