What Is Boyle's Law?

Boyle's Law, discovered by Robert Boyle in 1662, states that the pressure and volume of a fixed amount of gas are inversely proportional when temperature is held constant: P₁V₁ = P₂V₂. Squeeze a gas into half the space and its pressure doubles; let it expand into twice the space and the pressure halves.

The Mathematics

The product of pressure and volume is a constant for a given amount of gas at a fixed temperature. Given any three of P₁, V₁, P₂, V₂, the fourth is found by rearrangement: V₂ = P₁V₁ ÷ P₂ or P₂ = P₁V₁ ÷ V₂. This calculator lets you solve for either the final pressure or final volume.

Real-World Applications

Scuba divers experience Boyle's Law directly — pressure rises by roughly 1 atm per 10 meters of depth, compressing the air in their lungs and tanks. Syringes, bicycle pumps, and the intake stroke of engines all rely on the same principle. The chart above shows the characteristic hyperbolic curve of the pressure–volume relationship.