Boyle's Law Calculator - Gas Pressure

Boyle's law describes the isothermal behaviour of a fixed quantity of gas: when temperature and the number of moles are held constant, the product of absolute pressure and volume stays constant, so P1V1 = P2V2. This calculator simply rearranges that identity into V2 = P1V1 / P2, which is why the answer depends only on the ratio P1/P2 and never on which unit you pick, provided both pressures use the same absolute scale and both volumes use the same volume unit. The relation drops straight out of the ideal gas law PV = nRT: fixing n, R and T leaves PV equal to a constant. Physically, halving the volume packs the same molecules into half the space, doubling the number of wall collisions per unit area per second, and therefore doubling the pressure. Two cautions dominate practical use. Pressure must be absolute, not gauge. A tyre gauge reading 30 psi is really about 44.7 psi absolute, and feeding the gauge number into P1V1 = P2V2 gives a badly wrong volume. Real gases also depart from the ideal curve at high pressure and near their condensation point, where intermolecular attraction and the finite size of molecules both matter. Plotting P against V yields a hyperbola, while plotting P against 1/V yields a straight line through the origin; that straight-line test is the standard laboratory check for ideal behaviour. Finally, the compression must be slow enough for heat to leave the sample, otherwise the process is adiabatic rather than isothermal and the gas warms as it is squeezed.

Robert Boyle published the pressure-volume relation in 1662, in the second edition of New Experiments Physico-Mechanicall, Touching the Spring of the Air, and its Effects. Working in Oxford with his assistant Robert Hooke, who built the improved air pump the work required, Boyle sealed a pocket of air in the short closed arm of a J-shaped glass tube and poured mercury into the long open arm. As mercury piled up, the trapped column shortened, and his readings showed volume shrinking in the same proportion as pressure grew. Boyle described the effect as the spring of the air. He was among the founding figures of the Royal Society of London, which received its royal charter that same year. Credit for the discovery is genuinely shared. Richard Towneley and Henry Power had put the same proportionality to Boyle before publication, and Boyle acknowledged them, which is why the result is occasionally called Towneley's hypothesis. Across France and much of continental Europe it is instead known as Mariotte's law, after Edme Mariotte, who published his own account in 1679 and made explicit the condition Boyle had left implicit: the temperature must not change. The complementary volume-temperature relation came from Jacques Charles and Joseph Louis Gay-Lussac around 1800, and in 1834 Emile Clapeyron folded the separate gas laws into the single equation of state now written PV = nRT.