Combined Gas Law Calculator

The combined gas law links the pressure, volume and temperature of a fixed amount of gas before and after a change. Enter five of the six values and this calculator solves for the sixth, converting every unit for you: pressure in kPa, atm, bar, psi or mmHg, volume in liters, milliliters or cubic meters, and temperature in Celsius, Fahrenheit or kelvin. It also tells you when your problem is one of the classic special cases, Boyle's, Charles's or Gay-Lussac's law, and shows how much each quantity changed.

It works for any gas that behaves close to an ideal gas, which covers air and most common gases at everyday pressures and temperatures.

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂

P is absolute pressure, V volume and T absolute temperature in kelvin; the subscripts mark the states before and after. The relation comes from the ideal gas law PV = nRT with the amount of gas n held fixed. When temperature does not change it reduces to Boyle's law, P₁V₁ = P₂V₂; at constant pressure to Charles's law, V₁ ÷ T₁ = V₂ ÷ T₂; and at constant volume to Gay-Lussac's law, P₁ ÷ T₁ = P₂ ÷ T₂.

A rising weather balloon. 10 L of gas at 1 atm and 25 °C rises to where the pressure is 50 kPa and the temperature −23 °C. Its volume becomes 16.99 L: the drop in pressure roughly doubles it, while the cold shrinks it a little.

A tire warming up. A tire at 200 kPa absolute and 20 °C heats to 50 °C on the road without changing volume. The pressure rises to 220.5 kPa, about 10% more.

A sealed syringe. Pushing the plunger from 20 mL to 10 mL at constant temperature doubles the pressure to 2 atm.

Heating at constant pressure. One liter of gas warmed from 0 °C to 100 °C expands to 1.366 L.

The gas laws describe proportions, so temperature has to be measured from absolute zero. Using Celsius gives nonsense: going from 20 °C to 100 °C would appear to multiply the volume by 5, when the real factor is 373.15 ÷ 293.15, about 1.27. Add 273.15 to a Celsius temperature to get kelvin; the calculator does this automatically. Pressures must likewise be absolute. A tire gauge reads pressure above the atmosphere, so add about 101 kPa (14.7 psi) to a gauge reading before using it in the formula.

Real gases depart from ideal behavior at high pressures and low temperatures, close to the point where they condense, because the molecules' own size and attractions start to matter. Steam near boiling and gases compressed to hundreds of atmospheres are typical cases; there the van der Waals equation or published property tables are more accurate. The law also assumes no gas leaks in or out. When the amount of gas changes, or you need the number of moles, use the ideal gas law calculator.

A bag of chips puffs up on a flight or a mountain drive because the outside pressure falls. A basketball left outside on a cold night feels flat because its pressure drops with temperature. Aerosol cans carry warnings against heat because the pressure inside rises as they warm, and scuba divers learn Boyle's law early, since air in the lungs expands as they rise toward the surface.