Ideal Gas Law Calculator

Use the ideal gas law calculator to find the pressure, volume, and temperature of a gas.

Amount of gas1.000001 molPV ÷ RT — 602,214,894,258,503,225,966,592 molecules

Pressure101.325 kPa1 atm, 1.01325 bar

Volume22.414 litres

Temperature273.15 K0 °C — every gas law needs ABSOLUTE temperature, so Celsius cannot be substituted here

Molar volume22.414 litres/molat 0 °C and 1 atm this is 22.414 litres, the figure you may remember

Mass of gas28.9647 g

Density1.29226 kg/m³PM ÷ RT

Specific gas constant287.055 J/(kg·K)R ÷ M — 287.05 for air

RMS molecular speed485.002 m/s√(3RT/M)

Volume at the second state15.3099 litresP₁V₁/T₁ = P₂V₂/T₂ at 202.65 kPa and 373.15 K

Volume ratio0.68305×

Boyle's law alone (constant T)11.207 litresP₁V₁ = P₂V₂ — volume inversely with pressure

Charles's law alone (constant P)30.6197 litresV₁/T₁ = V₂/T₂ — volume directly with absolute temperature

Gay-Lussac's law (constant V)138.42 kPaP₁/T₁ = P₂/T₂ — pressure directly with absolute temperature

Compressibility factor Z1PV ÷ nRT — exactly 1 for an ideal gas. Real gases deviate below 1 where attraction dominates and above 1 at high pressure where molecular volume does

The formula

PV = nRT; and P₁V₁/T₁ = P₂V₂/T₂ between two states

Absolute temperature, without exception

The ideal gas law relates pressure, volume, amount and temperature, and the temperature must be absolute. Doubling from 10 °C to 20 °C does not double the volume — it raises it by about 3.5%, because 283 K to 293 K is a 3.5% increase. Substituting Celsius anywhere in these formulas produces answers that look reasonable and are wrong, and below 0 °C produces negative ones.

Boyle's, Charles's and Gay-Lussac's laws are not separate results; each is the combined law with one variable held fixed. All three are shown above so the relationship is visible rather than something to memorise separately.

The compressibility factor Z measures how far a real gas departs from ideal. It is exactly 1 for an ideal gas; real gases fall below 1 at moderate pressure, where intermolecular attraction pulls molecules together, and rise above 1 at high pressure, where the molecules' own volume becomes significant. Air near room conditions is within a fraction of a percent of ideal, which is why the approximation is so widely usable.