Ideal gas law calculator (PV = nRT)

The gas constant is exact since 2019: R = NA x kB = 8.314 462 618 153 24 J/(mol K), with no measurement uncertainty at all.

Pressure

Volume

Temperature

Amount of gas

1mol

= Exact Ideal gas law

Molar volume at these conditions: 22.414 L/mol
Moles per cubic metre: 44.615 mol/m3
Temperature used: 273.15 K

Show the working

Pressure = 101 325
Volume = 22.414
Temperature = 0
Temperature used = 0 + 273.15 = 273.15
v_m3 = 22.414 / 1000 = 0.022 414
Amount of gas = 101 325 * 0.022 414 / (Rgas * 273.15) = 1
Molar volume at these conditions = Rgas * 273.15 / 101 325 * 1000 = 22.414
Moles per cubic metre = 101 325 / (Rgas * 273.15) = 44.615

Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.

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The formula

P V = n R T
n = P V / (R T)
R = NA x kB = 8.31446261815324 J/(mol K), exact

Temperature must be absolute. The calculator converts whatever you enter to kelvin before using it.

The molar volume of an ideal gas is 22.414 L/mol at 0 degrees Celsius and one atmosphere, and 24.055 L/mol at 25 degrees Celsius and 100 kPa, which is what IUPAC now calls standard.

Real gases deviate from this at high pressure and near condensation.

Frequently asked

What is the molar volume of a gas at STP?

22.414 litres per mole at 0 degrees Celsius and 101 325 Pa. Under the current IUPAC standard state of 100 kPa it is 22.711 L/mol.