Last updated: 2026-06-16

The density of a gas is its mass per unit volume, and unlike a solid or liquid it changes dramatically with pressure and temperature because gases are so compressible. This calculator finds the density of an ideal gas from its pressure, molar mass, and temperature. It is used in stoichiometry, in comparing whether a gas will rise or sink in air, and in any setting where a gas must be weighed indirectly through its physical conditions.

From the ideal gas law to density

Begin with the ideal gas law, $PV = nRT$, and substitute the number of moles as mass divided by molar mass, $n = m/M$. Rearranging to mass per volume gives:

$\rho = \frac{m}{V} = \frac{PM}{RT}$

With pressure $P$ in atmospheres, molar mass $M$ in g/mol, temperature $T$ in kelvin, and $R = 0.08206\ \mathrm{L\cdot atm/(mol\cdot K)}$, the density comes out in grams per litre, which equals kilograms per cubic metre.

Worked example

Carbon dioxide ($M = 44.01\ \mathrm{g/mol}$) at standard temperature and pressure, $1\ \mathrm{atm}$ and $273.15\ \mathrm{K}$:

That is well above the density of air (about 1.29 g/L at the same conditions), which is why carbon dioxide pools in low-lying spaces.

Why density depends on conditions

Density is directly proportional to pressure and inversely proportional to absolute temperature. Compressing or cooling a gas packs the molecules closer and raises the density; heating it or dropping the pressure spreads them out. The molar mass sets the baseline: at a fixed temperature and pressure, every gas holds the same number of molecules per litre, so a heavier molecule means a denser gas. A useful shortcut at STP is that one mole occupies 22.41 litres, so $\rho = M/22.41$.

For the underlying relationship among pressure, volume, and temperature, see the Ideal Gas Law Calculator and the Combined Gas Law Calculator. Because lighter gases are less dense, they also effuse faster, as quantified by the Graham's Law of Effusion Calculator.