Gas Density Calculator

About the Gas Density Calculator

The density of an ideal gas follows from the gas law: it is the pressure times the molar mass divided by the gas constant times the absolute temperature.

Enter pressure (Pa), molar mass (kg/mol, air is 0.02896, note kilograms) and temperature (K). R = 8.314 J/(mol·K). Density is returned in kg/m³.

How to use this calculator

1. Enter the gas pressure, using a consistent unit such as pascals.
2. Enter the molar mass of the gas, usually in g/mol or kg/mol, matching the gas constant units you plan to use.
3. Enter the temperature in kelvin, because the formula requires absolute temperature.
4. Click calculate to get the gas density . The result uses the same unit system implied by your inputs.

The formula explained

The formula computes the density of an ideal gas from its pressure , molar mass , temperature , and the gas constant . It shows that density increases with pressure and molar mass, and decreases as temperature rises.

• \(\rho\) = gas density
• \(P\) = pressure of the gas
• \(M\) = molar mass of the gas
• \(R\) = ideal gas constant
• \(T\) = absolute temperature in kelvin

Step by step method

1. Write the known values for , , and using compatible units.
2. Multiply pressure by molar mass to get the numerator, .
3. Multiply the gas constant by temperature to get the denominator, , then divide to find .

Worked example

Problem. Find the density of oxygen gas at a pressure of \(101325\,\text{Pa}\), molar mass \(0.032\,\text{kg/mol}\), and temperature \(300\,\text{K}\). Use \(R=8.314\,\mathrm{J/(mol}{\cdot}\mathrm{K)}\).

1. Substitute into \(\rho=\frac{PM}{RT}\): \(\rho=\frac{101325\times 0.032}{8.314\times 300}\).
2. Compute the numerator and denominator: \(101325\times 0.032=3242.4\), and \(8.314\times 300=2494.2\).
3. Divide: \(\rho=\frac{3242.4}{2494.2}\approx 1.30\,\text{kg/m}^3\).

Tips and common mistakes

• Use temperature in kelvin, not degrees Celsius, or the result will be wrong.
• Make sure your molar mass units match your choice of \(R\). For example, if \(R=8.314\,\mathrm{J/(mol}{\cdot}\mathrm{K)}\), use molar mass in \(\text{kg/mol}\) for density in \(\text{kg/m}^3\).

Frequently asked questions