Ideal Gas Law Calculator: Mass and Density

The mass and density of air or another common gas from its absolute pressure, volume and temperature.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

For a gas at moderate pressure the ideal gas equation p V = m R T links pressure, volume, mass and temperature. Each gas has its own specific gas constant R: 287 J/kg·K for air, 296.8 for nitrogen, 259.8 for oxygen, 188.9 for carbon dioxide, 4124 for hydrogen.

Use absolute pressure (gauge plus atmospheric) and absolute temperature (degrees Celsius plus 273.15). The equation is accurate for air and most gases near atmospheric pressure, and less so at high pressure or near condensation.

Formulas used

  • p V = m R T
  • \rho = \frac{p}{R T}

Worked example

With the default numbers in the calculator above:

  1. Absolute temperature: 298 K
  2. Mass of gas: 1.17 kg
  3. Density: 2.34 kg/m³

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Absolute or gauge pressure?

Absolute. A gauge reads pressure above atmospheric, so add about 101.3 kPa.

When is the ideal gas law not accurate?

At high pressure, near the temperature where the gas condenses, and for steam near saturation. Use the property tables for those.

What is the density of air?

About 1.2 kg/m³ at 20 degrees Celsius and sea-level pressure.

Related calculators

Further reading: Cengel and Boles, Thermodynamics: An Engineering Approach; Moran and Shapiro, Fundamentals of Engineering Thermodynamics.

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