Ideal Gas Law Calculator (PV = nRT)

The ideal gas law

The pressure, volume, amount and temperature of a gas are tied together by one relation:

P × V = n × R × T

P is absolute pressure (Pa), V volume (m³), n the number of moles, T the temperature in kelvin and R = 8.314462618 J/(mol·K) the universal gas constant. Knowing three of the four quantities gives the fourth.

Two things to watch

• Temperature must be in kelvin. K = °C + 273.15. Putting a Celsius value straight into the formula is the most common mistake. The calculator converts for you.
• Pressure must be absolute. A gauge shows pressure above atmospheric. A tyre reading 2 bar holds about 3 bar absolute.

Example

How much space does 1 mol of gas take up at 0 °C and 1 atm (101.325 kPa)? V = 1 × 8.314462618 × 273.15 / 101 325 = 0.022414 m³, or 22.4 litres. The value is the same whatever the gas.

Change of state

If the amount of gas in a closed container does not change, P₁ × V₁ / T₁ = P₂ × V₂ / T₂. The special cases are:

• At constant temperature, pressure and volume are inversely proportional (Boyle's law).
• At constant pressure, volume is proportional to absolute temperature (Charles's law).
• At constant volume, pressure is proportional to absolute temperature (Gay-Lussac's law).

Limits

The ideal gas law works well at low pressure and high temperature. The deviation grows as pressure rises and as the gas approaches its condensation point. For liquefied gases in cylinders, steam and refrigerants this calculation is not reliable. Pressure vessel design is not what this tool is for.