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Ideal Gas Law Calculator

Solve the ideal gas law for pressure.

Result

4.923 atm

How it is calculated

The ideal gas law links the pressure, volume, amount and temperature of a gas: P V = n R T. This tool solves it for pressure: P = n × R × T / V. Here n is the amount of gas in moles, T is the absolute temperature in kelvin, V is the volume in litres, and R = 0.0820573 L·atm/(mol·K). With these units the pressure comes out in atmospheres (atm), rounded to three decimals. Volume must be greater than zero. The law treats gas molecules as points that do not attract each other, so it works well for gases at low pressure and fairly high temperature, and loses accuracy near condensation or at very high pressure.

Worked example

Take 2 mol of gas at 300 K in a 10 L container. Multiply: n × R × T = 2 × 0.0820573 × 300 = 49.234. Divide by the volume: 49.234 / 10 = 4.923 atm. To check the behaviour, halving the volume to 5 L would double the pressure to about 9.847 atm, while cooling the gas to 150 K would halve it.

Try this example →

Common mistakes

  • Entering the temperature in degrees Celsius; it must be in kelvin (add 273.15 to the Celsius value), otherwise the result is wrong.
  • Entering the volume in cubic metres or millilitres when the constant expects litres.
  • Using grams instead of moles; divide the mass by the molar mass first.
  • Reading the answer as pascals or bar when it is in atmospheres (1 atm is about 101,325 Pa).
  • Applying the law to a gas close to liquefying or at very high pressure, where real gases deviate from ideal behaviour.

About this calculator

This calculator solves the ideal gas law, PV = nRT, for pressure: P = nRT/V, where R is the universal gas constant, n is moles, T is temperature and V is volume. It's the equation of state that describes how an idealized gas behaves under most everyday conditions.

It's used by chemistry students working through gas-law problem sets, HVAC and refrigeration engineers estimating pressure changes in sealed systems, and scuba divers or gas-fill technicians working out expected tank pressure from a known fill volume and temperature.

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Comments (1)

  • Editorial team

    A quick benchmark: 1 mol at 273.15 K in 22.414 L should read about 1 atm, so if your setup is far from that you can see at a glance whether the answer is plausible. Pressure comes out in atmospheres; multiply by 1.01325 for bar or by 101.325 for kPa. The ideal model is unreliable at very high pressures, such as a full scuba cylinder at around 200 bar. What system are you working on, and what units are your inputs in?

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