Ideal Gas Law Calculator — pressure from PV = nRT

How it works

The ideal gas law ties together the four properties of a gas sample (OpenStax University Physics):

P × V = n × R × T

where P is pressure, V is volume, n is the amount of gas in moles, T is the absolute temperature in kelvin, and R is the universal gas constant. Using litre-atmosphere units, R = 0.082057 L·atm/(mol·K) (the same constant is 8.314 J/(mol·K) in SI). This calculator solves for pressure:

P = n × R × T ÷ V

Enter the amount in moles, the temperature in kelvin (not °C), and the volume in litres, and the pressure comes out in atmospheres. The relationship contains the familiar gas laws as special cases: at fixed temperature and amount, pressure and volume are inversely related (Boyle's law); at fixed volume, pressure rises in proportion to absolute temperature (Gay-Lussac's law). Real gases follow it closely at ordinary temperatures and low-to-moderate pressures, deviating when strongly compressed or near condensation.

Worked example

One mole of gas at standard temperature and pressure — 273.15 K in 22.4 L:

P = 1 × 0.082057 × 273.15 ÷ 22.4 ≈ 1.00 atm

This is exactly why 22.4 L is called the molar volume of an ideal gas at STP. Compress the same mole into 5 L and heat it to 300 K and the pressure jumps to about 4.9 atm.

Frequently asked questions

What is the ideal gas law?

It is the equation PV = nRT relating a gas's pressure, volume, amount and absolute temperature through the gas constant R. It models how an ideal gas responds when any of those quantities change.

What value of R should I use?

It depends on the units. With volume in litres and pressure in atmospheres, R = 0.082057 L·atm/(mol·K). In SI units (pascals and cubic metres) R = 8.314 J/(mol·K). This calculator uses the litre-atmosphere value.

Why must temperature be in kelvin?

The law uses absolute temperature, which starts at absolute zero. Celsius or Fahrenheit values can be zero or negative and would give wrong or impossible results, so always convert to kelvin (K = °C + 273.15) first.

How do I solve for volume or temperature instead?

Rearrange the same equation: V = nRT ÷ P, T = PV ÷ (nR), or n = PV ÷ (RT). This tool computes pressure; the others follow by algebra from the same three known quantities.

What is STP and the molar volume?

Standard temperature and pressure is 273.15 K and 1 atm. Under those conditions one mole of an ideal gas occupies about 22.4 litres — its molar volume — which is why that combination gives a pressure of essentially 1 atm here.

When does a real gas stop behaving ideally?

The ideal gas law assumes molecules have no volume and no attraction to one another. That holds well at low pressure and high temperature. At high pressure or near the point where a gas condenses into a liquid, those assumptions break down and real gases deviate noticeably from PV = nRT.