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PV = nRT

Ideal gas law calculator

Leave exactly one field empty. Enter pressure in atm, volume in litres, moles and temperature in kelvin, and the missing quantity is solved.

Short answer: PV = nRT. One mole of gas at 1 atm and 273.15 K occupies 22.41 L, which is the molar volume at STP and a good sanity check on any answer.

What each symbol means

P is pressure in atmospheres, V volume in litres, n the amount in moles and T the absolute temperature in kelvin. R ties the units together; changing any unit without changing R produces a number that is internally consistent and completely wrong.

Worked example

2 mol of gas at 1.5 atm and 300 K: V = nRT ÷ P = 2 × 0.082057 × 300 ÷ 1.5 = 32.8 L. Double the temperature at constant pressure and the volume doubles, which is Charles's law falling out of the same equation.

Ideal gas law questions

What is the ideal gas law?

PV = nRT, where P is pressure, V is volume, n is the number of moles, T is absolute temperature and R is the gas constant. Fill any three and the fourth follows, which is what this page does.

Which units does the calculator use?

Pressure in atmospheres, volume in litres, amount in moles and temperature in kelvin, with R = 0.082057 L·atm/(mol·K). If your data is in kPa or °C, convert first — mixing units is the most common source of a wrong gas-law answer.

Why must temperature be in kelvin?

Because the law is proportional to absolute temperature. Putting 25 °C into the formula gives 25 instead of 298.15 and an answer about twelve times too small. Add 273.15 to a Celsius reading before typing it in.

When does the ideal gas law fail?

At high pressure or low temperature, where molecules attract each other and take up volume. Steam near its boiling point, or gas in a nearly full cylinder, needs a real-gas equation such as van der Waals. At room conditions the ideal law is accurate to a fraction of a percent.

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Molarity calculatorMoles, mass and volume in solution.pH calculatorHydrogen-ion concentration and pH.Unit converterConvert pressure and volume units first.