Ideal Gas Law Calculator — PV = nRT

One mole of any gas at 0 °C and one atmosphere fills 22.4 litres. Helium, carbon dioxide and air all behave the same, and that single fact is the ideal gas law, PV = nRT. Choose which of pressure, volume, amount or temperature you want. Fill in the other three in whatever units the problem uses, whether atmospheres, psi, kilopascals, litres, cubic feet, moles, grams, Celsius, Fahrenheit or kelvin, and the calculator solves for the fourth.

Along with the answer it shows the whole state in the other common units, the molar volume and the gas density. Pick the gas from the list to enter its amount in grams instead of moles.

Worked Example: One Mole at Standard Temperature and Pressure

The calculator opens solving for volume with 1 atm, 1 mol and 0 °C. It reports:

• Volume: 22.414 L, the molar volume at STP from V = nRT ÷ P
• The same state as 101.33 kPa, 14.696 psi, 273.15 K and 0.79154 ft³
• Density of dry air: 1.2923 g/L, from the 28.965 g/mol molar mass

Load Sample moves on to 2 mol squeezed into 10 L at 25 °C (495.79 kPa), 5 L of carbon dioxide at 200 kPa and 300 K (17.644 g), and 5 mol in 2 ft³ at 30 psi, which works out at 8.6305 °C.

How the Math Handles the Units

Every value is converted to SI first: pascals, cubic metres, moles and kelvin. The equation is rearranged for the unknown, and the answer is converted back into the unit chosen for its box. R is 8.314462618 J/(mol·K), an exact value since the 2019 SI redefinition. Celsius and Fahrenheit are offset scales, so they are shifted to kelvin before anything is multiplied. A temperature at or below absolute zero is refused with “Temperature must be above absolute zero (0 K, −273.15 °C, −459.67 °F).” Switch Solve for and the answer you already have is written into its box, so the other numbers stay put.

Accuracy: When Real Gases Stop Being Ideal

The law assumes molecules take up no room and do not attract one another. That holds well for air, nitrogen and helium near room conditions, where the error is under 1%. It drifts as a gas is squeezed or cooled toward the point where it would condense. The tool warns above 1 MPa (about 10 bar) and below 150 K, where a real-gas equation such as van der Waals is the better tool. Results are shown to five significant figures.