Ideal Gas Law

Relate the pressure, volume, amount and temperature of a gas. Fill in any three and solve for the fourth, in the units you prefer.

Gas LawsThermodynamicsStoichiometry

Inputs

Click Solve next to the quantity you want to find: it moves into the result below. Then fill in the other three. Every field has its own unit.

Input examples

Pressure P

Volume V

Amount of gas n

Temperature T

What is an Ideal Gas?

An ideal gas is a model in which molecules are tiny points that only interact by bouncing off each other and the walls. Under everyday conditions real gases such as air, nitrogen and oxygen behave very close to this model.

The law combines three older discoveries: squeezing a gas raises its pressure (Boyle), heating it makes it expand (Charles), and equal volumes hold equal numbers of molecules (Avogadro). Temperature must always be in kelvin.

V ↓pressure rises

T ↑volume expands

1 mol, STPtakes 22.4 L

high P, low Treal gases deviate

Live Graph

isotherm

P against V at your temperature (Boyle’s law)

±50 K

your state

Result

Enter the values above

Gas Constant & Molar Volume

Quantity	Value
R (SI)	8.314 J/(mol·K)
R (litre·atm)	0.08206 L·atm/(mol·K)
R (litre·bar)	0.08314 L·bar/(mol·K)
R (litre·mmHg)	62.36 L·mmHg/(mol·K)
Molar volume at STP (0 °C, 1 atm)	22.414 L/mol
Molar volume at 25 °C, 1 bar	24.79 L/mol
Avogadro constant N_A	6.022×10²³ /mol

Related Gas Laws

Combined Gas Law

For a fixed amount of gas that changes from one state to another. Boyle’s, Charles’s and Gay-Lussac’s laws are special cases where one quantity stays constant.

Example:

Gas Density

Replace n by m/M to find the density of a gas from its molar mass. Heavier gases sink, which is why CO₂ collects at floor level.

Example:

Real Gases

The van der Waals equation corrects for attraction between molecules (a) and their own volume (b). It matters at high pressure or close to condensation.

Example: CO₂ at 50 bar deviates from the ideal law by roughly 10%.

Sources & Verification

References

S. S. Zumdahl & S. A. Zumdahl, Chemistry, 10th ed., Cengage, 2018 — Ch. 5 (Gases).
P. Atkins & J. de Paula, Atkins’ Physical Chemistry, 11th ed., Oxford University Press, 2018 — Focus 1 (Gases).
E. Tiesinga, P. J. Mohr, D. B. Newell & B. N. Taylor, “CODATA recommended values of the fundamental physical constants: 2018”, Reviews of Modern Physics 93, 025010 (2021) — values of the constants used.