Ideal Gas Law Calculator PV=nRT

The ideal gas law is PV = nRT, where P is pressure (Pa), V is volume (m³), n is the number of moles, R is the universal gas constant (8.314 J/(mol·K)) and T is absolute temperature (K). It describes the behaviour of an ideal gas — one whose molecules have no volume and do not interact with each other.

The universal gas constant R = 8.314462618 J/(mol·K). It can also be expressed as 8.314 Pa·m³/(mol·K), 0.08206 L·atm/(mol·K) or 62.36 L·mmHg/(mol·K), depending on the unit system used.

The ideal gas law requires absolute temperature because at 0 K (absolute zero) the kinetic energy of molecules is zero and the gas volume theoretically reaches zero. Using Celsius would give incorrect results because 0 °C ≠ 0 K. Convert: K = °C + 273.15.

In SI units: pressure in pascals (Pa) and volume in cubic metres (m³). 1 atm = 101 325 Pa, 1 bar = 100 000 Pa, 1 litre = 0.001 m³. Make sure all inputs are consistent — mixing units leads to incorrect results.

At STP (0 °C = 273.15 K, 101 325 Pa), the molar volume of an ideal gas is approximately 22.414 litres per mole (0.022414 m³/mol). At SATP (25 °C = 298.15 K, 100 000 Pa), it is approximately 24.789 litres per mole.

The ideal gas law is a good approximation at low pressures and high temperatures, where intermolecular forces are negligible and the volume of molecules is small compared to the container. It breaks down near the condensation point of the gas, at very high pressures (above ~10 atm) or at very low temperatures. For real gases, use the van der Waals equation: (P + a·n²/V²)(V − nb) = nRT.

From the ideal gas law: n = PV/(RT). For example, if P = 200 000 Pa, V = 0.01 m³ and T = 300 K, then n = (200 000 × 0.01) / (8.314 × 300) = 2000 / 2494.2 ≈ 0.802 mol.

Boyle's law states that at constant temperature, the pressure and volume of a gas are inversely proportional: P₁V₁ = P₂V₂. This is a special case of the ideal gas law with n and T constant, so PV = nRT = constant.

Charles's law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature: V/T = constant. This follows from PV = nRT when P and n are fixed: V = (nR/P) × T.

Yes, but only under Dalton's law of partial pressures: each gas in a mixture behaves as if it were alone in the container. Enter the total pressure and the number of moles of the component of interest, or use partial pressures for individual gases.