Ideal gas law and combined gas law calculator

Choose the law and the unknown, then enter the other values in any of the listed units. Temperatures are converted to kelvin before any multiplication or division.

PV = nRT R = 8.314 462 618… J mol⁻¹ K⁻¹ (exact)

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ (fixed amount of gas)

Since the 2019 SI revision R is exact: it is the product of the exact Avogadro and Boltzmann constants. Inputs are converted to SI (Pa, m³, mol, K), solved, and converted back. The combined law follows from the ideal gas law with n fixed, so any pressure and volume unit works as long as both states use the same one; Boyle’s, Charles’s and Gay-Lussac’s laws are its special cases.

Limits

Real gases deviate from ideal behaviour at high pressure and near condensation (typically by less than 1 % for air, nitrogen or helium near room temperature and 1 bar, more for CO₂, ammonia or steam). Use a real-gas equation such as van der Waals for those conditions. Answers keep the significant figures of the least precise number you enter (at least 3, at most 6); counts and coefficients are exact and do not limit precision.

Worked example

One mole at 273.15 K and 1 atm (101 325 Pa) occupies V = 1 × 8.314 462 618 × 273.15 ÷ 101 325 = 0.022 414 m³ = 22.41 L, the CODATA molar volume. Combined law: 500 mL at 25.0 °C and 1.00 atm, compressed to 2.00 atm and heated to 100.0 °C, gives V₂ = 1.00 × 500 × 373.15 ÷ (298.15 × 2.00) = 313 mL.

References

• BIPM, The International System of Units (SI Brochure), 9th edition (2019), with the prefixes added by the 27th CGPM (2022)
• NIST CODATA 2022: molar gas constant
• NIST CODATA 2022: molar volume of ideal gas (273.15 K, 101.325 kPa)