Molar gas constant, R

The constant in the ideal gas law, pV = nRT, and in every thermodynamic formula that works per mole. It has been exact since 2019, because it is the product of two constants that were fixed then.

In other units

Values marked … are exact, but their decimals run on, so they stop at ten significant figures instead of being rounded.

Where the value comes from

R is the Avogadro constant times the Boltzmann constant: k is the energy per particle per kelvin, and multiplying by the Avogadro constant scales it up to a mole. Both were fixed in 2019, so R has been exact since, and because both are short decimals their product ends after fifteen significant figures.

Before 2019 R was measured, most precisely from the speed of sound in a gas, and it carried an uncertainty in its sixth or seventh significant figure.

Which form to use

Choose the value whose units match the rest of the equation, so nothing needs converting afterwards: 8.314 with pascals and cubic metres, or with kilopascals and litres; 0.08206 with atmospheres and litres; 0.08314 with bar and litres; 62.36 with millimetres of mercury and litres.

For energy, as in ΔG° = −RT ln K or the Arrhenius equation, use 8.314 J/(mol·K), or 0.008314 kJ/(mol·K) when the energies are in kJ/mol.

The molar volume of an ideal gas follows from R: at 0 °C and 1 atm it is 22.414 L/mol, and at 0 °C and 1 bar, the standard pressure IUPAC has used since 1982, 22.711 L/mol.

Common mistakes

• Mixing the forms. 8.314 belongs with pascals and cubic metres, or kilopascals and litres; with atmospheres and litres R is 0.08206, and using the wrong one is out by a factor of 101.325.
• Treating millimetres of mercury and torr as the same unit to seven figures. The conventional millimetre of mercury is 133.322387415 Pa and the torr is 133.3223684… Pa, so R is 62.36358933… L·mmHg/(mol·K) against 62.36359822… L·Torr/(mol·K).
• Using the wrong calorie. Chemistry uses the thermochemical calorie, 4.184 J, which gives 1.987204 cal/(mol·K); the International Table calorie, 4.1868 J, gives 1.985875.
• Leaving the temperature in Celsius. The gas law needs kelvin, and 25 °C is 298.15 K, not 25.

Tools that use it

• Ideal Gas Law Calculator solves pV = nRT for whichever quantity is missing.
• Combined Gas Law Calculator reports the amount of gas, n = pV/RT.
• Heat Engine and Carnot Cycle Simulator uses it for the pressure, work and heat at each step of the cycle.
• Resting Membrane Potential Simulator uses it in RT/F, the scale of the Nernst and Goldman equations.
• Primer Tm Calculator uses it in cal/(mol·K), 1.9872, in the nearest-neighbour melting temperature Tm = ΔH°/(ΔS° + R ln(CT/4)).
• Photosynthesis Rate Simulator uses it in the Arrhenius terms for Rubisco and respiration, and to turn moles of oxygen into bubble volume.
• Galvanic Cell Simulator uses it in RT/F, which sets how far the voltage falls as the cell runs down.
• Arrhenius Equation Calculator turns the change in ln k between two temperatures into an activation energy.
• Gibbs Free Energy Calculator uses it in K = e^(−ΔG°/RT), the equilibrium constant a standard ΔG° implies.
• Diffusion and Osmosis Simulator gives each side’s osmotic pressure as cRT, and its water potential as minus that.
• Nernst Equation Calculator uses it in RT/nF, the size of the concentration correction in E = E° − (RT/nF) ln Q.

Related constants

• Boltzmann constant, k = 1.380649 × 10⁻²³ J/K
• Avogadro constant, N_A = 6.02214076 × 10²³ mol⁻¹
• Faraday constant, F = 96,485.33212… C/mol

See also

• The physical constants table, every constant side by side
• Pressure conversion table
• Energy conversion table
• Molar gas constant on Wikipedia

Source: BIPM, The International System of Units (SI Brochure), 9th edition. The same value in NIST’s CODATA listing.

The values are facts and free to use; this page’s selection and presentation are © 2026 ScienceQuest.