Values of the Gas Constant R
The universal gas constant R in every common unit: 8.314 J/(mol·K), 0.08206 L·atm/(mol·K), 62.36 L·Torr/(mol·K) and more, with how to pick the right one.
Values of the Gas Constant R
The most common mistake about the gas constant R is thinking it is a single number. It is not. R is a proportionality constant whose numerical value depends entirely on the units you choose for pressure, volume, amount and temperature. Use 8.314 J/(mol·K) when your pressure is in Pa and volume in m³. Use 0.08206 L·atm/(mol·K) when your pressure is in atm and volume in L. Pick the wrong one and you will get a number that looks right but means nothing. The molar gas constant R is exact since the 2019 SI redefinition at 8.314462618 J·mol⁻¹·K⁻¹ (NIST physics.nist.gov/cuu, CODATA 2018/2022). The table below gives the rounded values you will actually use.
R in SI Units
The fundamental SI value is 8.314462618 J·mol⁻¹·K⁻¹. For any student or engineer working in Pa and m³, this is the value to use. In practice, 8.314 J/(mol·K) is the standard rounded number for all coursework because input measurements rarely justify six significant figures. The same constant expressed in L·kPa is 8.314462618 L·kPa·mol⁻¹·K⁻¹. If your problem gives pressure in kPa and volume in L, use this directly, no conversion needed.
| Value | Units | Use When |
|---|---|---|
| 8.314 | J·mol⁻¹·K⁻¹ | Pressure in Pa, volume in m³ |
| 0.082057 | L·atm·mol⁻¹·K⁻¹ | Pressure in atm, volume in L |
| 62.3637 | L·mmHg·mol⁻¹·K⁻¹ | Pressure in mmHg (torr), volume in L |
| 0.083145 | L·bar·mol⁻¹·K⁻¹ | Pressure in bar, volume in L |
| 8.3145 | L·kPa·mol⁻¹·K⁻¹ | Pressure in kPa, volume in L |
| 1.986 | cal·mol⁻¹·K⁻¹ | Older thermochemistry problems |
| 10.731 | ft³·psi·lb-mol⁻¹·°R⁻¹ | Pressure in psi, volume in ft³, per pound-mole |
| 0.7302 | ft³·atm·lb-mol⁻¹·°R⁻¹ | Pressure in atm, volume in ft³, per pound-mole |
How to Choose R
Look at the units in your problem before you pick a value. If your pressure is in atm and your volume is in L, use R = 0.082057 L·atm·mol⁻¹·K⁻¹. If your pressure is in kPa and your volume is in L, use R = 8.3145 L·kPa·mol⁻¹·K⁻¹. If your pressure is in Pa and your volume is in m³, use R = 8.314 J·mol⁻¹·K⁻¹. The failure case: a student enters pressure in atm, volume in L, temperature in °C (not K), and uses R = 8.314. The answer will be off by a factor of roughly 101.3 because 1 L·atm = 101.325 J. Convert temperature to Kelvin first. Always.
R Per Lb-Mol for Engineering Units
Engineering in US customary units uses the pound-mole (lb-mol), not the gram-mole. The universal gas constant in these units is 10.731 ft³·psi·lb-mol⁻¹·°R⁻¹. A common error: a student uses R = 0.082057 (per gram-mole) with volume in ft³ and pressure in psi. The result will be off by a factor of 454 (grams per pound) times 14.696 (psi per atm), roughly 6670. If your problem gives pressure in psi and volume in ft³, you must use the lb-mol value. The R value for a mol (gram-mole) in ft³·psi is 0.73024 ft³·psi·mol⁻¹·°R⁻¹ (verify against a thermodynamics reference, as handbook values vary slightly).
R vs Specific Gas Constant (R/M)
The universal gas constant R applies to one mole of any ideal gas. The specific gas constant (often called R_specific) is R divided by the molar mass M of the gas: R_specific = R / M. For air, with M = 28.97 g/mol, R_specific = 8.314 / 0.02897 = 287 J·kg⁻¹·K⁻¹. Engineers use this form when working with mass flow instead of mole flow. Do not confuse them. The universal R belongs in PV = nRT. The specific version belongs in PV = mRT, where m is mass, not moles. Use the wrong one and your compressor design will fail.
Worked Example: Converting Units With R
Problem: 2.00 mol of nitrogen at 298 K occupies 24.5 L. What is the pressure in atm? Use PV = nRT. P = nRT / V = (2.00 mol × 0.082057 L·atm·mol⁻¹·K⁻¹ × 298 K) / 24.5 L = 48.9 / 24.5 = 2.00 atm.5 too high because 1 L·atm = 101.325 J. The failure mode is unit mismatch: using SI R with non-SI units.
Common Questions
What is the exact value of the gas constant R?
Since the 2019 SI redefinition, the molar gas constant R is exactly 8.314462618 J·mol⁻¹·K⁻¹ (CODATA 2018/2022). No uncertainty. The standard rounded value for student work is 8.314 J·mol⁻¹·K⁻¹.
Why is R not a single number in textbooks?
Because the numerical value depends on the units of pressure, volume, amount and temperature.They are the same constant, just expressed in different units.
How do I know which R value to use?
Match the units of your pressure and volume to the units in the R value. If pressure is in atm and volume in L, use 0.082057 L·atm·mol⁻¹·K⁻¹. If pressure is in Pa and volume in m³, use 8.314 J·mol⁻¹·K⁻¹. Always convert temperature to Kelvin first.
What is the difference between R and the specific gas constant?
The universal gas constant R applies to one mole of any ideal gas. The specific gas constant R_specific = R / M applies to one kilogram of a specific gas (M is molar mass in kg/mol). Engineers use R_specific for mass-based calculations like compressor work.
What happens if I use the wrong R value?
You will get a numerically correct but physically meaningless answer. For example, using 8.314 J/(mol·K) when pressure is in atm and volume in L will be off by a factor of 101.3. If you also mix lb-mol with g-mol, the error multiplies by 454.