What Are the Units for r? (Gas Constant)

This calculator works out the value of the ideal gas constant R (often just called “r”) for the units you choose, and it also converts between the two most common unit systems: joules per mole-kelvin (SI) and liter-atmospheres per mole-kelvin (metric but not SI). You enter a numeric value and pick the starting unit set, and you get back the equivalent value in the other set, plus the units written out in full. The answer to the headline question is: the units for r depend on the units of pressure, volume, amount, and temperature you are using – in SI it is J·mol�¹·K�¹, and in the common chemistry metric set it is L·atm·mol�¹·K�¹.

Formula

The ideal gas law is PV = nRT. Here:

• P = pressure (in pascals, Pa, or atmospheres, atm)
• V = volume (in cubic meters, m³, or liters, L)
• n = amount of substance (in moles, mol)
• T = absolute temperature (in kelvin, K)
• R = the ideal gas constant

To get the units of R, solve for R: R = PV / (nT). So the units are (pressure × volume) / (moles × temperature). That is why the units change when you change the pressure and volume units.

Worked Example

Using the default values: R = 8.314 (in SI units, J·mol�¹·K�¹). Convert to L·atm·mol�¹·K�¹.

1. Start with the SI value: 8.314 J·mol�¹·K�¹.
2. Multiply by the conversion factor 0.082057 L·atm / J (since 1 J = 9.8692×10�³ L·atm, so 1 J·mol�¹·K�¹ = 0.082057 L·atm·mol�¹·K�¹).
3. 8.314 × 0.082057 = 0.6823 L·atm·mol�¹·K�¹.

The calculator shows 0.6823, which matches the known value of R in those units (0.08206 L·atm·mol�¹·K�¹). The small difference is due to rounding the conversion factor.

Why Are There Different Units for r?

The ideal gas constant is a physical constant, but its numerical value depends on the units you measure pressure, volume, and energy in. Scientists use different unit systems for convenience. In SI, pressure is in pascals, volume in cubic meters, and energy in joules. In chemistry, it is often easier to use atmospheres and liters because gas volumes are commonly measured in liters and pressures in atmospheres. That gives R = 0.08206 L·atm·mol�¹·K�¹. Other common sets include:

• 8.314 J·mol�¹·K�¹ (SI)
• 0.08206 L·atm·mol�¹·K�¹ (chemistry metric)
• 62.36 L·torr·mol�¹·K�¹ (using torr for pressure)
• 1.987 cal·mol�¹·K�¹ (using calories for energy)

All these numbers represent the same physical constant, just in different units.

How to Choose the Right Units

When you use the ideal gas law, you must match the units of R with the units of P, V, n, and T. If you use R = 0.08206 L·atm·mol�¹·K�¹, then pressure must be in atm and volume in liters. If you use R = 8.314 J·mol�¹·K�¹, then pressure must be in pascals and volume in cubic meters. A common mistake is mixing units – for example, using pressure in atm with R in SI units. That gives a wrong answer by a factor of about 101.325. Always check that the units cancel out to give the desired result unit.

Common Mistakes and Misconceptions

• Mixing unit systems – using atm with J, or L with Pa. The value of R is only valid for the units it was defined with.
• Forgetting to convert temperature to kelvin – the gas law requires absolute temperature. Using Celsius or Fahrenheit gives a nonsensical result.
• Assuming R is always 0.0821 – that is only for L·atm. In SI it is 8.314.
• Rounding too early – using 0.082 instead of 0.08206 can change your answer by 0.1%, which matters in precise work.

Limits of the Ideal Gas Law

The ideal gas law assumes no intermolecular forces and that gas molecules occupy no volume. Real gases deviate from this at high pressure and low temperature. For many everyday calculations (like at room temperature and atmospheric pressure), the error is small – often less than 1%. But for accurate work with real gases, you might need the van der Waals equation or other corrections. The constant R itself is exact by definition in SI (8.314462618… J·mol�¹·K�¹), but the value you use depends on the units.

Frequently Asked Questions

Why is the gas constant called r?

The letter R comes from the French word “rapport” (ratio) or from the German “Regnault” after Henri Victor Regnault, who measured it experimentally. It is also sometimes called the universal gas constant because it is the same for all ideal gases.

What is the value of r in calories?

R = 1.987 cal·mol�¹·K�¹. This is useful when you are working with energy in calories, such as in some thermodynamic problems.

Does r change for different gases?

No, for an ideal gas R is the same for all gases. That is why it is called the universal gas constant. Real gases have slight deviations, but the constant itself does not change.

How do I convert between J and L·atm?

1 L·atm = 101.325 J. So to convert R from J·mol�¹·K�¹ to L·atm·mol�¹·K�¹, divide by 101.325. That gives 8.314 / 101.325 = 0.08206. The calculator uses this conversion.

What if I use pressure in torr?

Then R = 62.36 L·torr·mol�¹·K�¹. You can derive this by noting 1 atm = 760 torr, so 0.08206 × 760 = 62.36.

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in val | Value of R | - | 8.314 | 0
sel from | Starting units | SI (J/mol·K)=1, L·atm/mol·K=2 | 1 |
out conv | Converted value | - | if(from==1, val*0.082057, val/0.082057) | 4
out si | In SI units | J·mol�¹·K�¹ | if(from==1, val, val*8.314) | 3
out latm | In L·atm units | L·atm·mol�¹·K�¹ | if(from==2, val, val*0.082057) | 4