What this calculator does
The gas constant most people meet first is the universal gas constant, R, a single fixed value of 8.314462618 J/(mol·K) that applies to every ideal gas because it is written in terms of moles rather than mass. The specific gas constant restates that same relationship per unit of mass instead of per mole, and its value is different for every gas, since it depends on how much a mole of that particular gas weighs.
This calculator divides the universal gas constant by a gas’s molar mass to get its specific gas constant, in joules per kilogram-kelvin. Air, the default here, works out to about 287 J/(kg·K), a figure widely used in engineering because it lets the ideal gas law be applied directly to a mass of gas rather than a mole count.
The formula
The specific gas constant is the universal gas constant divided by molar mass, with molar mass converted from grams per mole to kilograms per mole first, since the universal constant is defined in moles and the specific constant is defined per kilogram.
| Term | Meaning |
|---|---|
| R (universal) | The universal gas constant, 8.314462618 J/(mol·K), the same fixed value for every ideal gas. |
| R_specific | The gas constant per unit mass for one particular gas: R ÷ molar mass, different for every gas. |
| Molar mass | The mass of one mole of the gas, in grams per mole; also called molecular weight. |
The inputs explained
| Field | What to enter |
|---|---|
| Molar mass of the gas (g/mol) | The molar mass of the gas in grams per mole. Common values: air ≈ 28.97, nitrogen ≈ 28.01, oxygen ≈ 32.00, carbon dioxide ≈ 44.01, hydrogen ≈ 2.016, helium ≈ 4.003. |
When to use it
Applying the ideal gas law to a mass of gas
Engineering forms of the ideal gas law are often written as PV = mR_specific T, using a mass in kilograms directly rather than converting to moles first, which needs the specific gas constant for whichever gas is involved.
Comparing gases of different molecular weight
Lighter gases have larger specific gas constants: hydrogen’s is more than fourteen times air’s, because the same universal constant is divided by a much smaller molar mass.
Working with compressible-flow or thermodynamics formulas
Many compressible-flow relationships, including the speed of sound in a gas, use the specific gas constant of the working fluid rather than the universal constant, so it is worth having on hand for that specific gas.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the specific gas constant changes with molar mass
A range of common gases, from lightest to heaviest.
| Molar mass | Specific gas constant |
|---|---|
| 2.016 g/mol | 4,124.24 J/(kg·K) |
| 4.003 g/mol | 2,077.06 J/(kg·K) |
| 16.04 g/mol | 518.36 J/(kg·K) |
| 28.97 g/mol | 287.00 J/(kg·K) |
| 32 g/mol | 259.83 J/(kg·K) |
| 44.01 g/mol | 188.92 J/(kg·K) |
Questions
What is the specific gas constant of air?
Using air’s average molar mass of about 28.97 g/mol, the specific gas constant works out to approximately 287 J/(kg·K), the figure this calculator returns at its default input and the one most commonly quoted in engineering references.
Why does every gas have a different specific gas constant?
The universal gas constant is the same for all gases because it is defined per mole, and a mole of any gas contains the same number of molecules. The specific gas constant is defined per unit of mass instead, and a mole of a heavier gas weighs more, so dividing by a larger molar mass gives a smaller result.
How is this different from the ideal gas law calculator?
The ideal gas law calculator solves PV = nRT for pressure, volume, temperature or moles using the universal gas constant. This calculator answers a narrower question: what R_specific equals for a particular gas, which is then the constant to use if you want to work with mass instead of moles.
What units come out of this calculator?
The specific gas constant is returned in joules per kilogram-kelvin, J/(kg·K), the standard SI unit, alongside the same value in kilojoules per kilogram-kelvin for convenience in thermodynamics problems that use kJ.
To work with the universal gas constant directly, solving for pressure, volume, temperature or moles, see the ideal gas law calculator.