Specific Gas Constant Calculator
This calculator finds the specific gas constant (Rs) for any pure gas or mixture. Choose the molar mass method (Rs = R / M) or the specific-heat method (Rs = Cp - Cv), pick a preset gas or enter your own molar mass, and get the result in J/(kg·K) or ft·lbf/(lb·R) instantly. Flip the mode to reverse-solve: enter Rs and recover the molar mass.
What is the specific gas constant?
The specific gas constant (Rs, also written R_s or r) is the universal gas constant (R = 8.314 J/(mol·K)) divided by the molar mass of the gas. It converts the ideal gas law from a per-mole basis to a per-unit-mass basis, so you can work directly with densities and mass flow rates rather than mole counts. Every gas has its own Rs, which is why it is called the "specific" constant. Air has Rs = 287.05 J/(kg·K), hydrogen has Rs = 4124 J/(kg·K), and propane has Rs = 188.6 J/(kg·K).
The two formulas: molar mass and Mayer's relation
There are two equivalent ways to find Rs. First, divide the universal gas constant by the molar mass: Rs = R / M. Second, use Mayer's relation from classical thermodynamics: Rs = Cp - Cv, where Cp is the specific heat at constant pressure and Cv is the specific heat at constant volume. Both give the same result for an ideal gas. The molar mass route is most convenient when the gas species is known; the Cp - Cv route is useful in experimental work where the two heat capacities have been measured directly. The heat-capacity ratio gamma = Cp / Cv is a free bonus from the second method and is central to compressible-flow and isentropic-process calculations.
Where is the specific gas constant used?
Rs appears whenever the ideal gas law is written in terms of mass density instead of amount of substance: P = rho * Rs * T, where P is pressure (Pa), rho is density (kg/m^3), T is absolute temperature (K), and Rs is in J/(kg·K). This form is routine in aerodynamics, meteorology, HVAC engineering, and compressible-flow analysis. In the atmosphere, air's Rs of 287.05 J/(kg·K) is used to convert between altitude, pressure and temperature. In gas turbine and compressor design, Rs combined with gamma determines the speed of sound, the Mach number, and isentropic efficiency. For pipe-flow and pneumatic systems, Rs lets engineers convert between mass flow rate and volumetric flow rate at any temperature and pressure without tracking moles.
SI and imperial units for Rs
In SI the specific gas constant is expressed in joules per kilogram-kelvin (J/(kg·K)), which equals N·m/(kg·K) or m^2/(s^2·K). In US customary engineering units it is expressed in foot-pounds-force per pound-mass-rankine (ft·lbf/(lb·R)). The conversion is 1 J/(kg·K) = 0.18504 ft·lbf/(lb·R). Air in SI: 287.05 J/(kg·K); in imperial: 53.35 ft·lbf/(lb·R). When working with the ideal gas law in imperial units, pressure is in lbf/ft^2, density in lb/ft^3, and temperature in Rankine (R = F + 459.67).
Specific gas constants for common gases
| Gas | Formula | M (g/mol) | Rs (J/(kg·K)) | Rs (ft·lbf/(lb·R)) |
|---|---|---|---|---|
| Air | 28.965 | 287.05 | 53.35 | |
| Argon | Ar | 39.948 | 208.13 | 38.68 |
| Butane | C4H10 | 58.122 | 143.05 | 26.58 |
| Carbon dioxide | CO2 | 44.009 | 188.92 | 35.11 |
| Chlorine | Cl2 | 70.906 | 117.26 | 21.80 |
| Helium | He | 4.003 | 2077.1 | 386.1 |
| Hydrogen | H2 | 2.016 | 4124.2 | 766.6 |
| Methane | CH4 | 16.043 | 518.26 | 96.33 |
| Neon | Ne | 20.180 | 411.99 | 76.57 |
| Nitrogen | N2 | 28.014 | 296.80 | 55.16 |
| Oxygen | O2 | 31.998 | 259.84 | 48.29 |
| Propane | C3H8 | 44.097 | 188.56 | 35.04 |
| Water vapor | H2O | 18.015 | 461.52 | 85.78 |
Values at standard conditions (0 °C, 1 atm). Rs = R / M where R = 8314.46 J/(kmol·K).
Frequently asked questions
What is the specific gas constant for air?
The specific gas constant for dry air is 287.05 J/(kg·K), or equivalently 53.35 ft·lbf/(lb·R). It is calculated by dividing the universal gas constant (8314.46 J/(kmol·K)) by the mean molar mass of dry air (28.965 g/mol). This value appears throughout atmospheric science and aerodynamics, for example in the barometric formula and in the equation of state for the International Standard Atmosphere.
How is the specific gas constant different from the universal gas constant?
The universal gas constant R = 8.314 J/(mol·K) is the same for every ideal gas. The specific gas constant Rs = R / M is different for every gas, because it accounts for the molar mass. Rs is used when you want to work with mass units (kilograms) rather than amount-of-substance units (moles). For a gas mixture, use the mixture's mean molar mass to get the mixture's Rs.
What does Mayer's relation Rs = Cp - Cv mean?
For an ideal gas, the difference between the specific heat at constant pressure (Cp) and the specific heat at constant volume (Cv) equals the specific gas constant. This comes from the first law of thermodynamics: at constant pressure, part of the heat input goes into work (PΔV), which equals Rs per unit mass for an ideal gas. In practice, if you measure Cp and Cv experimentally you can derive Rs without knowing the molar mass at all, which is useful for gas mixtures of uncertain composition.
Why does hydrogen have such a high specific gas constant?
Because Rs = R / M and hydrogen (H2) has an extremely low molar mass of about 2.016 g/mol, its specific gas constant is exceptionally high: 4124 J/(kg·K). This means that for a given mass of hydrogen, the gas generates more pressure per degree of temperature than any other common gas. It is one of the reasons hydrogen is used in high-speed centrifugal compressors and why hydrogen-cooled generators are efficient.
How do I calculate the specific gas constant for a gas mixture?
First calculate the mean molar mass of the mixture. For a mixture of gases with mass fractions w_i and molar masses M_i, the mean molar mass is found from 1/M_mix = sum(w_i / M_i). Then Rs_mix = R / M_mix. Alternatively, if you know the specific gas constants of each component and their mass fractions, Rs_mix = sum(w_i * Rs_i). Both give the same result for ideal-gas mixtures.
What is the heat-capacity ratio gamma and why does it matter?
The heat-capacity ratio, written gamma (or kappa in some fields), is gamma = Cp / Cv. For an ideal diatomic gas at moderate temperatures, gamma is approximately 1.4; for monatomic noble gases, it is 5/3 (about 1.667); for polyatomic gases such as CO2 or methane, it is lower (around 1.3 or less). Gamma governs adiabatic and isentropic processes: the speed of sound in a gas is sqrt(gamma * Rs * T), and isentropic compression ratios are P2/P1 = (T2/T1)^(gamma / (gamma - 1)).