Why is R for air about 287 and not 8.314?

8.314 J/(mol·K) is per mole. Dividing by the molar mass of air, 0.028965 kg/mol, gives the value per kilogram, about 287 J/(kg·K), which is what engineering formulas such as p = ρRT use.

Is the specific gas constant the same as cₚ − c v ?

Yes, for an ideal gas R = cₚ − cv per unit mass. For air, 1,005 − 718 ≈ 287 J/(kg·K).

Specific Gas Constant Calculator (R = Rᵤ/M for air, CO₂, steam and more)

Understanding the specific gas constant calculator — concept and principle

This calculator finds the specific gas constant of a gas, the universal gas constant divided by its molar mass, for dry air, nitrogen, oxygen, carbon dioxide, steam, helium, hydrogen, argon, methane or a molar mass you enter. It also gives the gas density and specific volume at a chosen temperature and pressure. Engineers and students use it in thermodynamics, aerodynamics and HVAC.

Dividing the universal constant by molar mass gives a per-kilogram constant; at 15 °C sea level air is 1.225 kg/m³.

How it is calculated

R = R_u ÷ M, with R_u = 8.314462618 J/(mol·K) and M in kg/mol

Density ρ = p ÷ (R T); specific volume = 1 ÷ ρ

T in °C is converted to kelvin; p in kPa. 1 J/(kg·K) = 0.18586 ft·lbf/(lbm·°R).

The principle

The ideal gas law pV = nR_uT counts gas in moles. Engineers often prefer to work per kilogram, which turns it into p = ρRT with a gas-specific constant. Since one mole of any gas contains the same number of molecules, dividing R_u by the mass of a mole gives the constant per kilogram. Light gases have large specific constants, so at the same pressure and temperature they are much less dense.

Worked example

Default inputs: dry air (28.965 g/mol), 15 °C, 101.325 kPa.

R = 8.314462618 ÷ 0.028965 = 287.052 J/(kg·K) = 0.287052 kJ/(kg·K) = 53.352 ft·lbf/(lbm·°R).
T = 15 + 273.15 = 288.15 K.
ρ = 101,325 ÷ (287.052 × 288.15) = 1.225 kg/m³.
Specific volume = 1 ÷ 1.225 = 0.8163 m³/kg; molar mass used 28.965 g/mol.

How to read the result

1.225 kg/m³ is the familiar sea-level standard air density. Helium's specific constant is about seven times air's, so it is about seven times less dense, which is why it lifts balloons. Steam's value applies only where steam behaves as an ideal gas, well away from saturation.

Common mistakes

Using the universal constant where the specific one is needed.
Using g/mol instead of kg/mol in the division.
Using gauge instead of absolute pressure for density.
Applying ideal-gas density to high-pressure or near-condensing gases.

Keep in mind: Ideal-gas behaviour is assumed. Real gases deviate at high pressure and low temperature.

Frequently asked questions

What is the specific gas constant of air?

About 287 J/(kg·K).

Why do different gases have different R?

R per kilogram depends on how many moles a kilogram contains.

What is the universal gas constant?

8.314462618 J/(mol·K), exact since 2019 as k_B × N_A.

How is it used in aerodynamics?

With p = ρRT to find air density from pressure and temperature.

Sources: NASA Glenn Research Center, Beginner's Guide to Aeronautics, "Equation of State" · BIPM, SI Brochure, 9th edition (2019)

Checked 9 Nov 2026. NASA Glenn Research Center, Beginner’s Guide to Aeronautics, “Equation of State” (gas constant = universal gas constant ÷ mass per mole; p = ρRT; air 0.286 kJ/(kg·K)); R_u = k_BN_A exact (2019 SI); standard atomic weights and dry-air molar mass: standard values; 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, 1 lbf = 4.4482216152605 N (exact definitions).

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