Density of air

The density of air ρ (Greek: rho) (air density) is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in temperature and humidity. At sea level and at 15 °C air has a density of approximately 1.225 kg/m³ (1.225 x10⁻³ g/cm³, 0.0023769 slug/(cu ft), 0.0765 lb/(cu ft)) according to ISA (International Standard Atmosphere).

Air density is a property used in many branches of science, engineering, and industry, including aeronautics; gravimetric analysis; the air-conditioning industry; atmospheric research and meteorology; agricultural engineering (modeling and tracking of Soil-Vegetation-Atmosphere-Transfer (SVAT) models); and the engineering community that deals with compressed air.

Density of air calculations

Depending on the measuring instruments used, different sets of equations for the calculation of the density of air can be applied. Air is a mixture of gases and the calculations always simplify, to a greater or lesser extent, the properties of the mixture.

Density of air variables

Temperature and pressure

The density of dry air can be calculated using the ideal gas law, expressed as a function of temperature and pressure:

$\rho ={\frac {p}{R_{\rm {specific}}T}}$

where:

$\rho =$ air density (kg/m³)

$p=$ absolute pressure (Pa)

$T=$ absolute temperature (K)

$R_{\rm {specific}}=$ specific gas constant for dry air (J/(kg·K))

The specific gas constant for dry air is 287.058 J/(kg·K) in SI units, and 53.35 (ft·lbf)/(lb·°R) in United States customary and Imperial units. This quantity may vary slightly depending on the molecular composition of air at a particular location.

Therefore:

• At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 1.2754 kg/m³.
• At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m³.
• At 70 °F and 14.696 psi, dry air has a density of 0.074887 lb/ft³.

The following table illustrates the air density–temperature relationship at 1 atm or 101.325 kPa:

Effect of temperature on properties of air

Celsius tempe­rature θ [°C]	Speed of sound c [m/s]	Density of air ρ [kg/m3]	Characteristic specific acoustic impedance z0 [Pa⋅s/m]
35	351.88	1.1455	403.2
30	349.02	1.1644	406.5
25	346.13	1.1839	409.4
20	343.21	1.2041	413.3
15	340.27	1.2250	416.9
10	337.31	1.2466	420.5
5	334.32	1.2690	424.3
0	331.30	1.2922	428.0
−5	328.25	1.3163	432.1
−10	325.18	1.3413	436.1
−15	322.07	1.3673	440.3
−20	318.94	1.3943	444.6
−25	315.77	1.4224	449.1

Humidity (water vapor)

Main article: Humidity

The addition of water vapor to air (making the air humid) reduces the density of the air, which may at first appear counter-intuitive. This occurs because the molar mass of water (18 g/mol) is less than the molar mass of dry air (around 29 g/mol). For any gas, at a given temperature and pressure, the number of molecules present is constant for a particular volume (see Avogadro's Law). So when water molecules (water vapor) are added to a given volume of air, the dry air molecules must decrease by the same number, to keep the pressure or temperature from increasing. Hence the mass per unit volume of the gas (its density) decreases.

The density of humid air may be calculated by treating it as a mixture of ideal gases. In this case, the partial pressure of water vapor is known as the vapor pressure. Using this method, error in the density calculation is less than 0.2% in the range of −10 °C to 50 °C. The density of humid air is found by:

$\rho _{\,\mathrm {humid~air} }={\frac {p_{d}}{R_{d}T}}+{\frac {p_{v}}{R_{v}T}}={\frac {p_{d}M_{d}+p_{v}M_{v}}{RT}}\,$  

where:

$\rho _{\,\mathrm {humid~air} }=$ Density of the humid air (kg/m³)

$p_{d}=$ Partial pressure of dry air (Pa)

$R_{d}=$ Specific gas constant for dry air, 287.058 J/(kg·K)

$T=$ Temperature (K)

$p_{v}=$ Pressure of water vapor (Pa)

$R_{v}=$ Specific gas constant for water vapor, 461.495 J/(kg·K)

$M_{d}=$ Molar mass of dry air, 0.028964 kg/mol

$M_{v}=$ Molar mass of water vapor, 0.018016 kg/mol

$R=$ Universal gas constant, 8.314 J/(K·mol)

The vapor pressure of water may be calculated from the saturation vapor pressure and relative humidity. It is found by:

$p_{v}=\phi p_{\mathrm {sat} }\,$

where:

$p_{v}=$ Vapor pressure of water

$\phi =$ Relative humidity

$p_{\mathrm {sat} }=$ Saturation vapor pressure

The saturation vapor pressure of water at any given temperature is the vapor pressure when relative humidity is 100%. One formula used to find the saturation vapor pressure is:

$p_{\mathrm {sat} }=6.1078\times 10^{\frac {7.5T}{T+237.3}}$

where $T=$ is in degrees C.

note:

• This equation will give the result of pressure in hPa (100 Pa, equivalent to the older unit millibar, 1 mbar = 0.001 bar = 0.1 kPa)

The partial pressure of dry air $p_{d}$ is found considering partial pressure, resulting in:

$p_{d}=p-p_{v}\,$

Where $p$ simply denotes the observed absolute pressure.

Altitude

Standard Atmosphere: p₀ = 101.325 kPa, T₀ = 288.15 K, ρ₀ = 1.225 kg/m³

To calculate the density of air as a function of altitude, one requires additional parameters. They are listed below, along with their values according to the International Standard Atmosphere, using for calculation the universal gas constant instead of the air specific constant:

$p_{0}=$ sea level standard atmospheric pressure, 101.325 kPa

$T_{0}=$ sea level standard temperature, 288.15 K

$g=$ earth-surface gravitational acceleration, 9.80665 m/s²

$L=$ temperature lapse rate, 0.0065 K/m

$R=$ ideal (universal) gas constant, 8.31447 J/(mol·K)

$M=$ molar mass of dry air, 0.0289644 kg/mol

Temperature at altitude $h$ meters above sea level is approximated by the following formula (only valid inside the troposphere):

$T=T_{0}-Lh\,$

The pressure at altitude $h$ is given by:

$p=p_{0}\left(1-{\frac {Lh}{T_{0}}}\right)^{\frac {gM}{RL}}$

Density can then be calculated according to a molar form of the ideal gas law:

$\rho ={\frac {pM}{RT}}\,$

where:

$M=$ molar mass

$R=$ ideal gas constant

$T=$ absolute temperature

$p=$ absolute pressure

Composition

Composition of dry atmosphere, by volume

Gas (and others)		Various		CIPM-2007		ASHRAE		Schlatter		ICAO		US StdAtm76		▼ Tap to expand or collapse table ▲
		ppmv	percentage	ppmv	percentage	ppmv	percentage	ppmv	percentage	ppmv	percentage	ppmv	percentage
Nitrogen	N2	780,800	78.080%	780,848	78.0848%	780,818	78.0818%	780,840	78.084%	780,840	78.084%	780,840	78.084%
Oxygen	O2	209,500	20.950%	209,390	20.9390%	209,435	20.9435%	209,460	20.946%	209,476	20.9476%	209,476	20.9476%
Argon	Ar	9,340	0.9340%	9,332	0.9332%	9,332	0.9332%	9,340	0.9340%	9,340	0.9340%	9,340	0.9340%
Carbon dioxide	CO2	397.8	0.03978%	400	0.0400%	385	0.0385%	384	0.0384%	314	0.0314%	314	0.0314%
Neon	Ne	18.18	0.001818%	18.2	0.00182%	18.2	0.00182%	18.18	0.001818%	18.18	0.001818%	18.18	0.001818%
Helium	He	5.24	0.000524%	5.2	0.00052%	5.2	0.00052%	5.24	0.000524%	5.24	0.000524%	5.24	0.000524%
Methane	CH4	1.81	0.000181%	1.5	0.00015%	1.5	0.00015%	1.774	0.0001774%	2	0.0002%	2	0.0002%
Krypton	Kr	1.14	0.000114%	1.1	0.00011%	1.1	0.00011%	1.14	0.000114%	1.14	0.000114%	1.14	0.000114%
Hydrogen	H2	0.55	0.000055%	0.5	0.00005%	0.5	0.00005%	0.56	0.000056%	0.5	0.00005%	0.5	0.00005%
Nitrous oxide	N2O	0.325	0.0000325%	0.3	0.00003%	0.3	0.00003%	0.320	0.0000320%	0.5	0.00005%	-	-
Carbon monoxide	CO	0.1	0.00001%	0.2	0.00002%	0.2	0.00002%	-	-	-	-	-	-
Xenon	Xe	0.09	0.000009%	0.1	0.00001%	0.1	0.00001%	0.09	0.000009%	0.087	0.0000087%	0.087	0.0000087%
Nitrogen dioxide	NO2	0.02	0.000002%	-	-	-	-	-	-	Up to 0.02	Up to 0.000002%	-	-
Iodine	I2	0.01	0.000001%	-	-	-	-	-	-	Up to 0.01	Up to 0.000001%	-	-
Ammonia	NH3	trace	trace	-	-	-	-	-	-			-	-
Sulfur dioxide	SO2	trace	trace	-	-	-	-	-	-	Up to 1.00	Up to 0.0001%	-	-
Ozone	O3	0.02 to 0.07	2 to 7×10−6%	-	-	-	-	0.01 to 0.10	1 to 10×10−6%	Up to 0.02 to 0.07	Up to 2 to 7×10−6%	-	-
Trace to 30 ppm	—	-	-	-	-	2.9	0.00029%	-	-	-	-	-	-
Dry air total	air	1,000,000	100.00%	1,000,000	100.00%	1,000,000	100.00%	1,000,000	100.00%	1,000,000	100.00%	1,000,080	100.00%
Not included in above dry atmosphere
Water vapor	H2O	~0.25% by mass over full atmosphere, locally 0.001–5% by volume.						~0.25% by mass over full atmosphere, locally 0.001–5% by volume.
▽ notes

See also

• Air
• Density
• Atmosphere of Earth
• International Standard Atmosphere
• U.S. Standard Atmosphere
• NRLMSISE-00

External links

• Conversions of density units ρ by Sengpielaudio
• Air density and density altitude calculations and by Richard Shelquist
• Air density calculations by Sengpielaudio (section under Speed of sound in humid air)
• Air density calculator by Engineering design encyclopedia
• Atmospheric pressure calculator by wolfdynamics
• Air iTools - Air density calculator for mobile by JSyA