Though it may seem like nothing, the air around you has a density. The density of air can be measured and studied for features of physics and chemistry such as its weight, mass or volume. Scientists and engineers use this knowledge in creating equipment and products that take advantage of air pressure when inflating tires, sending materials through suction pumps and creating vacuum-tight seals.

Air density varies with atmospheric pressure and air temperature. In general, higher altitudes correspond to lower atmospheric pressure and lower air density. Hotter temperatures correlate to a lower air density also. The density of the air also depends on humidity and other factors; moist air and dry air carry different densities.

## Air Density Formula

The most basic and straightforward air density formula is simply dividing the mass of air by its volume. This is the standard definition of density as:

for density ρ ("rho") generally in kg/m^{3}, mass m in kg and volume V in m^{3}. For example, if you had 100 kg of air that took up a volume of 1 m^{3}, the density would be 100 kg/m^{3}.

To get a better idea of the density of air specifically, you need to account for how air is made of a mixture of gases when formulating its density. At a constant temperature, pressure and volume, dry air is typically made of 78% nitrogen (N_{2}), 21% oxygen (O_{2}) and one percent argon (Ar). Other gasses – like carbon dioxide – are also present in the air, but they are only available in very minute amounts, so they don’t factor into the calculations at this level.

To take into account the effect that these molecules have on air pressure, you can calculate the mass of air as the sum of nitrogen's two atoms of 14 atomic units each, oxygen's two atoms of 16 atomic units each and argon's single atom of 18 atomic units.

If the air isn't completely dry, you can also add some water molecules (H_{2}O) which are two atomic units for the two hydrogen atoms and 16 atomic units for the singular oxygen atom. If you calculate how much mass of air you have, you can assume that these chemical constituents are distributed throughout it uniformly and then calculate the percent of these chemical components in dry air.

You can also use the specific weight, the ratio of the weight to volume in calculating density. The specific weight γ ("gamma") is given by the equation

that adds an additional variable g as the constant of gravitational acceleration 9.8 m/s^{2}. In this case, the product of mass and gravitational acceleration is the weight of the gas, and dividing this value by the volume V can tell you the gas's specific weight.

## Air Density Calculator

An online air density calculator can help you calculate theoretical values for air density at given temperatures and pressures. These calculations will also show how density and specific weight decrease at higher values of temperature and pressure.

You can demonstrate this because of Avogadro's law, which states, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules." For this reason, scientists and engineers use this relationship in determining temperature, pressure or density when they know other information about a volume of gas they are studying.

The curvature of these graphs means there is a logarithmic relationship between these quantities. You can show that this matches theory by rearranging the ideal gas law:

for pressure P, volume V, amount of the gas n, specific gas constant R (0.167226 J/kg K) and temperature T to get ρ

in which ρ is density in units of m/V mass/volume (kg/m^{3}). **Keep in mind this version of the ideal gas law uses the universal gas constant**** R**

**in units of mass, not molar mass.** Mols are commonly used with the coefficient

*n*, but for density calculations, mass is better.

#### Tips

Both temperature and pressure in these calculations are measured as absolute temperature, in Kelvin, and absolute pressure, meaning relative to a complete vacuum. Barometric pressure is not used in the equation, as it is measured against the pressure at sea level.

The variation of the ideal gas law shows that, as temperature increases, density increases logarithmically because 1/T is proportional to ρ. This inverse relationship describes the curvature of the air density graphs and air density tables.

## Air Density vs. Altitude

Dry air can fall under one of two definitions. It can be air without any trace of water in it or it can be air with low relative humidity, which can be changed at higher altitudes. Air density tables such as the one on Omnicalculator shows how air density changes with respect to altitude.

As altitude increases, air pressure decreases primarily due to the gravitational attraction between air and the earth. This is because the gravitational attraction between earth and the molecules of air decreases, lessening the pressure of the forces between the molecules when you go to higher altitudes.

Aircraft altimeters, instruments that measure altitude, take advantage of this by measuring pressure and using that to estimate altitude, usually in terms of mean-sea-level (MSL). Global positioning systems (GPS) gives you a more precise answer by measuring the actual distance above sea level.

#### Tips

An International Standard Atmosphere (ISA) is the unit used for aviation and many applications to measure the various attributes of gas.

## Air Density and Water Vapor

There is a very interesting relationship between the water content of air and density. Instead of increasing the density of air, humid air actually has a lower density than the density of dry air. This has to do with the molecular weight of water vapor compared to regular air. Since water molecules weigh less – but still take up the same volume of air by the ideal gas law – so the mass of water vapor is less than the mass of dry air. As such, under standard temperature and pressure, humid air is actually less dense than dry air.

## Units of Density

Scientists and engineers mostly use the SI units for density of kg/m^{3}. Other uses may be more applicable based on the case and purpose. Smaller densities such as those of trace elements in solid objects like steel can generally be expressed more easily using units of g/cm^{3}. Other possible units of density include kg/L and g/mL.

Keep in mind, when converting between different units for density, you need to account for the three dimensions of volume as an exponential factor if you need to change the units for volume.

For example, if you wanted to convert 5 kg/cm^{3} to kg/m^{3}, you would multiply 5 by 100^{3}, not just 100, to get the result of 5 x 10^{6} kg/m^{3}.

Other handy conversions include 1 g/cm^{3} = .001 kg/m^{3}, 1 kg/L = 1000 kg/m^{3} and 1 g/mL = 1000 kg/m^{3}. These relationships show the versatility of density units for the desired situation.

In the United States customary standards of units, you may be more accustomed to using units like feet or pounds instead of meters or kilograms, respectively. In these scenarios, you can remember some useful conversions like 1 oz/in^{3} = 108 lb / ft^{3}, 1 lb / gal ≈ 7.48 lb / ft^{3} and 1 lb/yd^{3} ≈ 0.037 lb / ft^{3}. In these cases, ≈ refers to an approximation because these numbers for conversion are not exact.

These units of density can give you a better idea of how to measure density of more abstract or nuanced concepts such as the energy density of materials used in chemical reactions. This could be the energy density of fuels cars use in ignition or how much nuclear energy can be stored in elements like uranium.

Comparing air density to density of electric field lines around an electrically charged object, for example, can give you a better idea of how to integrate quantities over different volumes.

## Pressure and Temperature of Gasses

Since the pressure of dry air plays a role in the air density, it is also important to understand how the mixture of gasses that make up air contribute to the total pressure and subsequent density relationship in the air. Each gas in a mixture contributes its own partial pressure to the system, and since air is composed of nitrogen, oxygen, argon, and other gasses, it is a complex system of the pressures from each of these gasses. These rules also apply to water vapor pressure, and how humid air differs from dry air.

These pressures rely on the thermodynamics of the gas and how the particles respond to various environmental conditions.

References

Resources

Tips

- Humidity in the air is actually a factor that would decrease the air density value.

About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.