Use the air density calculator to instantly find how tightly packed an object's molecules are. This online calculator lets you estimate the ρ parameter basing on the local temperature and pressure conditions. This value is vital for many further calculations, such as determining the aerodynamic drag forces or the performance of wind turbines. Continue reading to get a better understanding of the relationship between the local weather and ρ, and learn what air density levels you can expect in various regions.
The density of air depends on many factors and can vary in different places. It mainly changes with temperature, relative humidity, pressure and hence with altitude (take a look on the air density table below). The pressure of air can be related to the weight of the air over a given location. It is easy to imagine that the higher you stand, the less air is above you and the pressure is lower (check out our definition of pressure!). Therefore, air pressure decreases with increasing altitude. In the following text, you will find out what are air density at sea level and standard air density.
You might also want to check out our speed of sound calculator which is a tool that helps you calculate the speed of sound in dry air and water at any temperature.
What is the density of air? - density of air at sea level
The density of air is usually denoted by a Greek letter ρ, and it measures the mass of air per its unit volume. Dry air mostly consists of nitrogen (
~78%) and oxygen (
~21%). The remaining
1% contains many different gases, among others, argon, carbon dioxide, neon or helium. However, the air will cease to be dry air when water vapor appears.
As a mixture of gases, air doesn't have a constant density; this value depends in large on air composition. Most components have similar densities and don't influence the overall density in a substantial way. One of the exceptions is the water vapor; the more water vapor in the air, the lower its density.
For dry air, the density of air at sea level at a temperature of
59°F (15°C) and pressure of
14.7 psi (1013.25 hPa) (mean sea-level pressure), is approximately equal to
0.0765 lb/cu ft (1.225 kg/m³). If you change the air temperature, humidity, or the altitude (and hence the pressure), the air density will change, too. As a rule of thumb, you can expect a drop of
0.0022-0.0023 lb/cu ft (0.035-0.036 kg/m³) per
1000 ft of altitude change.
How to calculate the air density?
To find the air density at any given location, you will need some basic weather parameters. You can usually find them at the website of your local weather station.
- Air pressure: the barometric pressure expressed in hPa. If the analyzed location is at a high altitude, you can use our air pressure at altitude calculator to establish a more accurate value for this parameter.
- Air temperature: simply, the outside temperature in °C.
- Relative humidity or dew point: our air density calculator is able to use one of these values to compute the other, so you only need to know one of them. Dew point is measured in °C, as it is the temperature below which the water vapor starts to condensate.
The method of finding the air density is quite simple. You have to divide the pressure exerted by the air into two partial pressures: of the dry air and of the water vapor. Combining these two values gives you the desired parameter.
- Calculate the saturation vapor pressure at dew point T, using the formula
p₁ = 6.1078 * 10^[7.5T /(T + 237.3]. Saturation vapor pressure means that the relative humidity is equal to 100%.
- Find the actual vapor pressure, multiplying this value by the relative humidity:
pv = p₁ * RH.
- Subtract the vapor pressure from the total air pressure to find the pressure of dry air:
pd = p - pv.
- Input the calculated values into the following formula:
ρ = (pd / (Rd * T)) + (pv / (Rv * T))
pdis the pressure of dry air in hPa,
pvis the water vapor pressure in hPa,
Tis the air temperature in Kelvins,
Rdis the specific gas constant for dry air equal to 287.058 J/(kg·K), and
Rvis the specific gas constant for water vapor equal to 461.495 J/(kg·K).
Air density definition - what is the density of air formula?
The basic definition of air density is as simple as the general definition of density. It tells us how much does a certain volume of air weigh. We can express it with the following density of air formula:
ρ = mass of the air / volume
From the above equation, you may suspect that the density of air is a constant value that describes a certain gas property. However, the density of every matter (solids, liquids, gases) depends, stronger or weaker, not only on the chemical composition of the substance but also on the external conditions like pressure and temperature.
Because of those dependencies and the fact that the Earth's atmosphere contains various gases, mostly nitrogen, oxygen, argon and water vapor, the air density definition needs to be further expanded. A proper modification has been made in our air density calculator with the density of air formula shown in the section called "How to calculate the air density?".
By the way, we would like to bring up an interesting point. What do you think? Is moist air heavier or lighter than dry air? The correct answer may not be as intuitive as you can think at first. In fact, the more water vapor we add to the air, the less dense it becomes! You could find it hard to believe, but we will try to convince with some few logical argumentations.
First of all, we need to refer to the Avogadro's law which states that
equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.
Imagine that you put dry air into a container of fixed volume, temperature and pressure. The perfectly dry air is composed mostly with:
- 78% molecules of nitrogen N₂ that has two N atoms with atomic weight 14 u (total weight is 28 u),
- 21% molecules of oxygen O₂ that has two O atoms with atomic weight 16 u (total weight is 32 u), and
- 1% molecules of argon Ar (Ar has one atom with atomic weight 18 u).
Note that every single molecule is heavier or equal to the 18 u. Now, let's add some water vapor molecules to the gas with the total atomic weight of 18 u (H₂O - two atoms of hydrogen 1 u and one oxygen 16 u). According to Avogadro's law, the total number of molecules remains the same in the container under the same conditions (volume, pressure, temperature). It means that water vapor molecules have to replace nitrogen, oxygen or argon. Because molecules of H₂O are lighter than the other gases (and in case of argon they're equal), the total mass of the gas decreases. And the density of the air decreases too.
Air density table - the density of dry air
In the previous sections, we used the term dry air a couple of times. However, what does it actually mean? There are two ways of answering:
- The most common definition of dry air states that this is air without any water vapor inside it. The air in the atmosphere is never perfectly dry since it always contains some water, though.
- Another, more realistic definition says that dry air is air with low relative humidity and thus with a low dew point.
A well-known approximation of dew point is a logarithmic function of relative humidity. As you may know, when an argument of the logarithm approaches to zero, its value goes to minus infinity. Therefore, a dew point doesn't exist for the zero relative humidity. However, you can still calculate what is the density of dry air with our air density calculator! Just select dry air in the "air type" field, where we have ignored dew point/relative humidity in the computations.
For a better understanding of how temperature and pressure influence air density, let's focus on a case of dry air. It contains mostly molecules of nitrogen and oxygen that are moving around at incredible speeds. Use our particles velocity calculator to see how fast they can move! For example, the average speed of nitrogen molecules with a mass of 14 u (u - unified atomic mass unit) in room temperature is about 670 m/s - two times faster than the speed of sound! Moreover, at higher temperatures, gas molecules further accelerate. As a result, they push harder against their surroundings, expanding the volume of a gas (it is described by the ideal gas law). And the higher the volume with the same amount of particles, the lower the density. Therefore, air's density decreases as the air is heated.
The opposite effect is achieved with pressure. Imagine that you have a gas cylinder with a constant volume. The increased pressure of the cylinder translates into the increased number of molecules inside - the density of air becomes higher.
Altitude has a significant influence on the air density because as you go higher, the pressure and the temperature decreases. At high altitudes, the amount of oxygen in the air is smaller, because there is less air in total. Therefore, if climbers decide to reach the tops of the highest mountains, they usually need an oxygen cylinder with a mask to be able to breathe. This problem doesn't appear in airplanes since cabins are pressurized to keep the air density inside on the typical level. To feel how does the air properties changes with the altitude, take a look at the following air density table which concerns dry air. It follows that the density of dry air at 16 000 ft (~ 5 km) is nearly two times lower than the density at the sea level.
[lb/cu ft (kg/m³)]
|sea level||59 (15)||14.7 (1013.25)||0.077 (1.23)|
|2 000 (610)||51.9 (11.1)||13.7 (941.7)||0.072 (1.16)|
|4 000 (1219)||44.7 (7.1)||12.7 (873.3)||0.068 (1.09)|
|6 000 (1829)||37.6 (3.1)||11.7 (808.2)||0.064 (1.02)|
|8 000 (2438)||30.5 (-0.8)||10.8 (746.2)||0.06 (0.95)|
|10 000 (3048)||23.3 (-4.8)||10 (687.3)||0.056 (0.9)|
|12 000 (3658)||16.2 (-8.8)||9.2 (631.6)||0.052 (0.84)|
|14 000 (4267)||9.1 (-12.8)||8.4 (579)||0.048 (0.77)|
|16 000 (4877)||1.9 (-16.7)||7.7 (530.9)||0.045 (0.72)|
Standard air density
Because temperature and air pressure vary from place to place, we need to define reference air conditions. Recently, there is a variety of alternative definitions for the standard conditions (for example in technical or scientific calculations). If you study or work in the technology, engineering or chemical industry, you should always check what standards were used by the author of the publication, article or book you read. You must know what they meant by saying "standard" conditions. Not only do the standards change on a regular basis, but they are also set by various organizations (some have even more than one definition of standard reference conditions). In the list below, you can find several standard reference pressures
p₀ and temperatures
T₀ in current use (remember that there are many more of them):
- International Union of Pure and Applied Chemistry(IUPAC): Standard Temperature and Pressure (STP),
p₀ = 10⁵ Pa,
T = 0 °C;
- Institute of Standards and Technology (NIST): ISO 10780,
p₀ = 1 atm,
T = 0 °C;
- International Civil Aviation Organization (ICAO): International Standard Atmosphere (ISA),
p₀ = 1 atm,
T = 15 °C;
- United States Environmental Protection Agency (EPA): Normal Temperature and Pressure (NTP),
p₀ = 1 atm,
T = 20 °C;
- International Union of Pure and Applied Chemistry: Standard Ambient Temperature and Pressure (SATP),
p₀ = 10⁵ Pa,
T = 25 °C;
So if you want to answer the question what is the standard air density, you should choose the appropriate standard conditions. You can compute them with our air density calculator with an assumption that relative humidity is relatively small (dry air). For example, the standard air density for STP is
ρ₀ = 1.2754 kg/m³, for NTP is
ρ₀ = 1.2923 kg/m³ and for SATP is
ρ₀ = 1.1684 kg/m³.