Air Density Calculator

Use this air density calculator to instantly find how tightly packed an object's molecules are, allowing you to estimate $\rho$ based 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 air pressure 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. Therefore, air pressure decreases with increasing altitude. In the following text, you will find out what is the air density at sea level and the standard air density.

For dry air, its density at sea level at 59 °F (15 °C) and 14.7 psi (1013.25 hPa) (mean sea-level pressure) is approximately 0.0765 lb/(cu ft) (1.225 kg/(m^3)). If you change the air temperature, humidity, or altitude (and hence the pressure), the air density will change, too.

As a rule of thumb, you can expect a drop of $\mathrm{0.0022 - 0.0023 \ \frac{lb}{cu \ ft} \ (0.035 - 0.036 \ \frac{kg}{m^3})}$ per $1000 \text{ ft}$ of altitude change.

The density of air is usually denoted by the Greek letter rho, or ρ, and it measures the mass of air per unit volume (e.g. g/m³). Dry air mostly consists of nitrogen ($\sim 78 \%$) and oxygen ($\sim 21 \%$). 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 largely on air composition. Most components have similar densities and don't influence the overall density in a substantial way. One exception is water vapor; the more water vapor in the air, the lower its density.

To find the air density at any given location, you will need some basic weather parameters. You can usually find them on your local weather stations website.

• 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. This is 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, or you can also use our dew point calculator. Dew point is the temperature below which the water vapor starts to condensate, in °C.

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.

1. Calculate the saturation vapor pressure at given temperature $T$ using the formula:
   $p_1 = 6.1078 \cdot 10^{\frac{7.5T}{T + 237.3}}$
   where $T$ is measured in degrees Celsius. Saturation vapor pressure is the vapor pressure at 100% relative humidity (our calculator uses a more accurate, but also way more complicated equation that we didn't want to show here. If you are curious, check "FUNCTION ESW(T)" in the provided link).

2. Find the actual vapor pressure, multiplying the saturation vapor pressure by the relative humidity:
   $p_v = p_1 \cdot \text{RH}$.

3. Subtract the vapor pressure from the total air pressure to find the pressure of dry air:
   $p_d = p - p_v$.

4. Input the calculated values into the following formula:

where:

• $p_d$ is the pressure of dry air in Pa;
• $p_v$ is the water vapor pressure in Pa;
• $T$ is the air temperature in Kelvins;
• $R_d$ is the specific gas constant for dry air equal to 287.058 J/(kg·K); and
• $R_v$ is the specific gas constant for water vapor equal to 461.495 J/(kg·K).

The basic definition of air density is very similar to 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:

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 these 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 may find this 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 of:

• 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 39.8 u).

Note that every molecule listed is heavier that or equal to 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, the total mass of the gas decreases, decreasing the density of the air too.

In the previous sections, we used the term dry air a couple of times. However, what does it actually mean? There are two definitions:

• The most common definition 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 the function of a logarithm approaches 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 a nitrogen molecule with a mass of 14 u (u — unified atomic mass unit) at 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 the gas (it is described in the ideal gas law calculator). 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 air density because as you go higher, the greater the pressure and temperature drops. At high altitudes, the amount of oxygen in the air per unit volume is lower, 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 similar to ground level. To get a feeling of how air properties changes with the altitude, take a look at the following air density table for dry air (data from the NASA Technical Report Server, U.S. Standard Atmosphere, 1976). 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.

The SI unit for density is kilogram per cubic meter (kg / m³). However, in some cases it is more convenient to use:

• Gram per cubic centimeter (g /c m³), 1 g/cm³ = 0.001 kg / m³;
• Kilogram per liter (kg / L), 1 kg/L = 1000 kg / m³;
• Gram per milliliter (g / mL), 1 g/mL = 1000 kg / m³.

The choice of units depends on the situation. Sometimes you know the volume of the air container in liters, another time you need to measure its dimensions to obtain volume in cubic meters. Feel free to change the units in our air density calculator!

The same applies to the density of air in Imperial units. Example of these units include:

• Pound per cubic feet (lb / cu ft);
• Pound per cubic yard (lb / cu yd), 1 lb / cu yd ≈ 0.037 lb / cu ft;
• Ounce per cubic inch (oz / cu in), 1 oz / cu in = 108 lb / cu ft;
• Pound per gallon (US) (lb / US gal), 1 lb / US gal ≈ 7.48 lb / cu ft.

Because temperature and air pressure vary from place to place, we need to define reference air conditions. Recently, there has been 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 industries, you should always check what standards were used by the author of the publication, article or book. You need to know what they meant by "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 $p_0$ and temperatures $T_0$ in current use (remember that there are many more of them):

• International Union of Pure and Applied Chemistry(IUPAC): Standard Temperature and Pressure (STP), $p_0 = 10^5 \ \text{Pa}$, $T = 0 \ \degree \text{C}$;
• Institute of Standards and Technology (NIST): ISO 10780, $p_0 = 1 \text{ atm}$, $T = 0 \ \degree \text{C}$;
• International Civil Aviation Organization (ICAO): International Standard Atmosphere (ISA), $p_0 = 1 \text{ atm}$, $T = 15 \ \degree \text{C}$;
• United States Environmental Protection Agency (EPA): Normal Temperature and Pressure (NTP), $p_0 = 1 \text{ atm}$, $T = 20 \ \degree \text{C}$;
• International Union of Pure and Applied Chemistry: Standard Ambient Temperature and Pressure (SATP), $p_0 = 10^5 \ \text{Pa}$, $T = 25 \ \degree \text{C}$.

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 $\mathrm{\rho_0 = 1.2754 \ \frac{kg}{m^3}}$, for NIST is $\mathrm{\rho_0 = 1.2923 \ \frac{kg}{m^3}}$ and for SATP is $\mathrm{\rho_0 = 1.1684 \ \frac{kg}{m^3}}$.

Air pressure is a physical property of a gas that tells us with how much strength it has when acting on the surroundings. Let's consider a cubic container (see figure below) with some air closed inside. According to the kinetic theory of gases, the molecules of the gas are in constant motion with a velocity that depends on the thermal energy. Particles collide with each other and with the walls of a container, exerting a tiny force on them. However, since the number of the enclosed molecules reaches about ~10²³ (order of magnitude of Avogadro's constant), the total force becomes significant and measurable — this is pressure.

The relative humidity $\text{RH}$ is defined as the ratio of the partial pressure of the water vapor to the equilibrium vapor pressure of water at a given temperature. Partial pressure is the pressure of one component of the air if taken individually, at the same volume and temperature of the whole. When you sum the partial pressures of all the gases in the air, you will obtain its total pressure which we can directly measure:

The equilibrium vapor pressure of water is the pressure exerted by a vapor that is in thermodynamic equilibrium with its liquid phase at a given temperature. It is a measure of the tendency of molecules or atoms to escape from a surface of a liquid and become a gas. As the temperature increases, the equilibrium vapor pressure increases too.

Relative humidity $\text{RH}$ ranges between 0% and 100%, where 0% means the dry air, and 100% is air that is completely saturated with water vapor. You should be aware that relative humidity of 100% doesn't mean that air only consists of water. When relative humidity is of 100%, the cooling of the air gives rise to condensation of water vapor.

Dew point is the temperature at which the water vapor contained in the air reaches its saturation state. It is a physical quantity strictly related to the humidity of the air. When the air is further cooled past the dew point, the water vapor will condense to form water — dew.

There are several ways to approximate the dew point. Our air density calculator uses the following formula:

where $\alpha$ is a parameter that depends on the relative humidity $\text{RH}$ and temperature $T$:

Relative humidity is expressed in percents and temperature in Celsius degrees. Because dew point is directly linked to relative humidity you need to enter only one of those parameters in the air density calculator.

Human body uses the evaporation of sweat to cool down during a hot day. The evaporation speed of the perspiration depends on how much moisture is in the air. If the air is already saturated (relative humidity = 100%), perspiration will not evaporate, and you will be coated with sweat. Thankfully, when air is moved from your body by a wind, sweat will evaporate faster, making you feel a pleasant coolness. Discomfort also arises when the dew point is low (dry air) causing the skin to crack and become irritated more easily.

In the table below, you will find dew point and (related to it) relative humidity at the temperature of 68°F (20°C). The dew point can't be higher than the air temperature because relative humidity can't exceed 100%. On the other hand, when relative humidity equals 0%, we say that the air is a dry air (dew point loses its purpose because there is no water).