Air Density Calculator

Air density is the mass of air in a cubic meter of space. It's an obscure variable that affects aircraft takeoff performance, engine power output, wind turbine electricity generation and bullet drop rate. This calculator computes air density from temperature and pressure, optionally including humidity. It uses the ideal gas law which can be applied to a mixture of dry air and water vapor.

What is air density?

Air density (Greek letter rho) is defined as mass per unit volume.

At sea level and a standard temperature of 15 °C the air density is about 1.225 kg/m3. As the temperature increases, the air becomes less dense, and as it decreases, the air becomes denser. In mountains, the air density decreases because there is less air being pushed down from above.

The factors that determine air density are temperature, pressure and humidity. Higher pressure leads to higher air density as it brings the molecules closer together. Temperature has the opposite effect: As the molecules get warmer they spread out further apart so density and temperature vary in opposite directions.

Formula for air density.

For dry air the ideal gas law can be summarized in a simple formula. Density is the value that results from dividing the absolute pressure by the specific gas constant of dry air and the absolute temperature.

where P is the absolute pressure in pascals and T is temperature in kelvin (°C + 273.15). This formula can be used to calculate dry air completely.

For humid air another step is required. Since humid air is a mixture, from Dalton's law of partial pressures it follows that its density is the sum of the fractions of dry air and water vapor, each with their own specific gas constant.

P_v is the partial pressure of water vapour, while P_d = P - P_v is the fraction that is assigned to dry air. The vapour pressure can be calculated from relative humidity and saturation vapour pressure. This tool uses the Tetens approximation.

Why humid air is lighter than dry air:

Many people think that humid air is denser because on hot, muggy summer days the air often feels heavy and thick. In fact, it's just the opposite.

This is due to Avogadro's Law. At constant pressure and temperature the number of molecules in a given volume of gas is independent of the constituents of the mixture. For every water molecule that enters the air one nitrogen or oxygen molecule will be displaced. The molar mass of water is 18 g/mol, nitrogen 28 g/mol and oxygen 32 g/mol. As heavier molecules are replaced by lighter ones the overall weight of the air is reduced.

This effect is small but real and can be important in situations where there is little margin. In piston engines humid air leads to a lower amount of oxygen being drawn in and also slightly reduces the weight supported by the wing.

Example calculation:

Consider dry air at a temperature of 20 °C and standard pressure at sea level of 101,325 Pa. We convert the temperature to Kelvin (which gives 20 + 273.15 = 293.15 K) and perform the calculations.

At a relative humidity of 60% (at temperature 25 °C), the density falls to about 1.176 kg/m3. This is lighter than the same air in a completely dry state, which has a density of 1.184 kg/m3.

Density altitude: A figure that pilots pay attention to.

Density altitude is the altitude at which the air density matches the actual air density at a particular location in a standard atmosphere. It combines temperature, pressure and humidity into a single number that indicates how the air will affect wings or propellers.

At high altitude airports the density altitude can be several thousand feet higher than actual elevation in hot and humid weather. A fully loaded plane taking off from Denver at 38 °C could have a density altitude of nearly 9,000 feet. This results in reduced lift, reduced thrust, and dangerously long takeoff distances. The airline industry stresses the importance of "hot high weight" for this reason, and flights are scheduled for cooler morning hours.

It is important to note that this is not an altimeter reading but absolute pressure.

A common mistake when calculating air density is using the wrong pressure value. Weather forecasts and aircraft altimeters report a sea-level standard pressure (about 1013 hPa or 29.92 inHg) to allow comparisons between measurements made at different elevations.

To calculate density you need the actual pressure at your location, i.e. absolute or station pressure. If you use a sea level corrected value in a formula for a city in the mountains then you will mathematically be at sea level and this will lead to a significant overestimate of the density. If no barometer is available, this calculator can be set to "from altitude" to estimate actual pressure from standard atmosphere.

Applications of air density:

Air density affects lift, drag and combustion, so it is surprisingly important in many areas.

In motorsport the abbreviation RAD (Relative Air Density) is often used. On a typical day at sea level it will be 100%, but on hot humid tracks in high altitude it can be as low as 88%. A naturally aspirated engine will lose around 12% of power before the start light goes green, and that's exactly how much the turbocharger is trying to recover.

Standard conditions:

The "normal" air density depends on the standard used because different organizations have different temperature and pressure requirements.

How does air density change with altitude?

In the lower atmosphere both pressure and temperature decrease with increasing altitude, which leads to a corresponding decrease of density. At an increase of about 5 km, air density is only half of its value at sea level. This is why mountaineers get short of breath and in airplane cabins pressure regulation is necessary.

This calculator is for educational and general planning purposes only. It is based on the ideal gas law, Tetens approximation of vapor pressure, and the ISA standard atmosphere model. Under normal conditions it has an error of less than a fraction of one percent. For accurate aerodynamic or metrological work complete real gas models or measured pressures should be used.