Air Density From T P Calculator
Free Air density Calculator for meteorology & atmospheric science. Enter variables to compute results with formulas and detailed steps.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
rho = P / (R_d x T_v)
Where rho is air density in kg/m3, P is pressure in Pa, R_d is 287.058 J/kg/K, and T_v is virtual temperature in Kelvin accounting for moisture.
Worked Examples
Example 1: Standard Day Air Density
Problem:Calculate at 20 C, 101325 Pa, 50% RH.
Solution:Dry = 101325/(287.058 x 293.15) = 1.2041\nes = 2338 Pa, e = 1169 Pa\nTv = 295.26 K\nMoist = 101325/(287.058 x 295.26) = 1.1956
Result:Dry: 1.2041 | Moist: 1.1956 kg/m3 | Sound: 343.37 m/s
Example 2: Hot High-Altitude Airport
Problem:P=85000 Pa, T=35 C, RH=20%.
Solution:Dry = 85000/(287.058 x 308.15) = 0.9612\nes=5627 Pa, e=1125 Pa\nTv=309.42 K\nMoist = 0.9573
Result:Moist: 0.9573 kg/m3 | Density altitude: ~2764 m
Frequently Asked Questions
How is air density calculated from temperature and pressure?
Air density is calculated using the ideal gas law in the form rho equals P divided by the product of the specific gas constant R and absolute temperature T. For dry air R equals 287.058 joules per kilogram per kelvin. The temperature must be converted to Kelvin by adding 273.15 to the Celsius value. At standard sea level conditions of 101325 Pa and 15 C this yields approximately 1.225 kg per cubic meter. This calculation assumes air behaves as an ideal gas, which is an excellent approximation at atmospheric pressures. For humid air the calculation is modified using the virtual temperature concept to account for water vapor.
How does humidity affect air density?
Humid air is actually less dense than dry air at the same temperature and pressure, which is counterintuitive to many people. This occurs because water vapor molecules have a molecular weight of 18 grams per mole compared to 29 grams per mole for dry air. When water vapor molecules replace heavier nitrogen and oxygen molecules in a given volume the total mass decreases. The effect is quantified through the virtual temperature which is always higher than actual temperature for moist air. At 30 C and 100 percent humidity the density reduction compared to dry air is approximately 1.2 percent. This effect is important for aircraft performance calculations.
What is density altitude and why does it matter for aviation?
Density altitude is the altitude in the International Standard Atmosphere at which the actual air density would be found. It increases with rising temperature, increasing humidity, and decreasing pressure, all of which reduce air density. Pilots use density altitude because aircraft performance depends directly on air density rather than geographic altitude. At a hot high-altitude airport the density altitude can be thousands of feet higher than the field elevation, meaning reduced engine power, decreased lift, and longer takeoff rolls. Fatal accidents have occurred when pilots failed to account for high density altitude conditions during takeoff from mountain airports.
How does altitude affect air pressure and density?
Air pressure and density decrease approximately exponentially with increasing altitude because the weight of the overlying air column diminishes. In the International Standard Atmosphere pressure drops from 101325 Pa at sea level to about 89875 Pa at 1000 meters and 54048 Pa at 5000 meters. The corresponding density decreases from 1.225 to 1.112 and 0.736 kg per cubic meter. A useful rule of thumb is that pressure drops by about one percent for every 80 meters of altitude gain near sea level. The barometric formula describes this relationship mathematically and depends on the temperature lapse rate.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy