Air density calculator
Hot, humid, low-pressure air is thin. That matters for engines, wings, ballistics and anything else that pushes against it.
hPa
%
Air density
1.198 83kg/m3
- If the air were completely dry
- 1.204 08 kg/m3
- Relative to sea-level standard
- 97.864 %
- Density altitude
- 224.3
- Water vapour partial pressure
- 1169.10 Pa
- Saturation vapour pressure
- 2338.20 Pa
Show the working
- Temperature = 20
- Station pressure = 1013.25
- Relative humidity = 50
- tk = 20 + 273.15 = 293.15
- p_pa = 1013.25 * 100 = 101 325
- Saturation vapour pressure = 610.78 * exp(17.27 * 20 / (20 + 237.3)) = 2338.2
- Water vapour partial pressure = 2338.2 * 50 / 100 = 1169.1
- p_dry = 101 325 - 1169.1 = 100 156
- Air density = 100 156/(287.058*293.15) + 1169.1/(461.495*293.15) = 1.198 83
- If the air were completely dry = 101 325/(287.058*293.15) = 1.204 08
- Relative to sea-level standard = 1.198 83 / 1.225 * 100 = 97.864
- Density altitude = 44330 * (1 - (1.198 83/1.225)^(1/4.2559)) = 224.334
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- density = p_dry/(R_dry T) + p_vapour/(R_vapour T)
- Magnus formula for saturation pressure: 610.78 exp(17.27 t / (t + 237.3))
- R_dry = 287.058 J/(kg K), R_vapour = 461.495 J/(kg K)
Humid air is lighter than dry air, because a water molecule at 18 g/mol displaces nitrogen at 28.
Standard sea-level density is 1.225 kg/m3 at 15 degrees Celsius and 1013.25 hPa.