geoprimsField-grade geospatial math

Humidity and moist air

Dew point, relative humidity, and vapor pressure from each other, with the mixing ratio, virtual temperature, and how much lighter the moist air is than dry air.

Planning and education aid. Not for primary navigation. Full disclaimer

Experimental: not yet fully verified. How results are checked

1.1362kg/m³

Moist air here weighs 1.1362 kg/m³, against 1.1492 kg/m³ if it were dry; relative humidity is 70.3%.

Dry air density
Dew point
Relative humidity
Vapor pressure
Saturation vapor pressure
Mixing ratio
Provenance
Computed by
aviation.atmosphere.humidity 1.0.1, core 0.1.0
Model
e_s(T) = 6.1094 hPa × exp(17.625·T ÷ (T + 243.04)) (Alduchov and Eskridge 1996, over water); e = e_s(dew point) or RH × e_s(T); dew point by inverting the same form; mixing ratio = 622 × e ÷ (p − e) g/kg; virtual temperature T ÷ (1 − 0.378·e ÷ p); densities p ÷ (287.05287 × T)
Accuracy
The saturation pressure is within 0.4% from -40 °C to 50 °C, over liquid water; below freezing over ice it reads high. The densities follow from the ideal-gas law
Notes
1 shown with the answer
Cites
Alduchov, O. A., and R. E. Eskridge, Journal of Applied Meteorology, Improved Magnus Form Approximation of Saturation Vapor Pressure; International Civil Aviation Organization, Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet))

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How we got thisFormula, worked example, sources, and proof

Model: e_s(T) = 6.1094 hPa × exp(17.625·T ÷ (T + 243.04)) (Alduchov and Eskridge 1996, over water); e = e_s(dew point) or RH × e_s(T); dew point by inverting the same form; mixing ratio = 622 × e ÷ (p − e) g/kg; virtual temperature T ÷ (1 − 0.378·e ÷ p); densities p ÷ (287.05287 × T)

Show your work

  1. Virtual temperature

    Tv = T ÷ (1 − 0.378 × e ÷ p)

    303.15 K ÷ (1 − 0.378 × 29.78 ÷ 1,000) = 306.6 K

  2. Moist air density

    ρ = p ÷ (287.05287 × Tv)

    100,000 Pa ÷ (287.05287 × 306.6 K) = 1.1362 kg/m³

The same steps an agent gets from the MCP server with explain: true.

Accuracy: The saturation pressure is within 0.4% from -40 °C to 50 °C, over liquid water; below freezing over ice it reads high. The densities follow from the ideal-gas law

Worked example: 30 °C, dew point 24 °C, 1,000 hPa. Source: add-aviation-suite humid-density scenario: moist air is lighter than dry air at the same temperature and pressure, and both are reported. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Dew point
24 °C
Air pressure
1000 hPa
Temperature
30 °C

You get

Moist air density
1.1362 kg/m³
Dry air density
1.1492 kg/m³
Dew point
24 °C
Relative humidity
70.3
Vapor pressure
29.78 hPa
Saturation vapor pressure
42.37 hPa
Mixing ratio
19.09 g/kg
Virtual temperature
33.45 °C

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

Checked against: 10 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.