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Humidity Calculator

Computes the saturation pressure, vapor pressure, humidity ratio and vapor mass fraction from dry-bulb temperature and relative humidity.

Inputs

Moist-air state. Defaults are a comfortable room condition at standard atmospheric pressure.

Dry-bulb temperature in degrees Celsius.
0 to 100 percent.
Standard atmosphere is 101.325 kPa.

Results

Humidity ratio ω
-
Grams of vapor per kg of dry air.
Saturation pressure Pg
-
Vapor partial pressure Pv
-
Vapor mass fraction Y
-
Use as the species mass fraction at CFD inlets.

How it works

Relative humidity is defined against the saturation pressure at the dry-bulb temperature. The calculator evaluates that saturation pressure with the Arden Buck equation, converts it to a vapor partial pressure, then uses the ideal-gas relation between the two components to get the humidity ratio and the vapor mass fraction.

  1. Compute the saturation pressure Pg with the Arden Buck equation (one form above 0 C, one below), in kPa.
  2. Get the vapor partial pressure from the relative humidity: Pv = φ Pg.
  3. Compute the humidity ratio ω = 0.622 Pv / (P - Pv), where 0.622 is the ratio of molar masses of water and dry air.
  4. Convert to the vapor mass fraction Y = ω / (1 + ω).
Saturation pressure, T ≥ 0 C (Arden Buck)
Pg = 0.61121 exp[(18.678 - T/234.5)(T/(257.14 + T))]
Saturation pressure, T < 0 C (Arden Buck)
Pg = 0.61121 exp[(23.036 - T/333.7)(T/(279.82 + T))]
Vapor partial pressure
Pv = φ Pg
Humidity ratio
ω = 0.622 Pv / (P - Pv)
Vapor mass fraction
Y = ω / (1 + ω)
T
Dry-bulb temperature, C
φ
Relative humidity as a fraction
P
Total pressure, kPa
Pg
Saturation pressure of water vapor, kPa
Pv
Partial pressure of water vapor, kPa
ω
Humidity ratio, kg vapor per kg dry air
Y
Vapor mass fraction, kg vapor per kg mixture

References

  • Buck, A. L., "New equations for computing vapor pressure and enhancement factor", J. Applied Meteorology, 20, 1981.
  • ASHRAE Handbook, Fundamentals, 2021, Chapter 27 (Psychrometrics).