e = water-vapour pressure [hPa]
(after Smithsonian Meteorological Tables, 1984)

e(T) = e(T_w) - 6.6·10^-4 (1 + 1.15· 10^-3T_w) p |T-T_w|


T = temperature [°C]
e(T_w) = saturation vapour pressure at T_w [Pa]
T_w = wet-bulb temperature [°C]
p = pressure [Pa]

R = e / E = relative humidity
E = saturation vapour pressure at T [hPa]


Calculation of wet-bulb temperature (coarse approximation for p = 1013.25 hPa)
(after R. Stull, J. Appl. Meteor. and Clim., 2011)

T_w = T atan[0.151977(R + 8.313659)^1/2] + atan(T + R) - atan(R - 1.676331)
     + 0.00391838 R^3/2 atan(0.023101 R) - 4.686035     (T in °C and R in %)

Vapour pressure and relative humidity calculation

T: °C      T_w: °C      p: hPa   

e: hPa

R: %

Wet-bulb temperature calculation (only for p=1013.25 hPa)

T: °C      R: %     

T_w: °C