e = partial pressure of water vapour [Pa]
p = air pressure [Pa]

q = specific hmidity = 0.622 * e / (p - 0.378 *e)  [kg/kg]
r_w= mass mixing ratio = 0.622 * e / (p - e)  [kg/kg]

T = temperature
R^* = universal gas constant = 8314.472 J K⁻¹ mol⁻¹
m_w = molar mass of water vapour = 0.018015 kg/mol
R_w = individual gas constant of water vapour = R^*/m_w = 461.53 J K⁻¹ kg⁻¹

ρ_w = water-vapour density = e/(T R_w) [kg/m³]

T_D = dewpoint temperature = {2.0798233·10² - 2.0156028·10¹ ln e + 4.6778925·10^-1 (ln e)² -9.2288067·10^-6 (ln e)³ } /
        {1 - 1.3319669·10^-1 ln e + 5.6577518·10^-2 (ln e)² - 7.5172865·10^-5 (ln e)³ } [K]

E = saturation vapour pressure = exp { 54.842763 - (6763.22 / T) - 4.21 * ln(T) + 0.000367 * T
       + tanh [ 0.0415 * (T - 218.8) ] * [ 53.878 - 1331.22 / T - 9.44523 * ln(T) + 0.014025 * T ] } [Pa]

F = relative humidity = e/E

Water-vapour pressure given

e: hPa     p: hPa     T: K|°C     

Specific humidity given

s: g/kg     p: hPa     T: K|°C     

Mass mixing ratio given

r_w: g/kg     p: hPa     T: K|°C     

Water-vapour density given

ρ_w: g/m³     p: hPa     T: K|°C     

Dewpoint temperature given

T_D: K|°C     p: hPa     T: K|°C     

Relative humidity given

F: %     p: hPa     T: K|°C