A: Relative
humidity gives the ratio of how much moisture the air is holding to how
much moisture it could hold at a given temperature.

This can be expressed in terms of vapor pressure and
saturation vapor pressure:

RH = 100% x (E/Es)

where, according to an approximation of the Clausius-Clapeyron equation:

E = E0 x exp[(L/Rv) x {(1/T0) - (1/Td)}] and

Es = E0 x exp[(L/Rv) x {(1/T0) - (1/T)}]

where E0 = 0.611 kPa, (L/Rv) = 5423 K (in Kelvin, over a flat surface of water), T0 = 273 K (Kelvin)

and T is temperature (in Kelvin), and Td is dew point temperature (also in Kelvin).

So, if you know the temperature, you can solve for Es, and substitute the equation for E into the expression for relative humidity and solve for Td (dew point).

If you are interested in a simpler calculation that gives an approximation of dew point temperature if you know the observed temperature and relative humidity, the following formula was proposed in a 2005 article by Mark G. Lawrence in the Bulletin of the American Meteorological Society:

Td = T - ((100 - RH)/5.)

where Td is dew point temperature (in degrees Celsius), T is observed temperature (in degrees Celsius), and RH is relative humidity (in percent). Apparently this relationship is fairly accurate for relative humidity values above 50%.

More details can be found in the article:

Lawrence, Mark G., 2005: The relationship between relative humidity and the dewpoint temperature in moist air: A
simple conversion and applications. *Bull. Amer. Meteor. Soc.*, **86**, 225-233.
doi: http;//dx.doi.org/10.1175/BAMS-86-2-225

*--Michael Bell*