Q:  How do I calculate dew point when I know the temperature and the relative humidity?

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 (dewpoint).

--Michael Bell