Dewpoint from relative humidity and temperature
If you know the relative humidity and the air temperature, and want to calculate the dewpoint, the formulas are as follows.
First, if your air temperature is in degrees Fahrenheit, then you must convert it to degrees Celsius by using the Fahrenheit to Celsius formula.
(8) Tc=5.0/9.0*(Tf-32.0)
The next step is to obtain the saturation vapor pressure(Es) using formula (5) as before when air temperature is known.
(5) Es=6.11*10.0**(7.5*Tc/(237.7+Tc))
The next step is to use the saturation vapor pressure and the relative humidity to compute the actual vapor pressure(E) of the air. This can be done with the following formula.
(9) E=(RH*Es)/100
RH=relative humidity of air expressed as a percent.(i.e. 80%)
Now you are ready to use the following formula to obtain the dewpoint temperature.
Note: ln( ) means to take the natural log of the variable in the parentheses
(10) Tdc=(-430.22+237.7*ln(E))/(-ln(E)+19.08)
If you wish, you can convert the Celsius dewpoint back into the Fahrenheit scale using the following formula.
(11) Tdf=(9.0/5.0)*Tdc+32
For example, if you have a weather station that gave you an air temperature of 60 degrees Fahrenheit and a relative humidity of 47%(percent) and you wanted to compute the dewpoint temperature, you would proceed as follows.
First, convert the air temperature to degrees Celsius by using formula (8). You should get Tc=15.6
Next, using formula (5) again, compute the saturation vapor pressure for an air temperature of 15.6 degrees Celsius. You should get 17.7.
Next, compute the actual vapor pressure by using formula (9). You should get E=8.3
Finally, you can compute the dewpoint temperature by using formula (10). You should get Tdc=4.3
If you want to convert this dewpoint temperature back into degrees Fahrenheit, you can do so by using formula (11). You should get Tdf=39.7
Note: Due to the rounding of decimal places, your answer may be slightly different from the above answer, but it should be within two degrees.