Is there a mathematical relationship between air temperture, relative humidity, and the dew point...?

Question

such that if you knew 2 of these factors, you could determine the third factor? If so, what is the equation?
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Answer 1

Yes. An approximate value is:
T_dp = T - (100 - RH) / 5

That's for Celsius. For more information, see

http://en.wikipedia.org/wiki/Dew_point