Today, I had to calculate relative humidity using PHP and I have documented my findings below:
First, let's just use an example situation where we have a temperature of 60.1 and a dew point of 42.7, both in Fahrenheit, so...:
dew point in Fahrenheit: 42.7
temperature in Fahrenheit: 60.1
1) The first step is to convert to Celsius using the following formulas
Tc=5.0/9.0*(Tf-32.0)
Tdc=5.0/9.0*(Tdf-32.0)
Formulas explained:
Tc=air temperature in degrees Celsius, Tf=air temperature in degrees Fahrenheit
Tdc=dewpoint temperature in degrees Celsius
Tdf=dewpoint temperature in degrees Fahrenheit
Notice: If your temperature and dewpoint are in degrees Celsius, you can skip step 1 and proceed to step 2.
answer for equations:
Temp in Celsius: 15.61
Tc=5.0/9.0*(Tf-32.0)
5.0/9.0*(60.1-32.0)
5.0/9.0*28.1
0.5555555555555556 * 28.1 = 15.61111111111111
dewpoint in Celsius: 5.94
5.0/9.0*(Tdf-32.0)
5.0/9.0*10.7
0.5555555555555556 * 10.7 = 5.944444444444444
2) calculate saturation vapor pressure(Es) and actual vapor pressure(E) in millibars:
NOTE: first line is the equation and the subsequent lines represent one step solved at a time:
Es=6.11*10.0**(7.5*Tc/(237.7+Tc))
Es=6.11*10.0**(7.5*15.61/(237.7+15.61))
Es=61.1 ** (7.5*15.61/(237.7+15.61))
Es=61.1 ** (117.075/253.31)
Es = 61.1**0.4621807271722395
Es = 6.6907349413770067935260257174923
E=6.11*10.0**(7.5*Tdc/(237.7+Tdc))
E=6.11*10.0**(7.5*5.94/(237.7+5.94))
E=61.1 ** (7.5*5.94/(237.7+5.94))
E=61.1 ** (44.55/243.64)
E=61.1 ** 0.1828517484813659497619438515843
E = 2.1211957981192776150462474985589
3) Once you have the saturation vapor pressure and actual vapor pressure, relative humidity(RH) can be computed by dividing the actual vapor pressure by the saturation vapor pressure and then multiplying by 100 to convert the quantity to a percent:
RH =(E/Es)*100
RH =(2.1211957981192776150462474985589/6.6907349413770067935260257174923)*100
RH = 0.31703479762758596814611114744566 * 100
RH = 31.703479762758596814611114744566%
SO... Humidity is 31.7%
And note here that ** means to the power of. I figured I'de clue anyone in that is as ignorant is I was when I had to figure it out.