Thanks TD2K and CB for sending me spreadsheets. Both gave the same answer for a test case. TD2K's was a little easier for me to understand. Below are the equations that I extracted from his spreadsheet:
# Symbols are as follows:
> # TwbF - wet bulb temperature in degrees F
> # TdbF - dry bulb temperature in degrees F
> # TwbK - wet bulb temperature in degrees K
> # TdbK - dry bulb temperature in degrees K
> # Vwb - Vapor pressure associated with saturation conditions at wet bulb temperature.
> # Vdb - Vapor pressure associated with saturation conditions at dry bulb temperature.
> # RH - Relative Humidity
> TwbK:=(TwbF-32)*5/9+273;
TwbK := 5/9 TwbF + 2297/9
> TdbK:=(TdbF-32)*5/9+273;
TdbK := 5/9 TdbF + 2297/9
> Vwb:=6.11*exp((2453000/461)*(1/273-1/TwbK));
Vwb := 6.11*exp(2453000/125853-2453000/461/(5/9*TwbF+2297/9))
> Vdb:=6.11*exp((2453000/461)*(1/273-1/TdbK));
Vdb := 6.11*exp(2453000/125853-2453000/461/(5/9*TdbF+2297/9))
> RH:=Vwb/Vdb;
RH := exp(2453000/125853-2453000/461/(5/9*TwbF+2297/9))/exp(2453000/125853-2453000/461/(5/9*TdbF+2297/9))
> RH:=simplify(Vwb/Vdb);
RH := exp(239446.854663774*(TwbF-1.*TdbF)/(5.*TwbF+2297.)/(5.*TdbF+2297.))
The above expression for RH is suitable for plugging directly into an excel formula if you change the TwbF and TdbF to cell references.
An example calculation using TwbF=80,TdbF=90, yields RH= .724
Thanks again.