The computation of the heat index is a refinement of a result obtained by multiple regression analysis carried out by Lans P. Rothfusz and described in a 1990 National Weather Service (NWS) Technical Attachment (SR 90-23).  The regression equation of Rothfusz is

HI = -42.379 + 2.04901523*T + 10.14333127*RH - .22475541*T*RH - .00683783*T*T - .05481717*RH*RH + .00122874*T*T*RH + .00085282*T*RH*RH - .00000199*T*T*RH*RH

where T is temperature in degrees F and RH is relative humidity in percent.  HI is the heat index expressed as an apparent temperature in degrees F.  If the RH is less than 13% and the temperature is between 80 and 112 degrees F, then the following adjustment is subtracted from HI:

ADJUSTMENT = [(13-RH)/4]*SQRT{[17-ABS(T-95.)]/17}

where ABS and SQRT are the absolute value and square root functions, respectively.  On the other hand, if the RH is greater than 85% and the temperature is between 80 and 87 degrees F, then the following adjustment is added to HI:

ADJUSTMENT = [(RH-85)/10] * [(87-T)/5]

The Rothfusz regression is not appropriate when conditions of temperature and humidity warrant a heat index value below about 80 degrees F. In those cases, a simpler formula is applied to calculate values consistent with Steadman's results:

HI = 0.5 * {T + 61.0 + [(T-68.0)*1.2] + (RH*0.094)}

In practice, the simple formula is computed first and the result averaged with the temperature. If this heat index value is 80 degrees F or higher, the full regression equation along with any adjustment as described above is applied.

The Rothfusz regression is not valid for extreme temperature and relative humidity conditions beyond the range of data considered by Steadman.