Wind chill and NWS heat-index calculations with input checks

Distinguish apparent-temperature models from a safety decision

These educational examples do not determine safe working conditions, exposure time or an individual medical risk. Wind chill and heat index describe different effects and use different units here.

Wind chill uses Celsius and wind speed in km/h. This implementation applies the metric equation at T<=10 C and wind above 4.8 km/h (approximately 3 mph). Outside that range it reports Outside wind-chill domain rather than relabeling ambient temperature as a wind-chill result.

For heat index, enter Fahrenheit and humidity in percent from 0 to 100. The NWS sequence first averages a simple estimate with air temperature; at 80 F or above it uses the Rothfusz regression and applicable low/high humidity adjustments. It does not impose a universal RH>=40 threshold.

Heat-index assumptions concern shaded conditions. It is not WBGT and does not capture all effects of exertion, sun, clothing or individual susceptibility. Extreme conditions outside the underlying regression data need other methods.

Guarded Metric Wind Chill Index (°C) for T <= 10°C and Wind > 4.8 km/h

Rejects negative wind or missing data. Warm or low-wind inputs are reported outside this formula domain.

=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(B3<0,"Invalid inputs",IF(OR(B2>10,B3<=4.8),"Outside wind-chill domain",ROUND(13.12+0.6215*B2-11.37*B3^0.16+0.3965*B2*B3^0.16,2))))

NWS preliminary estimate, regression and humidity corrections

LET names keep the steps readable. The low-humidity subtraction is applied below 13% RH at 80–112 F; the high-humidity addition applies above 85% RH at 80–87 F. Only the final output is rounded.

=IF(COUNT(B4:B5)<>2,"Invalid inputs",IF(OR(B5<0,B5>100),"Invalid inputs",LET(temp,B4,humidity,B5,prelim,(0.5*(temp+61+(temp-68)*1.2+humidity*0.094)+temp)/2,ROUND(IF(prelim<80,prelim,-42.379+2.04901523*temp+10.14333127*humidity-0.22475541*temp*humidity-0.00683783*temp^2-0.05481717*humidity^2+0.00122874*temp^2*humidity+0.00085282*temp*humidity^2-0.00000199*temp^2*humidity^2-IF(AND(humidity<13,temp>=80,temp<=112),((13-humidity)/4)*SQRT(MAX(0,(17-ABS(temp-95))/17)),0)+IF(AND(humidity>85,temp>=80,temp<=87),((humidity-85)/10)*((87-temp)/5),0)),1))))

Further reading

• Microsoft Support — OR function
• National Weather Service — Heat index calculation
• National Weather Service — Wind Chill Questions