Heat Index and Wind Chill Formulas

I'm writing this because nobody seems to have an easy to copy and paste formula out there for coders or even for spread sheets.

It's all fine-and-dandy that somebody understands all the ins-and-outs of weather and the math behind it, but sometimes we just want to display the Wind Chill or Heat Index, and that's it. I don't need to know all about the weather … some of us have deadlines to meet. These formulas are for those of you who are of a similar mind set.

Here are the formulas to calculate the Heat Index and the Wind Chill in Spreadsheet formulas and for PHP scripts (programs).

Heat Index

The Heat Index should only be calculated when air temperatures are greater than 80°F (27°C), dew point temperatures are greater than 60°F (16°C), and relative humidities are higher than 40%.

Spreadsheet:

 =ROUND(16.923 + (1.85212 * 10^-1 * A1) + (5.37941 * B1) - (1.00254 * 10^-1 * A1 * B1) + (9.41695 * 10^-3 * A1^2) + (7.28898 * 10^-3 * B1^2) + (3.45372 * 10^-4 * A1^2 * B1) - (8.14971 * 10^-4 * A1 * B1^2) + (1.02102 * 10^-5 * A1^2 * B1^2) - (3.8646 * 10^-5 * A1^3) + (2.91583 * 10^-5 * B1^3) + (1.42721 * 10^-6 * A1^3 * B1) + (1.97483 * 10^-7 * A1 * B1^3) - (2.18429 * 10^-8 * A1^3 * B1^2) + (8.43296 * 10^-10 * A1^2 * B1^3) - (4.81975 * 10^-11 * A1^3 * B1^3)) 

Where A1 holds the TEMPERATURE, and B1 holds the HUMIDITY.

PHP:

$heat_index_f = round(16.923 + (1.85212 * pow(10, -1) * $temp_f) + (5.37941 * $humidity) - (1.00254 * pow(10, -1) * $temp_f * $humidity) + (9.41695 * pow(10, -3) * pow($temp_f, 2)) + (7.28898 * pow(10, -3) * pow($humidity, 2)) + (3.45372 * pow(10, -4) * pow($temp_f, 2) * $humidity) - (8.14971 * pow(10, -4) * $temp_f * pow($humidity, 2)) + (1.02102 * pow(10, -5) * pow($temp_f, 2) * pow($humidity, 2)) - (3.8646 * pow(10, -5) * pow($temp_f, 3)) + (2.91583 * pow(10, -5) * pow($humidity, 3)) + (1.42721 * pow(10, -6) * pow($temp_f, 3) * $humidity) + (1.97483 * pow(10, -7) * $temp_f * pow($humidity, 3)) - (2.18429 * pow(10, -8) * pow($temp_f, 3) * pow($humidity, 2)) + (8.43296 * pow(10, -10) * pow($temp_f, 2) * pow($humidity, 3)) - (4.81975 * pow(10, -11) * pow($temp_f, 3) * pow($humidity, 3))); 

Where $temp_f is the temperature in degrees Fahrenheit, and $humidity holds the humidity.

Wind Chill

The Wind Chill should only be calculated when temperatures are at or below 50°F and wind speeds are above 3 MPH. Bright sunshine may increase the wind chill temperature by 10°F to 18°F.

Spreadsheet:

=ROUND(35.74 + (0.6215 * A1) - 35.75 * (B1^0.16) + 0.4275 * A1 * (B1^0.16)) 

Where A1 holds the TEMPERATURE, and B1 holds the WIND VELOCITY (SPEED).

PHP:

$temp_chill_f = round(35.74 + (0.6215 * $temp_f) - (35.75 * (pow($wind_speed, 0.16))) + (0.4275 * $temp_f * (pow($wind_speed, 0.16)))); 

Where $temp_f is the temperature in degrees Fahrenheit, and $wind_speed holds the wind speed in Miles Per Hour (MPH).

I hope this helps to keep someone from spending an hour debugging their code when it was a simple typo that may have messed them up.