# Heat Index

This calculator calculates heat index (apparent temperature), which is used by US meteorologists to determine the human-perceived equivalent temperature, as how hot it would feel if the humidity were some other value in the shade.

After I had created a calculator for Humindex - heat index used in Canada, I decided what I will create a calculator for Heat Index, which is used in the USA, as well.

Below you can find calculators which calculate Heat Index given air temperature in the shade and relative humidity. The first outputs result in Celsius for those used to Celsius degrees, and the second outputs result in Fahrenheit, for those who used to Fahrenheit. As usual, all details are given below the calculators.

#### Heat index using Celsius temperature and relative humidity

Digits after the decimal point: 1
Heat Index

#### Heat index using Fahrenheit temperature and relative humidity

Digits after the decimal point: 1
Heat Index

#### Equations

The Heat Index (or apparent temperature) is based on R.G. Steadman's work published in 1979 under the title "The Assessment of Sultriness, Parts 1 and 2.", so it is the result of extensive biometeorological studies. Originally, results were in tables.

To arrive at an equation that uses more conventional independent variables, a multiple regression analysis was performed on the data from Steadman's tables. It was done by Lans P. Rothfusz and described in his work "The Heat Index "Equation" (or, More Than You Ever Wanted to Know About Heat Index) in 1990. You can find it here, for example.

So, the sequence of calculations is:

1. Heat Index is calculated using this formula:
$HI = -42.379 + 2.04901523*T + 10.14333127*RH - .22475541*T*RH - .00683783*T^2 - .05481717*RH^2 + .00122874*T^{2}*RH + .00085282*T*RH^2 - .00000199*T^{2}*RH^2$,
where T - air temperature in Fahrengeit and RH - relative humidity in percents.

2. If RH is less than 13% and air temperature is between 80 and 112F, the following adjustment is subtracted from HI:
$ADJUSTMENT = [(13-RH)/4]*\sqrt{[17-ABS(T-95.)]/17}$,
where ABS - absolute value.

3. If RH is more than 85% and air temperature is between 80 and 87F, the following adjustment is added to HI:
$ADJUSTMENT = [(RH-85)/10] * [(87-T)/5]$

4. If resulting HI is less than 80F, it is neglected and new Heat Index is calculated using siimpler formula, which approximates results from R. G. Steadman
$HI = 0.5 * {T + 61.0 + [(T-68.0)*1.2] + (RH*0.094)}$

Usually, HI is calculated using simpler formula (4), then averaged with air temperature. If the result is more than 80F, full formulas should be used.

However, these formulas are not usable for temperature and humidity outside of the range used by Steadman. For temperature, it ranges from 20 to 50 degrees Celsius. As for humidity, after the 30C graph is not linear, it is better to look it up for yourself, in Steadman, R.G., 1979: The assessment of sultriness. Part I, for example, here.

Source: National Weather Service

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