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Physics Formulas

Heat Index Formula

The heat index is a temperature that combines air temperature and relative humidity, in shaded areas. The temperature of the human body normally lowers by perspiration or sweating. The removal of heat from the body is by the evaporation of that sweat. However, high relative humidity reduces the evaporation rate.  The value of relative humidity for which, the heat index number equals the actual air temperature when the temperature is 32 °C and humidity is 70%. For a better understanding of heat index and heat index formula, let us now discuss in detail.

What is the Heat Index?

Heat Index Formula

The heat index is a thermodynamic value that relates to air temperature and humidity. This measurement is made in places that simulate the feeling or perception that the human body can feel. Thus, it is also called the felt air temperature because it is not necessarily the weather or environment temperature, it is the sensation that the body can feel.

The heat index is predicated on temperatures within the shade, while people often move across sunny areas, and then the heat index can give a much lower temperature than actual conditions of typical outdoor activities. Also, for people exercising at the time, then the heat index could give a temperature lower than the original conditions.

Heat Index Formula:

Heat Index (HI) = c1 + c2T + c3R + c4TR + c5T2 + c6R2 + c7T2R + c8TR2 + c9T2R2


HI the heat index (in degrees Fahrenheit)
T ambient temperature in Fahrenheit
R relative humidity
c1 – c9 constants
c1 -42.379
c2 -2.04901523
c3 -10.14333127
c4 -0.22475541
c5 -6.83783 x 10−3
c6 -5.481717 x 10−2
c7 -1.22874 x 10−3
c8 8.5282 x 10−4
c9 -1.99 x 10−6

Uses of Heat Index

It is used to approximate the perception of the human body of the humidity and heat in order to create healthy or public plans that can preserve human and animal safety. The areas in this environment that are exposed to sunlight could have a higher or lower heat index. Also, people doing different activities can perceive different heat and not necessarily feel the heat index calculated for that day or place.

Solved Examples for Heat Index Formula

Q.1: Calculate the HI for a temperature of 85 °C and 86%. Use Heat Index Formula.

Solution: Given: First, covert 85 °C by using formula F= \frac{9}{5}C + 32 gives 185 °F

R = 86%

By using formula of heat index we get

Heat Index (HI) = c1 + c2T + c3R + c4TR + c5T2 + c6R2+c7T2R+c8TR2+ c9T2R2

HI = -42.379 + -2.04901523 x 185 + -10.14333127 x 86 + -0.22475541 x 185 x 86 + -6.83783 x 10−3 x (185)2+-5.481717 x 10−2 x (86)2+ -1.22874 x 10−3 x (185)2× 86 + 8.5282 x 10−4 x 185 x (86)2 + -1.99 x 10−6 x (185)2 x (86)2

So, Heat Index is 1274 °F.

Q2: Determine the heat index if the temperature is 197∘F and the relative humidity is 80%.
Solution: Given,

  • T = 197F,
  • R = 80%

Substituting the values in the given formula,

Heat Index (HI) = c1 + c2T + c3R + c4TR + c5T2 + c6R2 + c7T2R + c8TR2 + c9T2R2

HI = -42.379 + -2.04901523 x 185 + -10.14333127 x 80 + -0.22475541 x 197 x 80 + -6.83783 x 10−3 x (197)2 + -5.481717 x 10−2 x (80)2 + -1.22874 x 10−3 x (197)2 x 80 + 8.5282 x 10−4 x 197 x (80)2 + -1.99 x 10−6 x (197)2 x (80)2

So, Heat Index = 1410.25 °F

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