Heat Index Formula

Heat Index

The heat index formula is based upon the temperature and relative humidity to indicate the air temperature perceived by the body. For instance, if the temperature is 32°C and 70% relative humidity, the heat index is 41°C. This heat index has an implied humidity of 20%. It’s the value of the relative humidity for which the heat index formula shows 41°C. A heat index temperature of 32°C holds implied relative humidity of 38%.

The heat index formula is expressed as,

HI= c₁+c₂T+c₃R+c₄TR+c₅T₂+c₆R₂+c₇T₂R+c₈TR₂+c₉T₂R₂

In this formula,
HI = heat index in degrees Fahrenheit
R = Relative humidity
T = Temperature in ∘F
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

It is found that whenever HI values exceed above 40^∘C during different temperature and humidity ranges, there is a threat of heatstroke.

Solved Examples

Example 1

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

Substituting the values in the given formula,

HI= c₁+c₂T+c₃R+c₄TR+c₅T₂+c₆R₂+c₇T₂R+c₈TR₂+c₉T₂R₂

Heat Index (HI) = 1410.25^oF

Therefore, the heat index is 1410.25 Fahrenheit.

Example 2

Determine the heat index for the relative humidity of 86% and the temperature of 85oC.
Solution:

Given:
T = 85^∘C
T= 185^∘F,
R = 86%

Substituting the values in the given formula,

HI= c₁+c₂T+c₃R+c₄TR+c₅T₂+c₆R₂+c₇T₂R+c₈TR₂+c₉T₂R₂

Heat Index = 1273.47 ^oF

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