Heat Index Calculator
Calculate the heat index (apparent temperature) using air temperature and humidity. Get instant results with the Rothfusz regression formula and OSHA safety zones.
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Biometeorology & Mathematical Derivation
Steadman’s human energy balance equation and the 9-term Rothfusz polynomial regression
The human body continuously generates metabolic heat ($M$). To maintain a vital core temperature of approximately 98.6°F (37.0°C), this thermal energy must be dissipated to the surrounding atmosphere. According to the classical human thermal energy balance equation:
Where S is rate of heat storage, R is radiation, C is convection, K is conduction, and E is evaporative cooling through sweat vaporization. Evaporating one gram of sweat absorbs approximately 2,430 Joules (0.58 kcal) of latent heat from cutaneous capillary beds. However, the rate of sweat evaporation is governed strictly by the vapor pressure gradient between saturated skin air (P_skin ≈ 5.62 kPa at 35°C) and ambient air (P_ambient).
When relative humidity rises, P_ambient approaches saturation, severely attenuating evaporative flux. In 1979, biometeorologist Dr. Robert G. Steadman quantified this "sultriness" by modeling a standard human walking outdoors in light shade (5 ft 7 in tall, 147 lbs, dressed in trousers and short-sleeved shirt). In 1990, Lans P. Rothfusz of the National Weather Service (NWS) fitted a multivariable 9-term polynomial regression to Steadman’s biometeorological tables:
c₆ = -0.05481717 | c₇ = 0.00122874 | c₈ = 0.00085282 | c₉ = -0.00000199
Boundary Adjustments and Preliminary Conditions
For temperatures where the preliminary equation $0.5 \times [T + 61.0 + ((T - 68.0)/1.2) + 0.094 \times RH]$ produces values below 80°F, the simple apparent temperature is utilized directly. For conditions triggering full Rothfusz regression, the NWS enforces two empirical adjustments:
Adjustment = [ (13 - RH) / 4 ] × √[ (17 - |T - 95|) / 17 ]
Subtracted from raw HI to account for enhanced evaporative cooling in arid desert atmospheres.
Adjustment = [ (RH - 85) / 10 ] × [ (87 - T) / 5 ]
Added to raw HI to account for vapor barrier saturation at sub-90°F tropical temperatures.
OSHA & NWS Heat Stress Classification Matrix
Apparent temperature bands, clinical heat disorders, and occupational work-rest schedules
| Heat Index (°F / °C) | Hazard Category | Clinical Risk Level | OSHA Hydration & Rest Protocol |
|---|---|---|---|
| < 80°F (< 26.7°C) | Normal / Minimal | Minimal heat illness risk for healthy, non-acclimatized adults. | Standard fluid consumption (water on demand). Normal work shifts. |
| 80°F - 90°F (26.7°C - 32.2°C) | Caution | Fatigue possible with prolonged exposure and sustained physical exertion. | 1 cup (8 oz) cool water every 20 minutes. Provide accessible shade breaks. |
| 91°F - 103°F (32.8°C - 39.4°C) | Extreme Caution | Sunstroke, muscle cramps, and heat exhaustion possible with prolonged activity. | 2-3 cups water/electrolytes per hour. Mandatory 10-min shade rest per hour. |
| 104°F - 124°F (40.0°C - 51.1°C) | Danger | Heat cramps and heat exhaustion likely; heat stroke possible with continued work. | 3-4 cups fluid per hour. Mandatory 15-20 min rest in conditioned area per hour. |
| ≥ 125°F (≥ 51.7°C) | Extreme Danger | Heat stroke highly imminent. Life-threatening medical emergency. | Stop all non-emergency outdoor labor. Seek immediate conditioned shelter. |
*Source: Compiled from National Oceanic and Atmospheric Administration (NOAA) National Weather Service directives and OSHA Technical Manual Section III: Chapter 4 (Heat Stress).
Frequently Asked Questions
Authoritative biometeorological answers on heat indices, human thermal strain, and formulas
Which formula does this Heat Index Calculator use?
It implements the National Oceanic and Atmospheric Administration (NOAA) Rothfusz regression equation—a 9-term polynomial derived from Dr. Robert Steadman's human biometeorological model—complete with low-humidity and high-humidity boundary adjustments.
Why is no heat index warning triggered for temperatures below 80°F?
At dry-bulb ambient temperatures below 80°F (26.7°C), the human body sheds metabolic heat predominantly through dry radiative and convective heat exchange. Sweat evaporation is not the limiting factor for core thermoregulation at low temperatures, making apparent heat stress calculations medically inapplicable.
How does direct sunlight impact the effective heat index?
The standard NOAA heat index assumes shady, light wind conditions. Direct exposure to solar radiation adds shortwave radiant thermal loading to the human body, elevating apparent thermal stress by up to 15°F (8.3°C) above ambient shade measurements.
What is the difference between the US Heat Index, Canadian Humidex, and Wet-Bulb Globe Temperature (WBGT)?
The US Heat Index uses Steadman's regression in the shade. The Canadian Humidex relies on dew point vapor pressure equations. Wet-Bulb Globe Temperature (WBGT) integrates dry temperature, natural wet-bulb humidity, wind speed, and solar radiant load, making WBGT the preferred standard for military, athletics, and industrial occupational safety.
Why does high relative humidity impair human evaporative cooling?
When ambient air approaches moisture saturation (high relative humidity), the ambient water vapor pressure approaches the saturation vapor pressure at skin temperature (approximately 35°C). This diminishes the vapor pressure gradient required for sweat to evaporate into the air, preventing latent heat loss and forcing core body temperature to surge.