Heat Index Formula
Reference for the Rothfusz heat index formula using temperature in °F and humidity to calculate apparent temperature.
Covers NWS danger zones.
The Formula
- 0.00683783T² - 0.05481717R² + 0.00122874T²R
+ 0.00085282TR² - 0.00000199T²R²
The heat index combines air temperature and relative humidity to show how hot it actually feels. High humidity prevents sweat from evaporating, making the body feel much hotter.
Variables
| Symbol | Meaning |
|---|---|
| HI | Heat index — apparent temperature (°F) |
| T | Air temperature (°F) |
| R | Relative humidity (%) |
Note: This formula is valid when T ≥ 80°F (27°C) and R ≥ 40%. For Celsius, convert first: °F = °C × 9/5 + 32.
Example 1
Temperature is 95°F (35°C) with 50% humidity
Plugging T = 95, R = 50 into the formula:
HI ≈ -42.4 + 194.7 + 507.2 - 1066.0 - 61.6 - 137.0 + 55.5 + 38.5 - 0.9
HI ≈ 107°F (42°C) — Danger zone: heat exhaustion likely
Example 2
Temperature is 85°F (29°C) with 80% humidity
Plugging T = 85, R = 80 into the formula:
HI ≈ 97°F (36°C) — Extreme Caution zone
When to Use It
Use the heat index formula when:
- Assessing outdoor safety for workers or athletes
- Planning outdoor events in hot, humid weather
- Issuing heat warnings and advisories
- Understanding the health risk of combined heat and humidity
Key Notes
- Valid range only: The heat index formula is only accurate when the temperature is at least 27°C (80°F) and relative humidity is at least 40%. Outside this range, the result is unreliable.
- Measures apparent temperature in shade: The heat index applies to shaded conditions. Direct sunlight can raise the apparent temperature by an additional 8°C (15°F) beyond the heat index value.
- Why humidity matters: The human body cools itself through sweat evaporation. High humidity reduces evaporation efficiency, making the body retain more heat — hence why humid heat feels hotter than dry heat.
- Heat index vs wind chill: Heat index is used in warm, humid conditions to show how hot it feels. Wind chill is used in cold, windy conditions to show how cold it feels. They measure opposite extremes of thermal comfort.
- Health thresholds: A heat index of 40–54°C (103–129°F) is considered "dangerous." Above 54°C (130°F) is "extremely dangerous" with heat stroke highly likely. These thresholds guide public health warnings.