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Heat Index Calculator

Heat Index equals c1 plus c2 times T plus c3 times R plus c4 times T times R plus c5 times T squared plus c6 times R squared plus c7 times T squared times R plus c8 times T times R squared plus c9 times T squared times R squared

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Heat Index (Rothfusz Regression)

The Rothfusz regression is the standard formula adopted by the U.S. National Weather Service. It is a nine-term polynomial in air temperature (T in °F) and relative humidity (R in %). The equation captures the nonlinear relationship between humidity and perceived heat.

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

How It Works

The heat index combines air temperature and relative humidity into a single number that represents how hot it actually feels. When humidity is high, sweat evaporates more slowly, reducing the body's ability to cool itself. This calculator uses the Rothfusz regression equation, the standard formula adopted by the U.S. National Weather Service. Enter the air temperature and relative humidity as a percentage to get the apparent temperature.

Example Problem

The air temperature is 96 °F and the relative humidity is 65%. What does it feel like outside?

  1. Enter T = 96 °F and R = 65% into the Rothfusz equation
  2. The nine-term polynomial evaluates to approximately 121 °F
  3. This falls in the "Danger" category — heat cramps, exhaustion, and heat stroke are probable

Key Concepts

The heat index combines air temperature and relative humidity into a single 'feels like' temperature. When humidity is high, sweat evaporates more slowly, reducing the body's primary cooling mechanism. The Rothfusz regression is a nine-term polynomial adopted by the U.S. National Weather Service. It is valid for air temperatures of 80 °F and above; below that threshold, humidity has minimal effect on comfort.

Applications

  • Workplace safety: OSHA uses heat index thresholds to trigger mandatory rest breaks and hydration protocols for outdoor workers
  • Sports medicine: coaches and athletic trainers use heat index to decide whether to modify or cancel outdoor practices
  • Public health: weather services issue heat advisories and warnings based on forecast heat index values
  • Military operations: heat index guides activity levels and work-rest cycles for troops in hot climates

Common Mistakes

  • Applying the formula below 80 °F — the Rothfusz regression is not designed for lower temperatures and gives misleading results
  • Using dew point instead of relative humidity — the formula requires RH as a percentage, not dew point temperature
  • Ignoring direct sunlight — the NWS heat index assumes shade; full sun exposure can add 10-15 °F to the perceived temperature
  • Treating heat index as a precise measurement — it is an approximation and individual responses vary based on fitness, clothing, and acclimatization

Frequently Asked Questions

What is the heat index and why does it matter?

The heat index is the "feels like" temperature that accounts for humidity. It matters because heat-related illness risk depends on apparent temperature, not air temperature alone. At 90 °F with 70% humidity, the heat index reaches about 106 °F, putting people at serious risk.

How do you calculate heat index from temperature and humidity?

The NWS uses the Rothfusz regression, a nine-term polynomial in air temperature (T) and relative humidity (R). The equation includes squared and cross terms to capture the nonlinear relationship between humidity and perceived heat.

What heat index is dangerous for outdoor activity?

The NWS classifies heat index values above 105 °F as "Danger" and above 130 °F as "Extreme Danger." At the Danger level, heat cramps, heat exhaustion, and heat stroke become probable with prolonged exposure.

Does the heat index work at any temperature?

The Rothfusz equation is designed for air temperatures of 80 °F and above. Below that threshold, the heat index approximation is less meaningful because humidity has minimal effect on comfort at lower temperatures.

What is the difference between heat index and wet bulb temperature?

The heat index is an empirical "feels like" number for general public use. Wet bulb temperature is a direct physical measurement of evaporative cooling potential. Both account for humidity, but wet bulb is used more in occupational safety and climate science.

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