Heat Index (Rothfusz Regression)
The Rothfusz regression is the standard U.S. National Weather Service formula for apparent temperature. It combines air temperature and relative humidity to estimate how hot conditions feel to the human body in shaded, low-wind conditions.
HI = c₁ + c₂T + c₃R + c₄TR + c₅T² + c₆R² + c₇T²R + c₈TR² + c₉T²R²
How It Works
Heat index combines air temperature and relative humidity into a single feels-like temperature. The higher the humidity, the harder it is for sweat to evaporate and cool the body, so the apparent temperature rises faster than the thermometer alone suggests. This calculator uses the Rothfusz regression, the polynomial adopted by the U.S. National Weather Service for hot, humid weather.
Example Problem
The air temperature is 96 °F and the relative humidity is 65%. What does it feel like outside, and how serious is the heat-stress risk?
- Confirm the formula is in range: 96 °F is above 80 °F and 65% humidity is above 40%, so the Rothfusz regression applies.
- Square the inputs for the polynomial terms: T² = 96² = 9,216 and R² = 65² = 4,225.
- Substitute T = 96 and R = 65 into the full NWS equation with all cross terms and squared terms.
- Evaluate the polynomial to get HI ≈ 121.03 °F.
- Compare 121 °F to the NWS danger bands: it falls in the Danger category, where heat cramps, heat exhaustion, and heat stroke become likely.
- Interpret the result operationally: strenuous outdoor activity should be shortened, hydrated carefully, and scheduled around shade or cooling breaks.
The published heat index assumes shade. Direct sunlight can push the apparent temperature another 10–15 °F higher.
Key Concepts
Heat index is not just hot air plus moisture; it is a proxy for reduced evaporative cooling. When the air is already full of moisture, sweat cannot evaporate efficiently, so the body loses heat more slowly and core temperature rises faster. That is why 90 °F with high humidity can be more dangerous than 100 °F in very dry desert air.
Applications
- Outdoor job-site planning: construction, utility, and landscaping crews use heat index thresholds to adjust work-rest cycles and hydration schedules.
- School and sports operations: coaches and athletic trainers use apparent temperature to shorten practices, add breaks, or move activities indoors.
- Public weather alerts: forecast offices use heat index to issue advisories and warnings because it better reflects human heat stress than temperature alone.
- Travel and event planning: organizers use heat index to estimate crowd comfort and risk during concerts, festivals, and long queue times.
Common Mistakes
- Using the formula below 80 °F or below 40% humidity — the Rothfusz regression is not intended for those conditions and can produce misleading numbers.
- Treating heat index as a direct thermometer reading — it is an apparent temperature meant to describe human heat stress, not the actual air temperature.
- Ignoring sunlight, clothing, or exertion — the standard heat index assumes shade and light wind, so real conditions can feel even hotter.
- Confusing relative humidity with dew point — the equation specifically requires relative humidity as a percentage.
Frequently Asked Questions
How do you calculate heat index?
You calculate heat index by combining air temperature and relative humidity in the Rothfusz regression, the formula used by the U.S. National Weather Service. The result estimates how hot it feels in shaded, humid conditions where sweat evaporation is less effective.
What is the formula for heat index?
The standard formula is the Rothfusz regression: HI = c₁ + c₂T + c₃R + c₄TR + c₅T² + c₆R² + c₇T²R + c₈TR² + c₉T²R², where T is air temperature in °F and R is relative humidity in percent. Those coefficients were fit to apparent-temperature data and are the published National Weather Service standard.
What heat index is considered dangerous?
A heat index above about 105 °F falls into the Danger category, where heat cramps, heat exhaustion, and heat stroke become much more likely with prolonged exposure. Values above 130 °F are considered Extreme Danger and can become life-threatening quickly.
Why does humidity make hot weather feel worse?
Humidity slows the evaporation of sweat, which is the body's main cooling mechanism in hot weather. If sweat cannot evaporate efficiently, the body retains more heat and the apparent temperature rises even if the actual air temperature stays the same.
Does heat index work in direct sunlight?
Not exactly. The published heat index assumes shaded conditions with light wind. In full sun, the apparent temperature can feel another 10–15 °F hotter depending on clothing, wind, and surface radiation.
What is the difference between heat index and wet-bulb temperature?
Heat index is a public-facing feels-like number built from temperature and relative humidity. Wet-bulb temperature is a physical thermodynamic quantity tied to evaporative cooling potential and is used more often in occupational safety and atmospheric science.
Can you calculate heat index in Celsius?
Yes, but the Rothfusz regression itself is defined in Fahrenheit. A calculator can convert your Celsius input to Fahrenheit for the computation, then convert the final apparent temperature back to Celsius for display.
Reference: U.S. National Weather Service, Weather Prediction Center. Heat Index equation and danger categories.
Heat Index Formula (Rothfusz Regression)
The National Weather Service uses the Rothfusz regression to estimate how hot the air feels when humidity slows sweat evaporation:
HI = c₁ + c₂T + c₃R + c₄TR + c₅T² + c₆R² + c₇T²R + c₈TR² + c₉T²R²
Where:
- HI — heat index or apparent temperature
- T — air temperature in degrees Fahrenheit (°F)
- R — relative humidity in percent (%)
- c₁ ... c₉ — the standard Rothfusz coefficients used by the U.S. National Weather Service
Valid range: T ≥ 80 °F and RH ≥ 40%. The published heat index also assumes light wind and shaded conditions; full sun can make it feel 10–15 °F hotter.
Worked Examples
Athletics — Summer Practice
How hot does a 90 °F afternoon feel at 55% humidity?
A high school soccer team is practicing in 90 °F air with 55% relative humidity. Coaches want to know the apparent temperature before deciding on water breaks.
- Set T = 90 °F and R = 55%.
- Substitute into the Rothfusz regression with T in °F and R in percent.
- Evaluate the polynomial to get HI ≈ 96.99 °F.
- Classify the result: about 97 °F falls in the Extreme Caution band.
Result: The heat index is about 97.0 °F, so prolonged drills need shade, hydration, and rest breaks.
Direct sun can make it feel another 10–15 °F hotter than the shaded heat index value.
Construction — Roofing Crew
What does 100 °F air feel like at 40% humidity?
A roofing crew starts work with an air temperature of 100 °F and relative humidity right at 40%. The site superintendent wants to know the heat-stress category.
- Set T = 100 °F and R = 40%.
- Use the NWS formula in its valid range: T ≥ 80 °F and RH ≥ 40%.
- Compute HI ≈ 109.26 °F.
- Compare the result to the heat danger bands used in weather alerts and work-rest planning.
Result: The heat index is about 109.3 °F, which is firmly in the Danger range.
At this level, supervisors should shorten work bouts and increase cooling breaks even if the humidity looks moderate.
Travel — Tropical Afternoon
How does 30 °C air feel at 70% humidity?
A traveler in Singapore sees 30 °C on the thermometer with 70% relative humidity and wants the feels-like temperature in Celsius.
- Set T = 30 °C and R = 70%, then convert 30 °C to 86 °F for the formula.
- Evaluate the Rothfusz regression in Fahrenheit.
- Convert the result back to Celsius for display.
- Interpret the result against the heat-risk bands for outdoor sightseeing.
Result: The heat index is about 35.0 °C (95.1 °F), which lands in the Extreme Caution range.
Even when the air temperature looks manageable, tropical humidity can push the apparent temperature into a higher heat-stress category.
Related Calculators
- Wind Chill Calculator — calculate how cold winter air feels when wind accelerates heat loss.
- Water Vapor Pressure Calculator — estimate saturation pressure at a given temperature using the Antoine equation.
- Relative Humidity Calculator — compute relative humidity from temperature and dew point data.
- Temperature Conversion Calculator — convert between Fahrenheit, Celsius, Kelvin, and Rankine.
- Cloud Base Calculator — estimate condensation height from temperature and dew point.
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