# What is the heat index?

Computes the heat index (how hot it feels) from the air temperature and relative humidity with the US National Weather Service algorithm, in °F and °C, with the NWS caution level.

- Page: https://www.acalculator.org/physics/heat-index-calculator
- JSON spec: https://www.acalculator.org/physics/heat-index-calculator.json
- Version: c759a4a2a53c

## Default answer

Example with the default inputs (Air temperature 100 °F, Relative humidity 40%): At 100 °F and 40% relative humidity, the heat index is 109.3 °F (42.9 °C).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| t | Air temperature | The air temperature in the shade. |
| rh | Relative humidity | The relative humidity, in percent. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| heatIndexF | Heat index (°F) | How hot it feels, in °F, by the NWS algorithm. |
| heatIndexC | Heat index (°C) | The same heat index in °C: (°F − 32) × 5 ÷ 9. |
| formula | Formula used | Steadman’s simple formula, or the Rothfusz regression with any NWS adjustment. |

## Method

HI = 0.5 × (T + 61 + (T − 68) × 1.2 + RH × 0.094); if (HI + T) ÷ 2 ≥ 80 °F, HI = −42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²·RH + 0.00085282T·RH² − 0.00000199T²·RH², with the NWS adjustments (T in °F, RH in %).

## Assumptions

- The temperature is measured in the shade; full sun can add up to 15 °F to the heat index (NWS).
- The formulas are the NWS algorithm; the regression was fitted to Steadman’s apparent temperature tables and is not meant for extreme temperatures or humidity.
- Temperatures from 40 °F to 130 °F (4.44… °C to 54.44… °C: the box takes 4.45 °C but not 4.4 °C) and humidity from 0% to 100%.

## Worked examples

1. t = 310.927778, rh = 40% gives heatIndexF = 109.255562, heatIndexC = 42.919757, formula = Rothfusz regression. Source: NWS Weather Prediction Center, The Heat Index Equation (Rothfusz 1990 regression).
2. t = 305.372222, rh = 50% gives heatIndexF = 94.596941, heatIndexC = 34.776078, formula = Rothfusz regression. Source: NWS Weather Prediction Center, The Heat Index Equation (Rothfusz 1990 regression).
3. t = 297.038889, rh = 50% gives heatIndexF = 74.55, heatIndexC = 23.638889, formula = Steadman simple formula.
4. t = 310.927778, rh = 10% gives heatIndexF = 94.122483, formula = Rothfusz regression, less the low-humidity adjustment.
5. t = 302.594444, rh = 90% gives heatIndexF = 101.780804, formula = Rothfusz regression, plus the high-humidity adjustment.
6. t = 305.15, rh = 70% gives heatIndexF = 104.736693, heatIndexC = 40.409274. Source: NIST SP 811 (2008), 4.2.1.1: °F = 1.8 × °C + 32.

## FAQ

### What is the heat index?

The heat index is how hot the air feels when humidity is added to the temperature. Sweat evaporates more slowly in humid air, so the body cools less and it feels hotter. At 90 °F and 50% humidity the heat index is about 95 °F.

### How is the heat index calculated?

The US National Weather Service first uses Steadman’s simple formula, 0.5 × (T + 61 + (T − 68) × 1.2 + RH × 0.094). If that result averaged with the temperature is 80 °F or more, it uses the Rothfusz regression instead, a formula in T and RH with nine terms, and adjusts it for very dry or very humid air. The steps are under How it works.

### What heat index is dangerous?

The NWS uses four levels: caution from 80 to 90 °F (fatigue with long exposure), extreme caution from 90 to 103 °F (heat cramps and heat exhaustion possible), danger from 103 to 125 °F (heat exhaustion likely, heat stroke possible), and extreme danger at 125 °F and above (heat stroke highly likely).

### Does sun change the heat index?

Yes. The heat index is for shade and light wind. The NWS notes that full sunshine can raise it by up to 15 °F. Strong hot winds can also make it feel worse.

### Can the heat index be lower than the temperature?

Yes, in dry air. At 100 °F and 10% humidity the heat index is about 94.1 °F, because sweat evaporates quickly. On a mild day the simple formula can also give a little less than the air temperature.

### Why is there no heat index for cold air?

The heat index was built for warm weather. The calculator takes temperatures from 40 °F to 130 °F; for cold air, the wind chill is the measure of how cold it feels.

## Sources

- National Weather Service, Weather Prediction Center, The Heat Index Equation (Rothfusz regression and adjustments). https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
- Rothfusz, L. P. (1990). The Heat Index “Equation” (or, More Than You Ever Wanted to Know About Heat Index). NWS Southern Region Technical Attachment SR 90-23.
- Steadman, R. G. (1979). The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science. Journal of Applied Meteorology 18(7), 861–873. https://doi.org/10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2
- National Weather Service, What is the heat index? (heat index chart, caution levels, and up to 15 °F more in full sun). https://www.weather.gov/ama/heatindex