Heat index calculator
This heat index calculator starts at 95 °F and 50% relative humidity. The heat index is the National Weather Service's apparent temperature: how hot the air feels in the shade once humidity slows the evaporation of sweat.
Notice: For general informational purposes only. Heat index values assume shade and light wind and do not account for exertion or individual health. Follow National Weather Service heat advisories, and seek medical attention for symptoms of heat-related illness.
Heat index
- Dew point td = 243.12 x ln(e' / 6.112 f) / (17.62 - ln(e' / 6.112 f)), with e' = 28.2 hPa the vapor pressure of the air and f = 1.0047 the enhancement factor (WMO-No. 8, eq. 4.B.6). Cool this air by 21.6 °F and dew forms.
- 73.4 °F (23.0 °C)
- Relative humidity As entered. Relative to saturation over liquid water, which is how WMO says relative humidity is reported even below freezing.
- 50%
- Dew point reading In the words of the National Weather Service office at La Crosse, whose "general comfort levels using dew point" for the summer months are: 55 °F or less "dry and comfortable"; between 55 and 65 °F "becoming "sticky" with muggy evenings"; 65 °F or more "lots of moisture in the air, becoming oppressive". It is a summer scale.
- lots of moisture in the air, becoming oppressive
- Wet-bulb temperature The reading of a thermometer wrapped in a wet wick with air drawn past it: evaporation cools it until the heat taken from the air balances the heat carried off by the water. Solved from WMO's psychrometer equation e' = f ew(tw) - 0.000653 x (1 + 0.000944 tw) x p x (t - tw) at 1,013 hPa (eq. 4.B.8). It always sits between the dew point and the air temperature.
- 79.2 °F (26.2 °C)
- Heat index NWS's Rothfusz regression, used because the simple formula came to 80 °F or more. NWS: "The Rothfusz regression is not valid for extreme temperature and relative humidity conditions beyond the range of data considered by Steadman."
- 105.2 °F (40.7 °C)
- NWS heat index class NWS Amarillo's classification, effect on the body: "Heat cramps or heat exhaustion likely, and heat stroke possible with prolonged exposure and/or physical activity." The same page gives its values for shady locations: "If you are exposed to direct sunlight, the heat index value can be increased by up to 15°F."
- Danger
- Vapor pressure The partial pressure of the water vapor in the air. Saturation at 95.0 °F would be 56.39 hPa: ew(t) = 6.112 x exp(17.62 t / (243.12 + t)) hPa (eq. 4.B.1) times the moist-air enhancement factor f = 1.0047.
- 28.2 hPa (0.8326 inHg)
- Absolute humidity Grams of water vapor in each cubic meter of air: e' / (Rv x T), with Rv = R / (0.62198 x M_air) = 461.5 J/(kg K). It changes with temperature even when the dew point does not, because warm air takes up more room.
- 19.8 g/m3
- Humidity ratio Mass of water vapor per mass of dry air, r = 0.62198 x e' / (p - e'), at 1,013 hPa. Grains per pound is the same figure times 7, since a pound is 7,000 grains. This is the number on the vertical axis of a psychrometric chart, and the one HVAC load calculations use.
- 17.8 g/kg (125 gr/lb)
- Air pressure used The 1976 U.S. Standard Atmosphere at sea level. A real day's pressure moves a few percent with the weather, which shifts the wet bulb and the humidity ratio slightly and the dew point not at all.
- 1,013.3 hPa (29.92 inHg)
| Relative humidity | Dew point | Wet bulb | Heat index | Humidity ratio |
|---|---|---|---|---|
| 10% | 29.9 °F | 61.0 °F | 89.4 °F | 3.48 g/kg |
| 20% | 47.6 °F | 66.2 °F | 91.5 °F | 7.00 g/kg |
| 30% | 58.7 °F | 71.0 °F | 94.4 °F | 10.6 g/kg |
| 40% | 66.9 °F | 75.3 °F | 99.0 °F | 14.2 g/kg |
| 50% | 73.4 °F | 79.2 °F | 105.2 °F | 17.8 g/kg |
| 60% | 78.9 °F | 82.8 °F | 113.1 °F | 21.5 g/kg |
| 70% | 83.7 °F | 86.2 °F | 122.6 °F | 25.2 g/kg |
| 80% | 87.9 °F | 89.3 °F | 133.8 °F | 29.0 g/kg |
| 90% | 91.6 °F | 92.3 °F | 146.6 °F | 32.8 g/kg |
| 100% | 95.0 °F | 95.0 °F | 161.1 °F | 36.7 g/kg |
- Saturation, dew point, frost point, relative humidity and the psychrometer equation are WMO's Annex 4.B formulas (WMO-No. 8, Volume I, Chapter 4), valid for -45 to 60 °C over water and -65 to 0 °C over ice. WMO calls them sufficiently accurate for all normal meteorological applications.
- The heat index is the National Weather Service's, computed in °F as its Weather Prediction Center describes. It is for shade; it is not a measure of what any particular person will feel.
- Relative humidity here is with respect to liquid water at every temperature, as WMO prescribes for reporting.
- Not modeled: supersaturation, salt or other solutes, and the heat a real wet-bulb thermometer gains from sunlight or loses through poor ventilation.
How the Dew Point Calculator works
The heat index is computed in two stages, both from the National Weather Service's Weather Prediction Center, in degrees Fahrenheit and percent relative humidity. First the simple formula:
HI = 0.5 x (T + 61.0 + (T - 68.0) x 1.2 + RH x 0.094)
If that comes to 80 °F or more, NWS replaces it with Lans Rothfusz's 1990 regression:
HI = -42.379 + 2.04901523 T + 10.14333127 RH - 0.22475541 T RH - 0.00683783 T^2 - 0.05481717 RH^2 + 0.00122874 T^2 RH + 0.00085282 T RH^2 - 0.00000199 T^2 RH^2
and then makes one of two adjustments. When the relative humidity is under 13% and the temperature is between 80 and 112 °F, it subtracts ((13 - RH) / 4) x sqrt((17 - |T - 95|) / 17). When the relative humidity is over 85% and the temperature between 80 and 87 °F, it adds ((RH - 85) / 10) x ((87 - T) / 5).
The worked example: 95 °F at 50%. The simple formula gives 0.5 x (95 + 61 + 32.4 + 4.7) = 96.6 °F, which is over 80, so the regression applies. Neither adjustment does (50% is neither under 13 nor over 85), and the regression gives 105.2 °F. NWS classes that as "Danger".
The adjustments matter at the edges. At 100 °F and 10% relative humidity the regression is lowered by 0.63 °F to 94.1 °F; desert air at 100 °F feels cooler than 100. At 82 °F and 95% it is raised by exactly 1.0 °F to 94.0 °F. Below 40 °F NWS's own calculator returns the air temperature, and so does this calculator: the heat index is a hot-weather measure.
As a check, the NWS's own worked examples come out the same here. NWS Amarillo: 100 °F at 55% is 124 °F (this calculator: 123.6), and 100 °F at 15% is 96 °F (95.9). NWS's national heat index page: 96 °F at 65% is 121 °F (121.0). The same Amarillo page notes that the regression "has an error of ±1.3 °F", so the decimal is arithmetic, not precision.
Two things the number does not include. Sunshine: NWS Amarillo says its heat index values are for shady locations, and that "if you are exposed to direct sunlight, the heat index value can be increased by up to 15°F." And extremes: NWS warns that "the Rothfusz regression is not valid for extreme temperature and relative humidity conditions beyond the range of data considered by Steadman", which is why very hot, very humid entries can produce figures nobody has measured.
The class on the result is NWS Amarillo's table, quoted word for word: Caution from 80 °F, Extreme Caution from 90 °F, Danger from 103 °F and Extreme Danger from 125 °F. The table prints its ranges with shared endpoints, so this calculator puts each endpoint in the higher class. These are general weather categories, not an assessment of any person; for decisions, follow your local NWS office's heat advisories.
Dew Point Calculator FAQ
How is the heat index calculated?
NWS computes HI = 0.5 x (T + 61 + (T - 68) x 1.2 + RH x 0.094) in °F first. If that is 80 °F or more it uses the Rothfusz regression instead, HI = -42.379 + 2.04901523 T + 10.14333127 RH - 0.22475541 T RH - 0.00683783 T^2 - 0.05481717 RH^2 + 0.00122874 T^2 RH + 0.00085282 T RH^2 - 0.00000199 T^2 RH^2, with a small adjustment for very dry or very humid air. At 95 °F and 50% the result is 105.2 °F.
What heat index is dangerous?
NWS Amarillo's classification puts a heat index of 103 to 124 °F in "Danger", described as "Heat cramps or heat exhaustion likely, and heat stroke possible with prolonged exposure and/or physical activity", and 125 °F or higher in "Extreme Danger". Caution starts at 80 °F and Extreme Caution at 90 °F.
Is the heat index measured in the sun or the shade?
The shade. NWS Amarillo: "If you are exposed to direct sunlight, the heat index value can be increased by up to 15°F." The formula has no input for sunshine or wind.
Can the heat index be lower than the air temperature?
Yes, in dry air. At 100 °F and 15% relative humidity it is 96 °F, and at 100 °F and 10% it is 94.1 °F, because sweat evaporates easily. It is above the air temperature once the air is humid enough to slow that evaporation.
More from the Dew Point Calculator
Sources
- WMO Guide to Instruments and Methods of Observation (WMO-No. 8), Volume I, Chapter 4 'Measurement of humidity', preliminary 2018 edition: Annex 4.B 'Formulae for the computation of measures of humidity' eqs. (4.B.1)-(4.B.11) and its range statement; Annex 4.A eqs. (4.A.5), (4.A.6) and (4.A.13) for the 0.621 98 mass ratio; section 4.1.2 for the units (hPa, °C) (2018)
- NOAA/NWS Weather Prediction Center, 'The Heat Index Equation' (Rothfusz regression from NWS Technical Attachment SR 90-23, 1990, its low- and high-humidity adjustments, and the simpler Steadman-consistent formula for heat indices below about 80 °F); the 40 °F pass-through is from the WPC heat index calculator's own script (https://www.wpc.ncep.noaa.gov/html/heatindex.shtml) (1990)
- NWS Amarillo, TX, 'Heat Index' page: the 'Classification / Heat Index / Effect on the body' table, and the statements that chart values are for shady locations and that direct sunlight can raise the heat index by up to 15 °F (2026)
- NWS La Crosse, WI, 'Dew Point vs Humidity': 'General comfort levels USING DEW POINT that can be expected during the summer months' (2026)
- U.S. Standard Atmosphere, 1976 (NOAA, NASA, USAF; NOAA-S/T 76-1562, NASA-TM-X-74335), Part 1: Table 2 'Adopted constants' (g0, R*, P0, r0, T0, gamma), Table 3 (O2 fractional volume), Table 4 'The defined reference levels and gradients of the linearly segmented temperature-height profile' (H_b, L_M,b), section 1.2.4 (M0 = 28.9644 kg/kmol), section 1.3.1 eqs. (33a)/(33b), eq. (18) for geopotential altitude, eq. (42) for density, eq. (50) for speed of sound, Table 10 (sea-level values); Part 4 Table I 'Geopotential Altitude, Metric Units' for the printed base temperatures and pressures (1976)