Heat Index Chart Explorer

What is the heat index formula?

The heat index (apparent temperature) measures how hot weather feels when relative humidity is factored into ambient air temperature. High humidity impairs the body’s natural cooling by slowing the evaporation of sweat from the skin, and the US National Weather Service calculates the figure with Rothfusz’s regression on Steadman’s apparent temperatures, switching to a simpler formula in mild conditions.

Using the chart

The chart opens on an illustrative humid day: the dew point stays at 24 °C while the air warms from 27 °C at 03:00 to 35 °C at 15:00 and cools again, and the heat index follows it from 30.1 °C, in Caution, to 41.9 °C, in Danger. Touch the chart or any field and the day stops where it is. Drag the point anywhere: across is air temperature and up is relative humidity. Switch on “Hold the dew point” to give the dew point instead, and a drag then slides along its blue curve, the same moisture in warmer or cooler air. “Table” shows the NWS-style grid in °C or °F, every other column of it on a phone, and “Save image” downloads the chart or the whole table at a size that prints.

How the heat index is worked out

The US National Weather Service (NWS) works in °F, with T the air temperature and RH the relative humidity in percent. It starts with a simple formula, HI = 0.5 × [T + 61 + (T − 68) × 1.2 + 0.094 RH]. If the simple value is 79 °F or less, it is the heat index: that is where the NWS’s own online calculator switches, and its equation page puts the switch at about 80 °F. Otherwise the heat index comes from Rothfusz’s regression, a multiple regression he fitted in 1990 to Steadman’s 1979 table of apparent temperatures, written here with R for the humidity:

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

Two adjustments refine the fit at the edges of its range. When the humidity is below 13 percent and T is between 80 and 112 °F, [(13 − RH)/4] × √[(17 − |T − 95|)/17] is taken off. When the humidity is above 85 percent and T is between 80 and 87 °F, [(RH − 85)/10] × [(87 − T)/5] is added. Rothfusz gave his fit an error of ±1.3 °F, about 0.7 °C.

The switch between the two formulas is not smooth. At 100 percent humidity it falls at 76.9 °F, where the simple formula reaches 79.0 °F but the regression gives 77.3 °F, so the heat index drops by 1.7 °F as the air warms past it; at 60 percent it falls at 78.6 °F, and the heat index jumps up by 1.3 °F instead. Isolines on the chart that meet the switch run along it for a while, because that is where the algorithm’s numbers change.

Worked example: 35 °C at 50 percent

• Convert the temperature: T = 35 × 9/5 + 32 = 95 °F. The unit converter does this conversion either way for any reading.
• The simple formula: 0.5 × [95 + 61 + (95 − 68) × 1.2 + 0.094 × 50] = 0.5 × 193.1 = 96.55 °F, which is above 79 °F, so the regression runs.
• The regression’s nine terms are −42.379, 194.656, 507.167, −1067.588, −61.711, −137.043, 554.469, 202.545 and −44.899, which add up to 105.216 °F.
• No adjustment applies, since 50 percent is between 13 and 85.
• Convert back: (105.216 − 32) × 5/9 = 40.7 °C.

So 35 °C at 50 percent humidity feels like 40.7 °C, which is 105.2 °F and in the Danger category, 39.4 to 51.7 °C. The working under the chart does the same for any point, with the numbers put in.

The NWS categories

The NWS prints its ranges in whole degrees, so Danger stops at 124 °F and Extreme Danger starts at 125. Here each category runs up to the next one’s edge, so a heat index of 124.5 °F counts as Danger. Below 80 °F the NWS names no category, which is not the same as safe.

Why humidity makes heat worse

The body makes heat all the time, more when it moves, and has to lose it. When the air is close to skin temperature, about 35 °C, sweating is almost the only way left, and sweat cools only when it evaporates: each gram that evaporates carries off about 2.4 kJ, the latent heat of vaporisation the latent heat calculator works with, while sweat that drips off carries away almost nothing. The wetter the air, the more slowly sweat evaporates, so humid air feels hotter. At 35 °C the heat index is 34.7 °C at 30 percent humidity, 40.7 °C at 50 percent and 50.3 °C at 70 percent.

The wet bulb measures that limit directly: it is the coolest that evaporating water can make anything in the air, wet skin included. At 35 °C it is 21.5 °C at 30 percent and 30.1 °C at 70 percent, which the gauge beside the chart sets against skin at 35 °C. The psychrometric chart explorer works out the wet bulb and the dew point from Hyland and Wexler’s saturation pressure, and this chart uses the same model.

The dew point is the steadier measure of how much water the air holds, since relative humidity falls as air warms with its water unchanged. On the illustrative day the dew point never moves from 24 °C, so the humidity falls from 83.7 percent at 03:00 to 53.0 percent at 15:00, and the heat index still climbs from 30.1 to 41.9 °C. The same saturation pressure, set against the air pressure, is what the boiling point at altitude simulator uses to find where water boils.

Heat index, wet bulb and WBGT are different numbers

They answer different questions, so they should not be read on one scale. The heat index is a feels-like temperature from a model of a person. The wet-bulb temperature is a physical temperature, the one a thermometer with a wet wick reads in moving air. The wet-bulb globe temperature, WBGT, used to set limits for sport and outdoor work, also counts the sun: outdoors it is 0.7 Tnwb + 0.2 Tg + 0.1 Ta, where Tnwb is a natural wet bulb, Tg the temperature inside a black globe and Ta the air temperature. At 35 °C and 50 percent the heat index is 40.7 °C and the wet bulb 26.1 °C at sea level, and a WBGT measured in sunshine would be a third number again.

Where the chart is hatched

Steadman’s table runs from 20 to 50 °C and from dry air to saturated, but in hot, humid air his model of the body has no answer: the sweat it needs would have to evaporate faster than the air can take it. Lu and Romps (2022) worked out where that happens; at 80 percent humidity, for instance, it is above 31 °C, or 88 °F. The NWS formula still gives numbers there, by extrapolating Rothfusz’s fit beyond the data it was fitted to, and Lu and Romps found those numbers run low, by as much as 28 °F (16 °C) on the NWS’s own chart. The hatched corner is that region. Even the NWS’s worked example, 96 °F at 65 percent, giving 121 °F, lies inside it. Lu and Romps extended the index to cover such air; their extended values are not computed here. Beyond the NWS’s chart, in the far corner, the formula climbs so steeply that it overshoots their index instead: at 50 °C and 100 percent it gives 206 °C, against about 152 °C.

This table and the NWS’s printed chart

The table follows the NWS algorithm, adjustments included, and rounds to whole degrees as the NWS chart does. Set beside the NWS’s current printed chart, it differs in a few cells, each for a reason. The printed chart leaves out the humid-air adjustment, so at 80 to 86 °F and 90 percent humidity or more its cells read up to 2 °F lower: it prints 87 °F for 80 °F at 100 percent, where the algorithm gives 89 °F. Two of its cells are also a degree off its own formula: 93 °F for 90 °F at 45 percent, where the formula gives 92.5 °F, and 105 °F for 90 °F at 70 percent, where it gives 105.9 °F. As on that chart, the table leaves its hottest cells empty, every one above 137 °F, the highest number the NWS prints; the printed chart also leaves 92 °F at 95 percent empty, where the formula gives 136.9 °F and the table prints 137. Each cell is coloured by its unrounded value, so a printed 103 can sit either side of the Danger line, and the printed 80 at 40 percent, 79.9 °F, is just short of Caution.

What it leaves out

• Sunshine. The values are for shade. The NWS says full sunshine can add up to 15 °F (8 °C); it is never added in here.
• Wind. Steadman assumed a 5 knot wind. A breeze helps sweat evaporate, but the CDC says that above 90 °F (32 °C) a fan can raise body temperature, and the NWS warns that strong winds in very hot, dry air can be extremely hazardous.
• Clothing and effort. The model person walks at 3.1 mph in long trousers and a short-sleeved shirt. Heavier clothing, protective gear or hard work make the same air more dangerous.
• The person. The model is one adult, 5 ft 7 in tall and 147 pounds. People who are not used to the heat, older people, babies and young children, pregnant women, people with heart, lung or kidney disease and people taking some medicines are at higher risk at any heat index.
• Other countries’ warnings. Many countries issue heat warnings from other indices, such as Canada’s humidex, with thresholds of their own. Follow the local warning; this page is a demonstration of the NWS index, not a safety or medical assessment.

Converting units first? Use the temperature conversion table.