Heat Index Calculator

What the heat index measures

Air temperature alone does not tell you how a summer afternoon will land on your body. The heat index pairs that temperature with relative humidity and reports an apparent temperature, meaning what the combination feels like to a person standing in the shade. The engine behind the number is sweat. Moisture evaporating off the skin carries heat away, and that evaporation is the body's main cooling route in hot weather. Humid air is already close to full of water vapor, so evaporation slows down and the same 95 F feels heavier in Miami than in Albuquerque.

Every figure on the official chart assumes shade, light wind, light clothing, and an average adult in reasonable health. Sunshine changes the answer a lot: the NWS heat index page states that direct sun can lift the felt temperature by up to 15 F above the shaded value. Wind cuts both ways. A breeze over sweaty skin helps while the air is cooler than skin temperature, but once the air itself is hotter than the body, blowing it past the skin adds heat instead of removing it.

The values come from a statistical fit rather than a physical model, so the weather service puts the error at about 1.3 F even inside the range where the equation was fitted. Treat the result as a planning number, not a measurement of your body.

The Rothfusz regression, term by term

In 1979 Steadman published a table of apparent temperatures across a grid of heat and humidity. The weather service fitted a polynomial to that table, now known as the Rothfusz regression, and that polynomial is what this calculator runs. Temperature is in degrees Fahrenheit and humidity is relative humidity in percent, so a Celsius reading plugged straight in produces nonsense.

HI = -42.379 + 2.04901523 T + 10.14333127 R - 0.22475541 T R - 0.00683783 T^2 - 0.05481717 R^2 + 0.00122874 T^2 R + 0.00085282 T R^2 - 0.00000199 T^2 R^2

Reading the shape of it helps. The two linear terms push the result up with heat and with moisture. The squared terms pull back, because the effect of each input flattens as it grows. The three interaction terms are what make humid heat compound: they multiply temperature and humidity together, which is why 90 F at 90 percent humidity lands near 122 F while 90 F at 20 percent lands near 86 F.

Below a heat index of about 80 F the polynomial is not used at all. The weather service switches to a plain average of the air temperature and a simple Steadman estimate, because the regression was not built for mild conditions. The NWS heat index calculation notes spell out both branches and the two corrections covered below.

The two corrections at the edges

The polynomial alone misbehaves at both ends of the humidity range, so the NWS applies a correction in two narrow cases.

Dry heat. When relative humidity is below 13 percent and the air is between 80 F and 112 F, the service subtracts ((13 - RH) / 4) x square root of ((17 - |T - 95|) / 17). The correction peaks at bone dry air right around 95 F, where it reaches 3.25 F. Worked case: 100 F at 10 percent humidity. The regression returns 94.75, the correction is 0.75 x 0.8402 = 0.63, and the reported heat index is 94.12.

Muggy heat at moderate temperatures. When relative humidity is above 85 percent and the air is between 80 F and 87 F, the service adds ((RH - 85) / 10) x ((87 - T) / 5). Worked case: 85 F at 90 percent. The correction is 0.5 x 0.4 = 0.2 F, so 101.58 becomes 101.78. The add-on is small but it is the reason swampy mornings near 85 F read higher than the polynomial suggests.

The boundaries are strict. At 13 percent humidity exactly there is no subtraction, and at 90 F or 112 F outside the stated window the dry correction is switched off as well. That is why the same humidity can matter more at 95 F than at 108 F.

Worked example: 95 F at 60 percent

Run the eight terms for 95 F and 60 percent humidity one at a time and the arithmetic stops looking mysterious.

• 2.04901523 x 95 = 194.66
• 10.14333127 x 60 = 608.60
• 0.22475541 x 95 x 60 = 1,281.11, subtracted
• 0.00683783 x 9,025 = 61.71, subtracted
• 0.05481717 x 3,600 = 197.34, subtracted
• 0.00122874 x 9,025 x 60 = 665.36, added
• 0.00085282 x 95 x 3,600 = 291.66, added
• 0.00000199 x 9,025 x 3,600 = 64.66, subtracted

Those eight pieces plus the constant of -42.379 come to 113.09 F. Neither correction applies, because humidity is well above 13 percent and below 85 percent. The calculator reports 113.1 F, which sits in the danger band where heat cramps and exhaustion are likely during activity.

The same 95 F at 30 percent humidity instead lands at 94.4 F, a drop of 18.7 degrees from the humidity alone. That gap is the practical reason a dry 95 F is a nuisance while a humid 95 F is a hazard.

A grid you can check against

These are the calculator's own outputs for a spread of conditions, to one decimal place in Fahrenheit. Use the grid to sanity check a number you read somewhere else, or to see how fast the felt temperature climbs once humidity passes 60 percent.

Read the left column against the right. At 20 percent humidity, adding 10 F of air temperature raises the heat index by 4 to 7 F. At 80 percent humidity, the same 10 F jump raises it by 16 to 29 F, because the interaction terms grow with both inputs.

Printed charts round to whole degrees and the two sources do not always agree to the last digit. The published chart puts 100 F at 55 percent at 124 F, while the polynomial gives 123.64, a difference of less than half a degree. Values above roughly 125 F are extrapolations beyond the weather service's comfort zone and should be read as directionally right, not exact.

Reading the danger bands

The weather service groups heat index values into four bands with different effects on the body. The bands below come from the Amarillo NWS office page on the heat index, which uses 80 to 90 F for caution, 90 to 103 F for extreme caution, 103 to 124 F for danger, and 125 F and above for extreme danger.

The bands are not a medical diagnosis and they assume a healthy adult. People over 65, infants, outdoor workers, and anyone taking diuretics or blood pressure medicine carry more risk at the same number. NIOSH heat stress guidance recommends water, rest and shade, plus a gradual build up of exposure for anyone new to hot work, since acclimatization takes days rather than hours.

A heat index of 113 F is a limit on hard outdoor work, not a forecast of collapse. Shift the labor to early morning, cut the pace, and plan water breaks before thirst arrives, since thirst lags behind fluid loss.

Why 100 F in Phoenix and Houston are different days

Both cities hit 100 F in summer, and the felt temperature differs by nearly 47 degrees.

• Phoenix at 100 F and 15 percent humidity: heat index 95.8 F.
• Houston at 100 F and 70 percent humidity: heat index 142.8 F.

Desert air lets sweat evaporate as fast as the body can produce it, so a dry 100 F can read below the air temperature itself. Gulf air holds so much vapor that sweat drips instead of evaporating, and the body's cooling loop stalls. The dry correction described above shaves less than a degree in Phoenix, not the 4.2 degree gap, so the difference is almost entirely the humidity term in the polynomial.

Phoenix has one more twist: the monsoon months from roughly July into September push dew points up sharply, and a 100 F afternoon that reads 96 F in June can read closer to 120 F in August. If you are pricing shade structures, evaporative coolers, or outdoor work schedules, use the humidity of the worst month rather than the annual average.

The companion question is dew point. The dew point calculator takes the same two inputs and reports the temperature at which air would be saturated, which tells you how well a swamp cooler will work and how sticky the evening will feel.

What the number leaves out

Heat index is a two variable screen. Real heat stress depends on more than temperature and humidity, and the gaps matter.

Sun and wind. The chart is for shade and light wind. Full sun can add up to 15 F, and hot dry wind adds heat once the air passes skin temperature. Occupational hygienists therefore prefer the wet bulb globe temperature, which folds in solar load and air movement, for setting work and rest cycles.

The person. Age, body fat, fitness, hydration, medication, alcohol, pregnancy and clothing all shift the real risk. A fit 25 year old and a 70 year old on a diuretic can share a heat index of 105 F and face sharply different outcomes, which is why the bands are a starting point and not a clearance.

Indoors. A top floor apartment with no air conditioning can run hotter than the outdoor reading, and the heat index formula says nothing about indoor radiant heat or humidity from cooking and showers.

Duration. Two hours at 105 F and eight hours at 105 F are not the same exposure. Track time as well as intensity, and treat confusion, a throbbing headache, or hot dry skin as reasons to call for help rather than to push through.

For the temperature side of the same question, the Celsius to Fahrenheit converter handles the unit change that the regression cannot, since the coefficients only work in Fahrenheit.