The heat index answers a question a thermometer cannot: how hot does the air actually feel to a human body? At 90 °F with dry air you can shed heat efficiently through sweat evaporation. At the same 90 °F with 70 percent relative humidity that evaporation slows dramatically, your body struggles to dump heat, and the physiological load matches what dry air at about 106 °F would impose. This heat index calculator implements the full Rothfusz regression published by NOAA, including both of the official correction terms that most online versions leave out.
Arb Digital builds free tools that implement the real published method rather than a simplified version of it, because in this case the simplification changes the answer by several degrees in exactly the conditions people most want to check. This page is a physics calculation, not a unit conversion — it derives a new quantity from temperature and humidity. If all you need is to move a number between Celsius, Fahrenheit and Kelvin, the temperature converter does that and nothing else.
What This Heat Index Calculator Does
It takes an air temperature and a humidity figure and returns the apparent temperature — the equivalent dry-air temperature that would place the same heat load on a human body. The result is shown in whichever unit you chose, with the other unit alongside it, plus the National Weather Service risk category, the number of degrees by which conditions feel hotter than the thermometer reads, and the relative humidity actually used in the calculation.
Humidity can be entered two ways. Relative humidity as a percentage is the direct input the equation expects. Dew point is often the more reliable figure to obtain, because it appears on aviation weather reports and most forecast feeds, and unlike relative humidity it does not swing wildly as the day warms. Select dew point mode and the tool converts it to relative humidity with the Magnus formula before running the heat index equation, showing you the derived percentage so nothing is hidden.
Crucially, the tool follows NOAA's own decision procedure rather than blindly applying one polynomial. It first computes a simple linear estimate, averages that with the air temperature, and only escalates to the full nine-term regression when that average reaches 80 °F. Below that threshold the regression is not valid, and using it anyway produces the nonsense results you sometimes see on other sites, where a mild 70 °F day is reported as feeling like 60 °F or worse.
How to Use It
- Enter the shade air temperature. Pick Fahrenheit or Celsius; the calculation runs internally in Fahrenheit because that is the unit the published regression was fitted in, and the result is converted back for display.
- Choose how you are supplying humidity. Relative humidity is the direct input. Dew point mode is there because dew point is what most weather reports actually publish.
- Enter the humidity value. In dew point mode it uses the same temperature unit you selected, so a Celsius air temperature pairs with a Celsius dew point.
- Read the category, not just the number. The four National Weather Service bands describe escalating physiological risk, and the boundary between them matters more than a degree either side of it.
- Adjust for your actual situation. The published index assumes shade and a light wind. Full sun pushes the effective value substantially higher, and the tool says so in the note beneath the results.
The Formula: How the Heat Index Is Calculated
NOAA's Weather Prediction Center publishes the exact procedure in its heat index equation reference, and this tool follows it step by step. The first step is a simple estimate: HI = 0.5 × {T + 61.0 + [(T − 68.0) × 1.2] + (RH × 0.094)}, where T is air temperature in degrees Fahrenheit and RH is relative humidity as a percentage. That value is averaged with T. If the average is below 80 °F, the simple estimate is the answer and the calculation stops there.
If the average reaches 80 °F, the full Rothfusz regression takes over. It is a nine-term polynomial fitted to Steadman's 1979 heat-balance model, which itself accounted for body dimensions, clothing, activity, thermal radiation and wind speed. The regression exists because Steadman's original model was a table, not an equation, and forecast systems needed something computable. Its published coefficients are: HI = −42.379 + 2.049 015 23·T + 10.143 331 27·RH − 0.224 755 41·T·RH − 0.006 837 83·T² − 0.054 817 17·RH² + 0.001 228 74·T²·RH + 0.000 852 82·T·RH² − 0.000 001 99·T²·RH².
Two adjustments then apply, and these are the parts commonly omitted. When relative humidity is below 13 percent and the temperature is between 80 and 112 °F, subtract [(13 − RH) ÷ 4] × √{[17 − |T − 95|] ÷ 17}. When relative humidity is above 85 percent and the temperature is between 80 and 87 °F, add [(RH − 85) ÷ 10] × [(87 − T) ÷ 5]. The first correction stops the regression overstating apparent temperature in genuinely arid heat; the second stops it understating the misery of warm, saturated air.
Work an example through. Take 90 °F and 70 percent relative humidity. The simple estimate gives 0.5 × (90 + 61 + 26.4 + 6.58) = 91.99, and averaging that with 90 gives 90.99, comfortably above 80, so the regression applies. Evaluating the nine terms gives approximately 105.9 °F. Neither adjustment applies, since humidity is neither below 13 percent nor above 85 percent. The published NOAA chart lists 105 °F for that cell, and the one-degree difference is the chart's own rounding. That result sits in the Danger band.
The Four Risk Categories as Published by NWS
The National Weather Service defines four bands, described on its explanation of the heat index. From 80 to 90 °F is Caution, where fatigue is possible with prolonged exposure or physical activity. From 90 to 103 °F is Extreme Caution, where heat stroke, heat cramps or heat exhaustion are described as possible under prolonged exposure or activity. From 103 to 124 °F is Danger, where heat cramps or heat exhaustion are likely and heat stroke is possible. At 125 °F and above the category is Extreme Danger, where heat stroke is described as highly likely.
Two features of those definitions deserve attention. Every one of them is conditioned on prolonged exposure or physical activity, so the same heat index means something quite different for someone resting in shade and someone working. And the bands are wide: the Danger band spans twenty-one degrees, so being at its bottom edge is not the same situation as being near its top.
Why the Index Is Not Simply Temperature Plus Humidity
The underlying physics is evaporative cooling. Your body sheds surplus heat mainly by evaporating sweat, and the rate of evaporation depends on the vapour pressure difference between your skin and the surrounding air. When the air already holds a great deal of water vapour, that difference shrinks and sweating becomes progressively less effective. Past a certain point, sweat simply runs off without evaporating, which cools nothing and costs you fluid.
This is why the humidity penalty is not linear and not additive. At 80 °F, going from 40 to 90 percent relative humidity adds only a handful of degrees to the apparent temperature. At 100 °F, the same humidity change adds more than thirty. The nonlinear cross-terms in the regression — T·RH, T²·RH, T·RH², T²·RH² — are exactly what encode that interaction. A tool that adds a fixed humidity penalty per percentage point cannot reproduce this behaviour at either end of the range.
It also explains the low-humidity adjustment. In very dry air the raw polynomial extrapolates past the region it was fitted to and starts overstating the load, because evaporation is already near its maximum and cannot improve further. The correction pulls the answer back toward reality. Try the hot-and-dry preset above and compare the result with what a naive polynomial would give.
What the Heat Index Does Not Account For
The published index assumes shade and a light wind of about 5 knots. Direct sunlight is not in it at all. NOAA notes that full sunshine can raise apparent temperature values by up to about 15 °F, which is enough to move conditions across a category boundary. If you are outdoors in the open, treat the calculated value as a floor rather than an estimate.
Wind is more complicated than it seems. A breeze at moderate temperature helps by carrying humid air away from your skin. Above roughly body temperature, moving air can transfer heat toward you faster than it removes it, which is why a hot desert wind offers no relief. Clothing, acclimatisation, age, fitness, medication and hydration all shift individual response too, and none of them appear in a two-variable equation. The index describes conditions, not people.
Nor does it capture duration or overnight recovery. A single afternoon at a given heat index is very different from the fifth consecutive day of it with nights that never drop below 80 °F, because the body relies on cool periods to shed accumulated heat. Forecasters weigh that when issuing advisories, and it is one reason official warnings do not map one-to-one onto index thresholds.
Dew Point Versus Relative Humidity
Relative humidity is a ratio, and it moves whenever temperature moves even if the actual water content of the air is unchanged. Air at 70 °F with 90 percent relative humidity, warmed to 90 °F with no moisture added or removed, drops to roughly 50 percent — same water, very different number. That is why a morning relative humidity reading tells you little about how the afternoon will feel.
Dew point is an absolute measure: the temperature at which the air would become saturated. It barely changes through the day unless an air mass moves in. A dew point in the low 50s °F is comfortable, the 60s feel noticeably sticky, and the 70s are oppressive for most people regardless of what the relative humidity percentage happens to read at that moment. Because it is the more stable quantity, dew point mode here converts to relative humidity at your stated air temperature and then runs the standard equation. The dew point calculator works the relationship in the opposite direction, and the wind chill calculator is the cold-weather counterpart to this page.
Using the Number Sensibly
The heat index is a planning input. The practical use is comparative: it tells you that today at 95 °F and 60 percent humidity will be harder work than yesterday at 100 °F and 20 percent humidity, which the raw thermometer readings would suggest the wrong way round. Scheduling demanding activity for cooler hours, and treating a category change as a signal to reconsider timing, is what the index is designed to support.
Fluid needs rise with heat load, and the water intake calculator gives a baseline figure to work from. If you are estimating energy expenditure for outdoor work or exercise, the calories burned calculator covers the activity side. For heat-related planning around home cooling loads, the AC BTU calculator sizes equipment to a space. And the free tools hub lists everything else Arb Digital has built.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Applying the regression below 80 °F — it is only valid once the simple estimate averaged with air temperature reaches 80 °F. Used outside that range it produces values below the actual temperature.
- Skipping the two adjustments — the low-humidity and high-humidity corrections change the answer by several degrees in precisely the conditions worth checking.
- Reading a sunlit value from a shade index — NOAA notes full sun can add up to about 15 °F to apparent temperature, which the published equation does not include.
- Entering dew point in the humidity percentage field — a dew point of 70 is not 70 percent humidity. Switch the input mode instead.
- Treating the index as a personal threshold — it describes conditions. Individual tolerance varies with fitness, age, acclimatisation and hydration, none of which are inputs.
Related Free Tools From Arb Digital
For the cold-weather equivalent use the wind chill calculator, and for the humidity relationship itself the dew point calculator. Unit work belongs in the temperature converter. For related planning, the water intake calculator gives a hydration baseline, the calories burned calculator estimates activity load, and the AC BTU calculator sizes cooling for a room. The free online tools hub has the rest.
Frequently Asked Questions
It uses the Rothfusz regression published by NOAA's Weather Prediction Center, together with both official adjustments — the subtraction applied below 13 percent relative humidity and the addition applied above 85 percent — and the simple linear estimate used when conditions fall below the regression's valid range.
Because at around 40 to 45 percent relative humidity the apparent temperature and the actual temperature roughly coincide. Below that, dry air can make conditions feel slightly cooler than the thermometer reads; above it, the index climbs steadily.
Caution from 80 to 90 °F, Extreme Caution from 90 to 103 °F, Danger from 103 to 124 °F, and Extreme Danger at 125 °F and above. Each description is conditioned on prolonged exposure or physical activity rather than on rest in shade.
No. The published index assumes shade and a light wind. NOAA notes that exposure to full sunshine can raise apparent temperature values by up to about 15 degrees Fahrenheit, which is enough to move conditions into a higher category.
Yes. Switch the humidity input mode to dew point and the tool derives relative humidity using the Magnus formula at your stated air temperature, then runs the standard heat index calculation and displays the derived percentage.
Because its coefficients were fitted to Fahrenheit data. Converting the coefficients to Celsius introduces avoidable rounding, so this tool converts your input to Fahrenheit, evaluates the published equation, then converts the result back for display.
NOAA describes the regression as reproducing the underlying Steadman table to within about 1.3 degrees Fahrenheit. The larger uncertainty is not the equation but the assumptions behind it — shade, light wind, and a standardised body with standardised clothing and activity.
This tool is provided for general information and educational use. It reports a published weather index and is not medical advice; for guidance on heat illness or any personal health concern, consult a qualified healthcare professional or your local weather authority.
