Why humidity changes what the temperature feels like
Your body holds its core near 37 °C by shedding heat, and above about 35 °C skin temperature the only mechanism left that works is evaporating sweat. Evaporation depends on the vapour pressure gradient between wet skin and the surrounding air. When the air is already close to saturated, that gradient collapses, sweat runs off you instead of evaporating, and the heat you are producing has nowhere to go.
The heat index puts a number on that. It answers a specific question: at a reference humidity, what dry-bulb temperature would impose the same physiological strain as the temperature and humidity you actually have? That is why the units are degrees — it is a temperature equivalent, not a measured temperature.
The underlying model is Robert Steadman's 1979 work on sultriness, which built a heat-balance model of a standard person — a specified height and weight, walking at a set pace, in shade, in a light wind, wearing long trousers and a short-sleeved shirt. Lans Rothfusz then fitted a nine-term polynomial to Steadman's table so that a forecaster could compute it without looking anything up. That polynomial is what the National Weather Service uses and what this calculator implements, including the two correction terms Rothfusz added for the corners where the fit drifts.
Everything about the model is a set of assumptions about a person who is not you. If you are heavier, older, unacclimatised, taking a medication that suppresses sweating, or wearing anything remotely impermeable, the strain is higher than the number says.
The three-part procedure the NWS actually uses
The published method is not one formula, it is a decision and then a formula.
First, the screening step. Compute a simple linear estimate, average it with the air temperature, and if the result is below 80 °F, stop — that value is the heat index. Below 80 °F humidity barely moves apparent temperature, and the polynomial is not fitted there. This is why the calculator's answer sits within a degree or so of the air temperature on a mild day.
Second, the regression. When that screening value is 80 °F or above you evaluate the nine-term polynomial in temperature and humidity. Note what the terms do: the linear humidity term is large and positive, and the T·R cross term is large and negative, so humidity's effect is not independent of temperature. That is the whole point — at 80 °F, going from 40% to 90% humidity adds about 6.5 °F, while at 105 °F the same change adds nearly 88 °F.
Third, the two adjustments. Below 13% humidity between 80 and 112 °F, the fit overestimates, so you subtract a correction that peaks at 95 °F and tapers either side. Above 85% humidity between 80 and 87 °F it underestimates slightly, so you add a small correction. Both are in the calculator, and both appear as their own step when they apply.
The regression is written in Fahrenheit and percent. If you work in Celsius, convert to Fahrenheit, evaluate, and convert back — which is what this page does when you switch the unit selector, so the Celsius answer is the exact conversion of the official Fahrenheit one rather than a separate approximation.
Worked example: 95 °F at 60% relative humidity
Take T = 95 °F and R = 60%. First the screening step: ½(95 + 61 + 1.2 × 27 + 0.094 × 60) = ½(95 + 61 + 32.4 + 5.64) = 97.02, averaged with 95 gives 96.01, which is well above 80, so the regression applies.
Now the nine terms, grouped so you can check them:
- Constant and linear terms. −42.379 + 2.04901523 × 95 + 10.14333127 × 60 = −42.379 + 194.65645 + 608.59988 = 760.87733.
- Cross and square terms. −0.22475541 × 5,700 − 0.00683783 × 9,025 − 0.05481717 × 3,600 = −1,281.10584 − 61.71142 − 197.34181 = −1,540.15907.
- Higher-order terms. +0.00122874 × 541,500 + 0.00085282 × 342,000 − 0.00000199 × 32,490,000 = +665.36271 + 291.66444 − 64.65510 = +892.37205.
- Sum. 760.87733 − 1,540.15907 + 892.37205 = 113.09 °F.
Neither adjustment applies: humidity is above 13% and the temperature is above 87 °F. So the heat index is 113.09 °F, which is (113.09 − 32) × 5/9 = 45.05 °C. It exceeds the air temperature by 18.09 °F, and it sits in the danger band.
Two further readings fall out of the same conditions. The dew point, from the Magnus form, is 78.94 °F — oppressive by any standard. And solving the regression for the humidity that reaches the extreme-danger threshold of 125 °F at this same 95 °F air temperature gives 72.27%: a twelve-point rise in humidity, which a single afternoon thunderstorm can deliver.
How to read the result
The NWS bands are the operational answer. Below 80 °F there is no named risk. From 80 to 90 °F is caution: fatigue is possible with prolonged exposure or activity. From 90 to 103 °F is extreme caution: heat cramps and heat exhaustion are possible, and heat stroke is possible with continued activity. From 103 to 125 °F is danger: cramps and exhaustion are likely and heat stroke is possible. Above 125 °F is extreme danger: heat stroke is highly likely.
Two adjustments matter before you act on the band. Add for sun. The NWS states plainly that full sunshine can raise heat index values by up to 15 °F, because the model assumes shade. A reading of 100 °F in the shade is a danger-band reading on an unshaded roof. Add for exertion and clothing. The model's reference person is walking, not carrying shingles, and is not in a Tyvek suit.
The difference from the air temperature output is worth watching for its sign. In genuinely dry heat it goes negative: at 100 °F and 10% humidity the heat index is 94.1 °F, nearly six degrees below the thermometer, because sweat evaporates faster than the reference conditions assume. That is real relief, but it comes with a hidden cost — you are losing that water, and you may not notice sweating at all because it evaporates before it beads.
The dew point is the more honest single number for how oppressive air is, because unlike relative humidity it does not change when the temperature does. A dew point below 60 °F is comfortable, the mid-60s starts to feel sticky, and above 70 °F most people find it genuinely oppressive. If you track one moisture number through a summer day, track this one.
For the opposite end of the year, the wind chill calculator does the equivalent job for cold and wind, and the UV index sunburn time calculator covers the other hazard of the same afternoon, which is not correlated with the heat index at all.
Heat index reference grid
| Air temp | 40% | 50% | 60% | 70% | 80% | 90% |
|---|---|---|---|---|---|---|
| 80 °F | 79.8 | 80.8 | 81.8 | 83.0 | 84.2 | 86.3 |
| 85 °F | 84.3 | 86.5 | 89.3 | 92.7 | 96.8 | 101.8 |
| 90 °F | 90.7 | 94.6 | 99.7 | 105.9 | 113.3 | 121.9 |
| 95 °F | 99.0 | 105.2 | 113.1 | 122.6 | 133.8 | 146.6 |
| 100 °F | 109.3 | 118.3 | 129.5 | 142.8 | 158.2 | 175.7 |
| 105 °F | 121.5 | 133.9 | 148.9 | 166.4 | 186.5 | 209.2 |
| 110 °F | 135.7 | 152.0 | 171.2 | 193.5 | 218.8 | 247.0 |
The rows are not equally spaced in effect: at 80 °F, moving from 40% to 90% humidity adds 6.5 °F, while at 105 °F the same move adds 87.7 °F. That accelerating response is the T·R and T²R terms at work, and it is why a modest humidity rise on an already hot day is far more dangerous than the same rise on a warm one. The bottom-right values are extrapolations well beyond conditions that occur together in nature.
The heat index assumes shade, and it assumes you are a specific person
Steadman's model fixes clothing, activity, body size and wind. Anyone who differs from that reference faces different strain at the same heat index. Older adults, young children, people with cardiovascular disease, anyone taking anticholinergics or diuretics, and anyone not yet acclimatised to the season all carry higher risk than the band suggests. So does anyone wearing protective equipment: an impermeable suit can make a comfortable heat index dangerous, which is why occupational heat standards use wet bulb globe temperature with clothing adjustment factors rather than the heat index. If you are managing outdoor workers, treat this number as a screening tool and use a WBGT-based programme for the decisions.
Mistakes and limits
- Using a thermometer in the sun. The formula wants shade air temperature. A dark thermometer in direct sun can read 15 °F or more above true air temperature, and that error then propagates through a polynomial with squared terms.
- Pairing temperature and humidity from different times. Relative humidity falls through the morning as the air warms even when no moisture leaves. A 7 a.m. humidity with a 3 p.m. temperature produces a badly wrong answer.
- Reading the heat index as a real temperature. It is an equivalence, so it will not match anything a thermometer shows and it can legitimately exceed any temperature the air actually reaches.
- Extrapolating the grid. Values in the far bottom-right of the table describe combinations that do not occur together in the atmosphere. Treat anything past about 130 °F as a warning flag, not a measurement.
- Ignoring the wind. The model assumes a light breeze. Still air is worse than the number says; strong dry wind is better, until air temperature exceeds skin temperature, at which point wind delivers heat rather than removing it.
- Assuming the number covers overnight risk. Heat illness accumulates. A night that does not drop below the mid-70s °F prevents recovery, and the following day's identical heat index is more dangerous than the first.
Key terms
- Apparent temperature
- A temperature equivalent describing the physiological effect of a combination of conditions. The heat index is the humid-heat case; wind chill is the cold-wind case.
- Dew point
- The temperature to which air must be cooled, at constant pressure, for water vapour to begin condensing. It measures absolute moisture and does not change as the air warms or cools during the day.
- Relative humidity
- The ratio of the air's vapour pressure to its saturation vapour pressure at the same temperature, as a percentage. It falls as air warms even with no change in actual moisture.
- WBGT
- Wet bulb globe temperature, a composite index combining natural wet bulb, black globe and dry bulb readings. It accounts for solar load and radiant heat, which the heat index does not, and it is the basis of occupational heat standards.
Where the heat index sits among the alternatives
The heat index is the right tool for a forecast and a rough field judgement, and the wrong tool for a compliance programme. Its strength is that it needs only two numbers you always have. Its weakness is everything it leaves out: solar load, radiant heat from surfaces, wind speed, and what you are wearing.
WBGT is the standard where those matter. It weights a natural wet bulb reading, a black globe reading and dry bulb air temperature, so it responds to sun and to radiant surfaces. Occupational heat guidance from ACGIH and NIOSH is written against WBGT, with clothing adjustment factors and work-rest schedules keyed to it. If you are setting rest breaks for a crew, that is the framework to use.
Humidex, used in Canada, is a different construction again: it adds a dew-point-derived term to the air temperature rather than fitting a physiological model, so a humidex value and a heat index value for the same conditions are not interchangeable and generally will not match.
For household decisions, the heat index is also the number that drives your air conditioning bill on the worst days — the appliance energy cost calculator turns a unit's rated wattage and run hours into dollars, and during an extended heat event with grid strain the emergency water storage calculator covers the other half of preparedness, since hydration requirements rise sharply in exactly these conditions.