How to calculate heat index, step by step
To calculate heat index, take the air temperature in degrees Fahrenheit and the relative humidity in percent, and put them into the National Weather Service Rothfusz formula: HI = −42.379 + 2.04901523T + 10.14333127R − 0.22475541·T·R − 0.00683783·T² − 0.05481717·R² + 0.00122874·T²·R + 0.00085282·T·R² − 0.00000199·T²·R², where T is the air temperature and R is the relative humidity. Work out the nine terms, then add them up. On the defaults — 90°F air with 40% humidity — the answer is 91°F. Work it out in the heat-index-calculator.
The worked example: 90°F at 40% humidity
The worked example, term by term. Step 1 — the constant: −42.379. Step 2 — the temperature term: 2.04901523 × 90 is 184.41. Step 3 — the humidity term: 10.14333127 × 40 is 405.73. Step 4 — the interaction term: −0.22475541 × 90 × 40 is −809.12. Step 5 — the temperature squared: −0.00683783 × 90² is −55.39. Step 6 — the humidity squared: −0.05481717 × 40² is −87.71. Step 7 — temperature squared times humidity: 0.00122874 × 90² × 40 is 398.11. Step 8 — temperature times humidity squared: 0.00085282 × 90 × 40² is 122.81. Step 9 — both squared: −0.00000199 × 90² × 40² is −25.79. Step 10 — add them up: −42.379 + 184.41 + 405.73 − 809.12 − 55.39 − 87.71 + 398.11 + 122.81 − 25.79 is 91°F in whole degrees. Step 11 — the rise: 91 − 90 is 1, so the air feels one degree hotter than the thermometer reads. The same ten steps work for any temperature and humidity: work out the nine terms, add them up, and read the danger level.
What the formula is measuring
Heat index is how hot the air feels once humidity stops sweat from cooling you. Sweat cools you by evaporating, and evaporation slows as the air gets damper: in dry air sweat evaporates freely and carries heat away, in damp air sweat sits on the skin and the cooling stalls, so your body holds more heat. The formula turns that rate of cooling into a temperature: 90°F at 40% humidity feels like 91°F because the damp air is carrying heat away a little slower than dry air would. It is a rate of cooling written as a temperature, not a temperature a thermometer would read — a thermometer in the shade still reads 90°F. What changes is how fast your body sheds heat, and that is what the 91°F describes.
When the formula applies — and when it does not
The formula applies at 80°F or above. Below 80°F there is no heat index to work out: the humidity does not make the air feel hotter in any sense the formula measures, and a calculator that prints a heat index below 80°F is answering a question the formula does not ask. At the edge of the range the formula has two adjustments and a fallback. When the humidity is below 13% and the temperature is between 80°F and 112°F, dry air takes a little off the regression. When the humidity is above 85% and the temperature is between 80°F and 87°F, damp air adds a little. And when the regression comes out below 80°F, the simple formula is used instead — and at 80°F and 40% humidity that gives a value below the air temperature, so the heat index is about the air temperature there: it feels like 80°F. If a calculator refuses your numbers or answers with the air temperature, check the range before you trust a number from anywhere else.
Danger levels: the four bands
The National Weather Service bands are Caution from 80 to 90°F, Extreme Caution from 90 to 103°F, Danger from 103 to 125°F, and Extreme Danger at 125°F and above. On the defaults the heat index is 91°F, in Extreme Caution: heat cramps or exhaustion are possible, and heatstroke is possible with long exposure or hard work. In Caution, fatigue is possible with long exposure. In Danger, heat cramps or exhaustion are likely, and heatstroke is possible. In Extreme Danger, heatstroke is highly likely with continued exposure. The bands are headline thresholds, not a stopwatch: sunshine, exertion, clothing, age and health all move the real risk, and full sunshine can add up to 15°F to the feels-like temperature. Drink water and take shade breaks well before the band you are in, not when the symptoms start.
Reading a forecast: heat index vs air temperature
A forecast gives you two numbers in summer: the air temperature and the heat index. The air temperature is what the thermometer reads; the heat index is what your body feels. Plan for the heat index, not the air temperature: 90°F at 40% humidity feels like 91°F, so the water, the shade and the rest breaks have to match 91°F, not 90°F. The gap between the two is the rise — one degree on the defaults — and the gap grows as the humidity rises and shrinks as the humidity falls. When the forecast says the heat index is 105°F, the air is cooler than that: the heat index describes heat stress on people, not the temperature of a car interior or a roof, which can be far hotter than the air.
Common mistakes
The first is reading the heat index as the temperature: the thermometer reads the air temperature, and the heat index is how that air feels on skin. The second is applying the formula below 80°F, where it does not apply — the result looks like a number, but it means nothing. The third is forgetting the humidity: the same 90°F feels very different at 40% humidity and at 90% humidity, and a calculator that only asks for the temperature is not calculating a heat index at all. The fourth is mixing up the two adjustments: dry air below 13% humidity takes a little off the regression, damp air above 85% adds a little, and the two never apply at the same time. The fifth is treating the danger bands as exact minutes for one person: clothing, activity, sunshine and health all move the real risk. Work it out in the heat-index-calculator, and check the heat-index-chart and the celsius-to-fahrenheit-chart before you decide what the answer means.
A quick check you can do in your head
You cannot do a nine-term regression in your head, but you can sanity-check an answer. At 90°F, 40% humidity adds about one degree; very damp air at the same temperature adds far more, because the squared terms in the formula grow with the humidity. The rise grows fast as the humidity climbs: doubling the humidity from 40% to 80% at the same temperature adds far more than twice the rise. If a calculator says 90°F at 40% humidity feels like 75°F, or like 120°F, the number is wrong — the answer is 91°F, and anything far from it is a unit error or a different formula. Run your numbers through the heat-index-calculator and compare them with the worked example above.