Heat index calculator: the whole NWS procedure, not one equation

What is the heat index?

The heat index answers a question a thermometer cannot: not how hot the air is, but how hot it feels. Your body cools itself by evaporating sweat, and humid air slows that down, so the same ninety degrees is far harder work for you at seventy percent humidity than at twenty. The index expresses that as a single number — the temperature that would feel the same in dry air.

The version used across the United States and Canada comes from a multiple-regression analysis Lans P. Rothfusz published in a 1990 National Weather Service technical attachment, itself a fit to earlier work by R. G. Steadman. It is the number behind every heat advisory, every "feels like" figure on a forecast, and every warning about working outdoors in summer.

This calculator implements the whole published procedure rather than the single equation that circulates, and it shows its working: which of the two formulas ran, what each adjustment contributed, and how far the popular equation on its own would have been.

How to use it

1. Pick your units. Fahrenheit or Celsius. The coefficients were fitted in Fahrenheit, so the calculation happens there and converts — switching units converts the temperature you already typed rather than reinterpreting it.
2. Enter the air temperature and the relative humidity. Use the thermometer reading and the humidity percentage a forecast gives you. The sample buttons load the agency's own worked example plus four readings chosen to show a different part of the procedure each.
3. Read the panel headed "how that number was reached". It names which formula ran, what the printed equation alone would have said, and each adjustment's signed contribution. Below it you get both of the National Weather Service's warning scales, and a flag when the answer comes out cooler than the actual air.

The equation everyone copies is the first line of a procedure

Search for the heat index formula and you will find the Rothfusz regression — a long polynomial in temperature and humidity. It is on the National Weather Service's own pages. It is also not, on its own, the heat index. The complete procedure adds a subtraction for dry air, an addition for very humid air in a narrow temperature band, and a different, much simpler formula for readings at the cool end where the regression was never fitted.

That is measurable rather than arguable, because NOAA publishes a full heat index chart as a PDF: 976 values covering 76 to 126 degrees Fahrenheit and 4 to 100 percent humidity. Scored against every one of those cells, the bare regression on its own reproduces 819 of them exactly and is off by as much as 3.2 degrees. The full procedure this page implements reproduces 972 of the 976 exactly, and all 976 to within a single degree.

The four it misses are worth stating rather than rounding away. All four sit at 48 percent humidity, all four land between 0.46 and 0.50 above a whole number, and in every case NOAA's chart rounded up where ordinary rounding rounds down. That is a difference in the last step of printing, not in the arithmetic.

The agency disagrees with itself in four places

The page publishing the procedure says the regression is used when the cool-end value is "80 degrees F or higher". The agency's own online calculator says, in its source, that the regression is used when that value is above 79. Ten cells of the published chart distinguish the two readings, and the chart follows the calculator on all ten and the prose on none. This page follows the chart.

The warning bands are published twice, differently. The safety pages give Caution 80 to 90, Extreme Caution 90 to 103, Danger 103 to 124, Extreme Danger 125 and above. The full chart PDF gives Very Warm 80 to 89, Hot 90 to 104, Very Hot 105 to 129, Extremely Hot 130 and above — different names and different boundaries. A heat index of 103.4 is Danger on one document and merely Hot on the other, which is one of the sample buttons. Both are shown here, each labelled with where it came from.

And there is a sentence in the published procedure — the simple formula "is computed first and the result averaged with the temperature" — that reads like an extra averaging step and is not one. It describes the halving already inside that formula, as the agency's own calculator code makes explicit. Reading it the other way costs up to 3.3 degrees, and it drops agreement with the published chart in that branch from 92 percent to 40. It is an easy mistake; this page took it and the chart corrected it.

Honest limitations

The heat index is defined for shade. The National Weather Service states that exposure to full sunshine can increase it by up to 15 degrees Fahrenheit, and that is a range it does not model at all. This page shows the upper end of that range beside the answer rather than adding a fixed amount for sun, because a "sunny" checkbox that added, say, twelve degrees would be inventing a precision the source does not have.

In dry air the index comes out below the actual temperature, which surprises people and is not a bug. The agency states it plainly: at 100 degrees with 15 percent humidity the heat index is 96. Of the 976 cells in the published chart, 294 are lower than their own row's temperature, and the extreme is 126 degrees at 4 percent humidity printed as 113 — thirteen degrees below the air. The familiar chart that circulates starts at 40 percent humidity, which is why so few people have seen this.

The procedure is also discontinuous, because the two formulas do not meet. Between roughly 77 and 81 degrees the answer steps by up to 1.4 degrees as the calculation crosses from one to the other, in either direction — so in that narrow band the published heat index can actually fall as humidity rises. Above it the index behaves monotonically, as you would expect. Finally, this is the North American index; other countries publish quite different heat-stress measures, and a number from one is not comparable with a number from another.

Why is it free?

It is a polynomial, two conditional adjustments and a threshold, and your browser evaluates the lot as you type. No server is involved, so there is nothing to meter and no account to create.

Nothing is uploaded. The numbers you enter stay in this tab.