Heat Index (Rothfusz Regression)

Also known as apparent temperature · feels like temperature hot

\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2

Worked example: 35 C at 50 % RH → 40.675 C — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

Here the solver did the work — could you?

Feels-Like Temperatures →

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Heat Index (Rothfusz Regression) explained

The heat index is the American cousin of the humidex, and it comes from a much more elaborate model. In 1979 Robert Steadman published a multi-page thermoregulation calculation involving clothing, activity, skin resistance and evaporation, producing tables of the apparent temperature. Nobody wanted to run that on air, so in 1990 Lans Rothfusz fit a nine-term polynomial regression through Steadman's tables. That regression is what the National Weather Service broadcasts and what this page computes.

Since it is a fit to a model, it inherits every assumption underneath: a person of average build walking at about 5 km/h in the shade, with a light breeze and normal clothing. Full sun can add up to 8 °C to the effective value. The regression is published for temperatures of 80 °F (26.7 °C) and above with humidity of 40 % or more, which is why this page declines outside that box, and the NWS applies small corrections at very low and very high humidity that are not included here.

Solving it backwards is left out on purpose. Taken as a function of temperature it is a quadratic with two roots, and there is no honest way to tell a user which branch the weather is on, so the page offers the forward calculation only. A regression that gives one confident answer in the direction it was fit, and an ambiguous one in reverse, should say so rather than pick.

Heat Index (Rothfusz Regression) formula

\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2

Where

$\mathrm{HI}$ = Heat index (°C)
$T$ = Air temperature (°C)
$R$ = Relative humidity (%)

Missing one of these? Work it out first, then come back

Heat index — Wind Chill (2001 North American Formula), Dew Point (Magnus Approximation)
Air temperature — Wind Chill (2001 North American Formula), Dew Point (Magnus Approximation)
Relative humidity — Dew Point (Magnus Approximation), Blood Alcohol Estimate (Widmark Equation)

Part of this formula set

What the weather feels like

4 formulasWind chill, humidex, heat index and dew point — the four numbers that explain why the thermometer lies.