The formula
How to calculate heat index
Heat index folds humidity into the air temperature to describe how hot it actually feels, on the same logic as wind chill for cold weather: high humidity slows sweat evaporation, the body's main cooling mechanism, so a humid day feels considerably hotter than a dry day at the same thermometer reading.
The formula used here — the Rothfusz regression — is the one the US National Weather Service issues heat warnings from. It is a statistical fit to earlier physiological research on apparent temperature, not a formula derived from first-principles physics, which is why it looks like a long polynomial rather than a clean equation.
What to enter:
- Air temperature (°C)
- Relative humidity (%)
No submit button: type and the answer moves. Your inputs end up in the link, so the page can be shared already filled in.
Where more decimal places matter than the fields above display, the underlying calculation is not rounded until the final figure is shown — the precision used internally is higher than what is printed, which matters for anyone chaining this result into a further calculation of their own.
Why heat index matters
A heat index calculation gets used both to check work already done by hand and to explore how a formula behaves without redoing the algebra every time an input changes — this page exists for both, since the underlying arithmetic is the same either way.
Beyond a single check, the same calculation is worth rerunning whenever a measured input changes — a new reading, a corrected value, an updated assumption — since the result here always reflects exactly what is currently in the fields above rather than a value calculated once and then left stale.
A formula like this one is rarely the last step in a piece of work — the figure it produces usually feeds into a further calculation, a comparison against a published value, or a write-up that needs to state both the result and how confident it is. Getting this step right the first time, rather than propagating a small arithmetic slip through several more steps, is the main practical reason to check a manual calculation against a tool like this one before building on top of it.
Where a calculation like this one is part of a larger piece of work, it is generally worth running it with a round, easy-to-check set of numbers first — inputs of exactly 1, 10 or 100 — purely to confirm the formula is being applied correctly, before switching to the real measured values the actual result depends on.
Worked example
Take the figures the calculator starts with:
- Air temperature: 32 °C
- Relative humidity: 60 %
That gives:
- Heat index: 37.1 °C
The figures above are the calculator's own default values, shown purely so the working is visible rather than hidden — the same steps apply exactly to your own numbers, entered in the fields at the top of this page.
Reading the result
US heat-warning categories built on this figure: 27–32 °C (80–90 °F) is caution, 32–39 °C (90–103 °F) is extreme caution, 39–51 °C (103–124 °F) is danger, and above 51 °C (124 °F) is extreme danger, referring to the heat index value itself, not the air temperature.
Where this goes wrong. The regression is only valid above roughly 27 °C (80 °F) air temperature and 40% relative humidity — below that range the formula is not meaningful and the plain air temperature is the better figure to use. It also assumes shade; full sun exposure can add several more degrees to how conditions actually feel.
A result that is wrong by an exact factor of ten, a hundred or a similar round number is almost always a units error rather than a mistake in the formula itself — checking each input against the unit stated beside it is the fastest way to track it down.
Heat index is one specific feels-like formula, built for hot and humid conditions and not accounting for wind. This site's general feels-like calculator uses a different formula that includes wind, and will give a different number for the same air temperature and humidity.
It is a polynomial regression fitted to an earlier, more complex physiological model of heat exchange between skin and air, chosen because a polynomial is fast to compute by hand or by the simple hardware early weather systems ran on — accuracy of fit mattered more than mathematical elegance.
The headline figure is heat index. With 32 °C air temperature and 60 % relative humidity, that comes to 37.1 °C. Change any field and the figure moves with it.
Generally, no more than the least precise input justifies — a result reported to six decimal places from inputs measured to two significant figures is implying a precision the calculation does not actually have. The calculator shows full precision so you can round appropriately for your own use.
Yes — the equation shown in the formula section above is the standard form used in textbooks and reference material for this calculation, not a simplified or approximate version.
Yes, in the sense that it applies the correct standard formula and returns an accurate result for the inputs given — but check your own course or publication's requirements for how results should be rounded, presented and referenced, since those conventions vary and are not something a calculator can know on your behalf.