The official NWS and Environment Canada formula, with the frostbite exposure bands that actually matter when deciding what to wear.
Wind chill is not the air getting colder. The thermometer reads what it reads regardless of wind. What changes is the rate at which your body loses heat.
Still air lets a thin layer of warmth build up against your skin, which then insulates you. Wind strips that layer away as fast as it forms, so your skin keeps losing heat to genuinely cold air rather than to the warmed film. Wind chill expresses that accelerated loss as the still-air temperature that would cool you at the same rate.
WC = 35.74 + 0.6215T − 35.75V0.16 + 0.4275·T·V0.16
with T in Fahrenheit and V in miles per hour. It is valid only at or below 50 °F (10 °C) with wind of at least 3 mph (4.8 km/h), and the calculator refuses to return a value outside that range rather than extrapolating into territory the equation was never fitted to.
The V0.16 term is the interesting part. Because the exponent is well below one, the effect saturates: going from calm to 10 mph makes a large difference, while going from 30 to 40 mph adds relatively little. Past about 40 mph, extra wind barely changes the number.
The formula in use before 2001 came from a 1945 Antarctic experiment by Siple and Passel, who measured how fast water froze in plastic cylinders suspended in the wind. It produced dramatically low numbers, and it was wrong in ways that mattered — cylinders of water are not human faces, and the wind speed was taken at 10 metres up rather than at head height.
The current formula came from human trials: volunteers in a refrigerated wind tunnel with thermal sensors on their faces, run jointly by the US and Canadian weather services. It also assumes wind at 1.5 metres, roughly face height, rather than at the anemometer. The result is warmer-sounding but more accurate figures — at strong winds the new formula typically reads 10 to 15 °F higher than the old one.
| Wind chill | Frostbite on exposed skin |
|---|---|
| Above −18 °F (−28 °C) | Low risk with normal precautions |
| −18 to −32 °F (−28 to −36 °C) | Possible in about 30 minutes |
| −32 to −48 °F (−36 to −44 °C) | Possible in about 10 minutes |
| Below −48 °F (−44 °C) | Possible in about 5 minutes |
These are the bands the NWS publishes on its wind chill chart, and they are the practical output of the whole calculation. The number itself is abstract; "exposed skin freezes in ten minutes" is actionable.
It describes exposed human skin and nothing else. Your car's engine will not cool below the air temperature because of wind, and neither will your pipes — wind speeds up the approach to air temperature but cannot take anything below it. A water pipe at −5 °C air temperature freezes at the same point whether it is windy or calm; the wind only makes it get there faster.
It also assumes you are dry. Wet skin or damp clothing loses heat far faster than the formula allows for, because evaporation carries away heat on its own. Immersion in cold water is a different and far more dangerous situation that wind chill does not describe at all.
Covering exposed skin removes the effect almost entirely, which is why the practical answer to a severe wind chill warning is a face covering rather than a heavier coat.
No. Wind chill describes heat loss from exposed human skin, and nothing can be cooled below the actual air temperature by wind alone. Wind makes an object reach air temperature faster, but not go past it. A pipe in −5 °C air freezes at the same point windy or calm — the wind just shortens the time. This is one of the most common misreadings of a wind chill warning.
The old formula came from a 1945 experiment measuring how fast water froze in plastic cylinders in Antarctic wind — not a good model for a human face, and it used wind speed measured 10 metres up rather than at head height. The current formula came from human volunteers in a refrigerated wind tunnel with facial thermal sensors, run jointly by the US and Canadian weather services. It reads 10 to 15 °F warmer at strong winds, and it is more accurate.
Around −18 °F (−28 °C) frostbite becomes possible on exposed skin within about 30 minutes. Below −32 °F it drops to roughly 10 minutes, and below −48 °F to about 5. Those numbers apply to skin left uncovered — covering your face, ears and hands removes almost all of the effect, which is why the practical response to a wind chill warning is better coverage rather than simply a heavier coat.
Because the NWS formula is only defined at or below 50 °F (10 °C) with wind of at least 3 mph. Outside that range it produces numbers that look plausible and mean nothing, since the equation was never fitted to those conditions. Wind still cools you on a mild day through evaporation, but that is a different mechanism and wind chill does not describe it.
No — it saturates. The formula raises wind speed to the power of 0.16, an exponent well under one, so each additional mile per hour matters less than the last. Going from calm to 10 mph makes a big difference; going from 30 to 40 mph adds only a couple of degrees. Beyond about 40 mph, extra wind barely moves the figure at all.
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