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Wind chill and heat index: two formulas for one question

What the air feels like is not what the thermometer says, and the reason differs at each end of the scale. In the cold, wind strips away the thin layer of warm air your skin has heated, so heat leaves faster than the temperature alone implies. In the heat, humidity stops sweat evaporating, so the body's only real cooling mechanism stops working. Two different physical problems, and the US National Weather Service uses a different formula for each.

Wind chill (°F) = 35.74 + 0.6215T − 35.75V^0.16 + 0.4275T·V^0.16

T is the air temperature in Fahrenheit and V the wind speed in miles per hour. The formula replaced an older one in 2001, based on a model of heat loss from a human face with trials on volunteers, and it applies when the wind is above about 3 mph and the temperature is at or below 50 °F.

What wind chill does and does not describe

Notice the diminishing returns: the first 10 km/h of wind costs more than the next 40. Heat loss rises with the wind, but the relationship flattens because the boundary layer at the skin can only be stripped away once.

Wind chill applies to exposed skin and nothing else. It does not cool a car engine, a water pipe or a thermometer below the actual air temperature — wind cannot make anything colder than the air around it. A pipe will freeze faster in wind, because it loses heat faster, but it will not freeze at an air temperature above zero no matter how hard the wind blows. This is one of the most widely misunderstood points in weather reporting.

The cold risk bands

Fingers, ears, nose and cheeks go first, because they have a high surface area relative to their volume and the body restricts blood flow to them to protect the core. Covering those four things changes the practical risk far more than an extra layer on the torso.

The heat index works on a completely different principle

HI = −42.379 + 2.04901523T + 10.14333127R − 0.22475541TR − 0.00683783T² − ...

The heat index is a nine-term regression fitted to a biometeorological model, which is why it looks nothing like the wind chill formula. T is in Fahrenheit and R is relative humidity as a percentage. Below about 80 °F a simpler expression is used instead, and two correction terms apply at very low and very high humidity.

The curve steepens sharply as humidity rises, which is the whole point. At 30% humidity sweat evaporates freely and 32 °C is manageable; at 85% it barely evaporates at all and the same air temperature becomes genuinely dangerous. Dry heat at 40 °C can be more comfortable than humid heat at 32 °C.

The heat index assumes shade and a light breeze. Full sun can add as much as 8 °C to what you feel, so a reported heat index is a shade figure and outdoor work in direct sun is worse than the number suggests.

The heat risk bands

Heat exhaustion means heavy sweating, weakness, nausea and a fast weak pulse, and it responds to shade, fluid and cooling. Heat stroke is different in kind: the body stops being able to regulate, sweating may stop altogether, the skin becomes hot and dry, and confusion sets in. It is a medical emergency and the single most useful thing to know is that the sweating stopping is a worsening sign and not an improvement. Fluid needs rise steeply in heat — see the water intake calculator.

The gap where neither applies

Between about 10 °C and 27 °C neither formula is defined: there is not enough cold for wind to matter much and not enough heat for humidity to matter at all, so the air temperature is the honest answer. Other indices such as the Australian apparent temperature or the universal thermal climate index cover the whole range and add radiation and wind together, but the two NWS formulas remain the ones quoted in American forecasts.

A worked example

At −5 °C with a 30 km/h wind, the wind chill is −13 °C, which puts exposed skin in the 30-minute frostbite band — fine for a walk with a hat and gloves, not fine for an hour's cycling with bare hands. At 32 °C and 70% humidity, the heat index is 40.4 °C, inside the danger band, so outdoor physical work needs shade breaks, fluid and salt rather than willpower. The same person on the same day would describe both as “about what the thermometer said” only if the air were still and dry.

Two neighbours worth knowing: the conversion calculator, for the question this one leads into, and the BTU calculator, which answers it from the other direction.

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