Wind chill explained: the formula, its limits and what it measures

Wind chill is a number for how cold exposed skin feels when wind moves air past it. It does not describe the air temperature itself. The index combines air temperature and wind speed into the still-air temperature that would cause the same rate of heat loss from skin. On a hike, it matters most on an exposed ridge in cold air, when hands, face or the back of the neck are uncovered.

What wind chill measures, and what it does not

The National Weather Service describes wind chill as based on the rate of heat loss from exposed skin caused by wind and cold. Moving air carries heat away from skin faster than still air does, so skin cools more quickly. The NWS page puts it plainly: wind makes it feel much colder.

The index applies to people and animals only. For objects, the NWS says wind only cools them more quickly toward the air temperature. An object does not go below the actual air temperature: its example is a car radiator at −5 °F with a wind chill of −31 °F, which stays at −5 °F. Frostbite also depends on the air, not the index. The NWS says that for frostbite to develop on exposed skin, the actual air temperature near the skin must be below freezing, whatever the wind chill reads.

The formula in two unit systems

The NWS formula takes air temperature in degrees Fahrenheit and wind speed in miles per hour:

Wind chill (°F) = 35.74 + 0.6215T − 35.75V^0.16 + 0.4275T·V^0.16
T = air temperature (°F), V = wind speed (mph)

The metric form takes T in °C and V in km/h:

WCI (°C) = 13.12 + 0.6215T − 11.37V^0.16 + 0.3965T·V^0.16
T = air temperature (°C), V = wind speed (km/h)

The metric form is the same index converted to metric units, not a separate model. Check: at −10 °C and 30 km/h, the metric form gives −19.52 °C. Convert the same inputs to °F and mph (−10 °C is 14 °F, and 30 km/h is 18.64 mph), apply the NWS formula, and the result is −3.09 °F, which is (−3.09 − 32) × 5 ÷ 9 = −19.49 °C. The two agree to within 0.05 °C. The Environment and Climate Change Canada calculator takes the air temperature in °C and the wind speed in km/h. When no instrument is available, it suggests estimating the wind speed from the movement of trees and flags.

Where the index applies

The NWS defines the index only for temperatures at or below 50 °F and wind speeds above 3 mph. In metric terms those limits are 10 °C and 4.8 km/h. The conversions are 50 °F = 10 °C, and 3 mph × 1.609 = 4.8 km/h. Outside those limits the index is not defined, so read the air temperature instead.

A wind chill chart in °C and km/h

The grid applies the metric formula across a range of temperatures and wind speeds. Each value is the wind chill in °C, rounded to 0.1 °C. Every cell is inside the formula's limits.

Read across a row to see how much wind alone does. At −20 °C the value moves from −27.2 °C at 10 km/h to −35.4 °C at 50 km/h. That is a change of 8.2 °C (−35.4 − (−27.2) = −8.2), with the air still at −20 °C.

13.12 + 0.6215 × (−10) − 11.37 × 1.7232 + 0.3965 × (−10) × 1.7232
= 13.12 − 6.215 − 19.593 − 6.833
= −19.5 °C

The tool also takes humidity, because the heat index uses it. Wind chill does not. The NWS notes that relative humidity changed its test results by less than 1 °F, so it was left out of the formula.

Environment Canada's risk levels and freezing times

Environment and Climate Change Canada attaches a risk level to each range of wind chill values, with the time in which exposed skin can freeze at the colder levels. The Feels like tool shows the matching level beside every result.

ECCC adds that in sustained winds over 50 km/h, frostbite can occur faster than the table shows. Read against the chart above, −20 °C with a 40 km/h wind gives −34.1, inside the high band, where exposed skin can freeze in 10 to 30 minutes.

Reading the number on the ground

The NWS gives a worked case: at 0 °F with a 15 mph wind, the wind chill is −19 °F, and exposed skin can freeze in 30 minutes. The formula gives −19.4 °F before rounding, which converts to −28.6 °C ((−19.4 − 32) × 5 ÷ 9 = −28.6). That 30-minute figure belongs to that one case. A different temperature or wind speed gives a different freezing time, and the NWS does not give a general one.

Sunshine changes the reading. The NWS says bright sunshine may raise the wind chill temperature by 10 °F to 18 °F. The index assumes no sun, which the NWS describes as a clear night sky, so on a bright afternoon the figure overstates the cold on skin in direct light.

The NWS tested the index on adult volunteers. For children, older people and people with compromised health, it advises using the chart as a starting point and being even more cautious. For the signs of cold stress and what to do, the site's cold stress note covers emergency preparation.

Wind speed at the height the forecast uses

The NWS index starts from wind at an average face height of about 5 ft, calculated from readings at the standard anemometer height of 33 ft. A height of 33 ft is 10.06 m (33 × 0.3048). A forecast or station wind speed given at that standard height is therefore the right input for the formula.

The reading still describes the air at one point. Exposed ridges and saddles can be windier than a valley station shows, while sheltered trees and the lee side of a rock can be calmer. The wind chill on your skin depends on the wind where you stand. For how a shelter changes the wind at ground level, see pitching a tarp for wind.

What the index leaves out

The formula uses only air temperature and wind speed. It does not include clothing, body size, fitness, how hard you are working, or how long you stay out. The NWS did not test children, and its volunteers were adults. Those gaps mean the chart gives a starting point for planning layers and turnaround times, not a measure of what your own body will do.

For the gear to carry in cold weather, see the ten essentials. Cold also affects battery performance, so see batteries in cold weather. For how the same thinking applies to heat, see heat index for hiking.