How to calculate wind chill, step by step
To calculate wind chill, take the air temperature in degrees Fahrenheit and the wind speed in miles per hour, and put them into the National Weather Service formula: WC = 35.74 + 0.6215T − 35.75·V^0.16 + 0.4275·T·V^0.16, where T is the air temperature and V is the wind speed. Work out V^0.16 first — the wind raised to the power 0.16 — then the four terms, then add them up. On the defaults — 20°F air with a 15 mph wind — the answer is 6°F. Work it out in the wind-chill-calculator.
The worked example: 20°F at 15 mph
The worked example, line by line. Step 1 — the wind power: 15^0.16 is about 1.54. Step 2 — the first term: 35.74. Step 3 — the second term: 0.6215 × 20 is 12.43. Step 4 — the third term: 35.75 × 1.54 is about 55.14. Step 5 — the fourth term: 0.4275 × 20 × 1.54 is about 13.19. Step 6 — add them up: 35.74 + 12.43 − 55.14 + 13.19 is about 6.22, which is 6°F in whole degrees. Step 7 — the drop: 20 − 6 is 14, so the wind makes it feel 14 degrees colder than the air. The same seven steps work for any temperature and wind speed: raise the wind to 0.16, work out the four terms, and add them up.
What the formula is measuring
Wind chill is how cold the air feels on exposed skin once the wind is pulling heat away. Still air lets your body warm a thin layer of air against your skin, and that layer insulates you; wind strips it away as fast as it forms, so heat leaves your skin faster. The formula turns that rate of heat loss into a temperature: 20°F at 15 mph feels like 6°F because the wind is stripping heat at the rate 6°F air would in calm conditions. It is a rate of heat loss written as a temperature, not a temperature a thermometer would read — a thermometer in the wind still reads 20°F. What changes is how fast your skin cools, and that is what the 6°F describes.
When the formula applies — and when it does not
The formula applies at 50°F or below with wind from 3 to 110 mph. Above 50°F there is no wind chill to work out: the wind does not make the air feel colder in any sense the formula measures, and a calculator that prints a number above 50°F is answering a question the formula does not ask. Below 3 mph the wind chill is the air temperature — 20°F at 2 mph feels like 20°F — because a breeze that light barely disturbs the warm layer on your skin. Above 110 mph the formula does not apply either. If a calculator refuses your numbers or answers with the air temperature, check the range before you trust a number from anywhere else.
Frostbite times: the three bands
The National Weather Service lists frostbite within 30 minutes once the wind chill reaches −18°F, within 10 minutes at −32°F, and within 5 minutes at −48°F — and it lists no frostbite time at all above −18°F, so at the 6°F headline there is no frostbite time on the chart. The times are bands, not a stopwatch: exposed skin can freeze within half an hour in the first band, and the chart's exact zone boundaries shift a little with wind speed, so treat the bands as the headline thresholds. Cover exposed skin well before the band you are in, not when the minutes run out. If skin goes numb, white or waxy, get warm and get help, whatever the calculator says.
Reading a forecast: wind chill vs air temperature
A forecast gives you two numbers in winter: the air temperature and the wind chill. The air temperature is what the thermometer reads; the wind chill is what exposed skin feels. Dress for the wind chill, not the air temperature: 20°F at 15 mph feels like 6°F, so the layers, the hat and the gloves have to match 6°F, not 20°F. The gap between the two is the drop — 14 degrees on the defaults — and the gap grows as the wind rises and shrinks as the wind falls. When the forecast says the wind chill is −20°F, the pipes are still at the air temperature, not at −20°F: wind chill describes heat loss from warm skin, and it does not apply to cars, pipes or plants, which cool to the air temperature and no lower.
Common mistakes
The first is reading the wind chill as the temperature: the thermometer reads the air temperature, and the wind chill is how that air feels on skin. The second is applying the formula above 50°F, where it does not apply — the result looks like a number, but it means nothing. The third is expecting a frostbite time at every wind chill: above −18°F the chart lists none, and a wind chill of 6°F carries no frostbite time at all. The fourth is forgetting the wind speed's units: the formula wants miles per hour, and kilometres per hour fed in as miles per hour gives a wind chill that is far too warm. The fifth is treating the bands as exact minutes for one person: clothing, activity, sunshine and health all move the real risk, and bright sunshine can raise the feels-like temperature by 10 to 18 degrees. Work it out in the wind-chill-calculator, and check the wind-chill-chart and the celsius-to-fahrenheit-chart before you decide what the answer means.
A quick check you can do in your head
You cannot do the 0.16 power in your head, but you can sanity-check an answer. At 20°F, a 15 mph wind takes about 14 degrees off; a 5 mph wind takes about 7 degrees off, and a 30 mph wind takes about 19 degrees off. The drop grows fast at first and then flattens: doubling the wind from 15 to 30 mph takes only about 5 more degrees off, because the 0.16 power grows slowly. If a calculator says 20°F at 15 mph feels like 15°F, or like −10°F, the number is wrong — the answer is 6°F, and anything far from it is a unit error or a different formula. Run your numbers through the wind-chill-calculator and compare them with the worked example above.