Wind Chill Calculator

WC = 35.74 + 0.6215 · T − 35.75 · V^0.16 + 0.4275 · T · V^0.16, with T in °F and V in mph

T

Air temperature in Fahrenheit, because that is the scale the equation was fitted in. The field takes Celsius as well — most of the world reads a thermometer in Celsius — so the conversion happens once on the way in and once on the way out, and the equation itself never sees anything but Fahrenheit. Note the upper limit: the formula is defined at or below 50 °F, which is why the temperature field stops there rather than at some round hundred. Above 50 °F wind chill is not a thing people notice, and the equation quietly stops describing anything real — feeding it 70 °F produces a number, and that number is not a wind chill.

V

Wind speed in miles per hour, the unit the coefficients were fitted in, with the other four units converting into it before the equation runs. The lower limit of 3 mph is part of the definition rather than a convenience: the 2001 formula was calibrated so that at a wind of about 3 mph the result is close to the air temperature, and below that it stops behaving — at a wind of zero the equation returns a value warmer than the air, which is nonsense. The exponent 0.16 is what makes the wind curve flatten: the difference between 5 and 25 mph is several times the difference between 25 and 45 mph, and the reference table below shows that as a row that stops moving.

35.74, 0.6215, 35.75, 0.4275, 0.16

The five fitted constants of the 2001 revision all come from one model rather than from one measurement: heat transfer was worked out for a bare face facing the wind and walking into it at about 3 mph, over a range of air temperatures and wind speeds. The older 1945 Siple and Passel formula that had been in use for half a century was based on something else entirely — how fast water froze in a small plastic bottle standing out in the Antarctic cold — and what it describes is a bottle losing heat, not a person. The two temperature terms and the two wind terms combine to make the wind penalty grow with cold: the same wind costs more at −20 °F than at 20 °F.

WC

The result in Fahrenheit, printed in Celsius as the main row. It is not a temperature, and the distinction is not pedantry: it is the air temperature that would take heat off exposed skin at the same rate as the actual temperature and wind together, in a person walking at 3 mph. A thermometer still reads the air temperature, water still freezes at 0 °C, and a car radiator does not care about this number at all — what the wind chill describes is how fast you personally lose heat, which is exactly the thing that decides whether your hands hurt after ten minutes.

Use it before going outside on a cold, windy day — the days when the forecast temperature and the walk to the car disagree. It is most useful at the two ends: checking whether a child's walk to school is a fifteen-minute or a five-minute problem, and deciding how much of the commute to spend outdoors. It is the wrong tool for anything that is not about a person's skin: whether pipes will freeze, whether a road will ice, and whether a plant needs covering are all questions about the air temperature, and the answer there is the ordinary forecast, not this page.

1. First screen: 10 °F and 20 mph

   1. Air at 10 °F is already cold — that is −12.2 °C
   2. Wind factor: 20^0.16 = 1.6150
   3. WC = 35.74 + 0.6215 · 10 − 35.75 · 1.6150 + 0.4275 · 10 · 1.6150
   4. WC = 35.74 + 6.215 − 57.74 + 6.90 = −8.88 °F
   5. Celsius row: (−8.88 − 32) · 5/9 = −22.7 °C

   The air is −12.2 °C and the wind makes it feel like −22.7 °C — a full 10.5 °C of extra load, taken off exposed skin by nothing but moving air. That gap is the whole point of the page, and it is the reason a reader who only looks at the forecast temperature under-dresses. This is also the case most people meet in practice: a bright, still-feeling winter morning where the wind is the thing that decides whether the walk is pleasant or painful.

2. A mild day with a light wind: 40 °F and 5 mph

   1. Air at 40 °F is 4.4 °C
   2. Wind factor: 5^0.16 = 1.2937
   3. WC = 35.74 + 24.86 − 46.25 + 22.12 = 36.47 °F
   4. Celsius row: (36.47 − 32) · 5/9 = 2.5 °C

   Barely any wind, barely any penalty: 4.4 °C of air feels like 2.5 °C, a difference of less than two degrees. The page is worth keeping honest about this end of its range too — a wind chill calculator that produced a dramatic number for a still, mild day would be telling readers that the formula is a scare device. Read the pair of examples together and the shape of the equation appears: at 5 mph the wind term is small, at 20 mph it is the largest single term.

3. The cold corner: −20 °F and 25 mph

   1. Air at −20 °F is −28.9 °C
   2. Wind factor: 25^0.16 = 1.6737
   3. WC = 35.74 − 12.43 − 59.83 − 14.31 = −50.83 °F
   4. Celsius row: (−50.83 − 32) · 5/9 = −46.0 °C

   This is the corner of the table where a reading stops being about comfort and starts being about frostbite. Note which number carries the warning: the air is −28.9 °C, which is survivable for a long while with the right clothing, while the wind chill is −46 °C, which is a different kind of number. The equation does not know how long you will be out, what you are wearing, or whether your face is covered, so treat the reading as the reason to shorten the exposure rather than as a measurement of your own risk.

4. Where the two scales disagree about the sign: 35 °F and 10 mph

   1. Air at 35 °F is 1.7 °C — above freezing
   2. Wind factor: 10^0.16 = 1.4454
   3. WC = 35.74 + 21.75 − 51.67 + 21.63 = 27.45 °F
   4. Celsius row: (27.45 − 32) · 5/9 = −2.5 °C

   A case that exists only because the page prints both scales: 35 °F of air is 1.7 °C, comfortably above freezing, and the wind chill is 27.4 °F — which in Celsius is −2.5 °C, below freezing. The two readings are the same temperature said twice; the sign difference is just where zero sits on each scale. It is worth knowing because readers compare the wind chill against 0 °C to judge frost risk, and the Fahrenheit row on the same screen will not confirm it.

The equation is defined only inside a box: air at or below 50 °F, wind at or above 3 mph. Outside it the arithmetic still runs happily and the result is meaningless, which is why this page refuses rather than warns — a wind chill of 60 °F at 65 °F of air looks like a normal number and is not. The value is a heat-loss equivalent, not a temperature: pipes freeze, roads ice, and plants die at the air temperature, and no reading on this page changes any of those. It assumes shade — the NWS lists no sun among the conditions the index is defined under, since radiant heat is not something a wind speed can account for. It assumes a person walking at about 3 mph in dry clothing, with a face exposed; lying still in wet clothes is worse than the number, moving briskly is better. And it says nothing about duration: two people at the same wind chill, one out for five minutes and one for an hour, are not in the same danger at all. The NWS's own explainer is careful about the same boundary — it notes that frostbite strikes exposed skin only once the wind chill is below freezing, and that the index describes people and animals rather than cars, pipes or plants, none of which have a skin temperature to defend.

What is the wind chill formula?

WC = 35.74 + 0.6215 · T − 35.75 · V^0.16 + 0.4275 · T · V^0.16, with the air temperature T in Fahrenheit and the wind speed V in miles per hour. It is the equation the National Weather Service (NWS) and the Meteorological Service of Canada adopted in 2001, replacing a 1945 formula that had been derived from how fast water froze in a small plastic bottle left standing in the Antarctic cold. The 2001 constants describe a bare face walking into the wind, and the NWS tested the index on twelve adult subjects — people doing roughly what you are about to do.

Is wind chill the same as the temperature?

No, and the difference matters. Wind chill is not a temperature at all: it is the air temperature that would remove heat from exposed skin at the same rate as the real temperature and the real wind together, for a person walking at about 3 mph. Your thermometer still reads the air temperature, water still freezes at 0 °C, and your car's radiator is unaffected. What the number describes is how fast you lose heat, which is why it is the right thing to look at when deciding how long to stay outside and the wrong thing to look at when deciding whether to cover the plants. It is also the number that tells you when frostbite stops being a distant possibility on an exposed cheek — that is a statement about your skin, not about the air, and no thermometer can make it.

Why does the calculator refuse temperatures above 50 °F?

Because that is the top of the range the equation is defined over — a condition of the formula, not a setting on this page. Above 50 °F a wind makes little difference to how cold you feel, and the fitted curve stops describing anything real; fed 60 °F and 20 mph it returns 56.7 °F, a number that looks plausible and means nothing. Keeping the field's maximum at 50 °F means the page can never print that number. (If you are looking for how hot it feels, that is the other half of the same idea and lives on the heat index page.)

Why can't I enter a wind speed below 3 mph?

The 2001 formula was calibrated so that at a wind of roughly 3 mph the wind chill is close to the air temperature, and below that it degrades: at a wind of zero the equation returns 35.74 + 0.6215 · T, which is warmer than the air, and at 1 mph it is only slightly less absurd. Rather than print a wrong number for a still day, the field's minimum stops there. Entering 0 to mean "no wind" is the most common way to meet this limit, and the honest answer for a still day is simply the air temperature.

Which wind speed should I enter — the forecast, or what it feels like at my door?

The forecast wind speed is the intended input, and it is the number the chart is drawn against. It is measured in an open area, typically well above head height, so a sheltered street, a courtyard, or a stand of trees can genuinely be calmer, and the wind chill you experience will be milder than the page says. The reverse is also possible on a exposed corner or a bridge. Treat the reading as the value for open ground and adjust with your own knowledge of the place you are going — no wind speed typed into a form can know about the wall you are about to walk behind.

Does sunshine change the wind chill?

Yes, and the equation does not know about it. The wind chill assumes shade: it accounts for heat lost to moving air, and says nothing about heat gained from the sun. The National Weather Service notes that bright sunshine can make a windy winter day feel noticeably warmer than the chart's value, which is why a sunny −10 °C with a stiff wind can be pleasant while the same reading on an overcast day is not. The reference chart on this page is drawn for shaded skin, and it is the conservative reading of the two.

Can the wind chill ever be warmer than the air temperature?

Not on this page, and that is a useful sanity check on the arithmetic. At the mildest end of the valid range — 50 °F and the minimum 3 mph — the answer is 49.7 °F, very slightly below the air temperature, and every colder or windier combination moves further down. The reason is in the equation: at or below 50 °F the wind terms always subtract more than they add, so more wind means a lower reading. If you ever see a wind chill above the air temperature from a calculator, it is being fed conditions outside the range this page accepts.

• Understanding wind chill — the NWS explainer behind this calculator: the validity conditions it enforces (at or below 50 °F, above 3 mph), the published equation, and the note that the index applies to people and animals rather than to objects — National Weather Service
• Wind chill safety — what the value means for people, and the caveats the NWS attaches to it — National Weather Service
• Wind chill calculation worksheet (PDF) — the one-page NWS worksheet carrying the equation with its published coefficients, plus the metric (W/m²) form — National Weather Service
• Wind chill — the history behind the two formulas this page contrasts: the 1945 index built on the cooling rate of a small plastic bottle as its contents turned to ice, measured by Siple and Passel in the Antarctic, and the 2001 model computed for a bare face walking into the wind — Wikipedia