Does a 1 m/s wind really make it feel 1°C colder?
― Close to right in light wind, an exaggeration in strong wind
You hear this rule of thumb in winter forecasts and mountaineering books. Work it out with the formula weather agencies actually use, and it holds up well to about 5 metres per second. But the stronger the wind, the more slowly the felt temperature keeps dropping. That's because wind doesn't take away "temperature". It strips away the warm film of air that covers your skin.
It's 0°C one morning, and the forecast says "strong north wind, 10 metres per second".
By the "1 metre, 1°C" rule, it feels like −10°C. You might brace for northern-Hokkaido cold and pull out a heavy coat.
But once you step outside, it's certainly cold, yet not that cold. How far can this rule be trusted?
Why the rule works, and two reasons it fails
Around your skin is a thin layer of air warmed by your body. Wind blows this layer away and keeps pressing cold air against you. So the same air temperature feels colder when it's windy.
Stronger wind thins the film, but the thinner it gets, the harder it is to thin further. So doubling the wind speed does not double the cold.
In other words, "1 metre, 1°C" is a straight-line approximation of the drop in light wind. In strong wind, where the true curve starts to bend, the rule exaggerates.
Wind is peeling off a warm film of air
Imagine standing still on a windless day. Heat leaks slowly from your skin and warms the surrounding air. That warmed air forms a thin layer, a few millimetres thick, clinging to your skin. Like a blanket, it blocks the escape of heat.
When wind blows, this layer is carried away again and again. Your skin keeps meeting "air that hasn't warmed up yet", so heat escapes faster. Your body feels that speed of heat loss as "cold".
The "wind chill" published by weather agencies puts this idea into numbers. The question is: at what temperature in nearly still air would your face lose heat as fast as it does in the current wind? That temperature is called the wind chill. Use the slider in Figure 1 to change the wind speed and compare the rule of thumb with the real formula.
The thinner the film, the harder it is to peel
The solid line in Figure 1 flattens because of how the air film on your skin behaves. In light wind, a small increase in speed peels away a lot of film, and heat loss changes sharply. But once the film is already thin, even stronger wind can remove only a little more.
Besides, heat has to travel from inside your body to the skin before it can escape. However thin the air film gets, your skin and the tissue beneath it remain as a wall that holds heat back. So no wind, however strong, can make the felt temperature drop without limit.
Work it out at 0°C, and the wind chill at 5 metres per second is about −5°C, nearly the same as the rule. But at 10 metres per second it is about −7°C, and even at 20 metres per second only about −9°C. That is more than 10°C away from the rule's −20°C.
On the other hand, the colder the air, the bigger the drop the wind causes. At an air temperature of −10°C, a 10 metres per second wind gives a wind chill of about −20°C, almost exactly the rule. In colder places, the range where this rule works is wider.
Wind chill is about the speed of heat loss. A dry water pipe or a car body never gets colder than the air, however strong the wind. Wind only shortens the time it takes to cool down to the air temperature. Wet things are different: water takes heat away as it evaporates, so they can get colder than the air.
The wind speed in a weather forecast is usually measured 10 metres above the ground. At face height, friction with the ground makes the wind weaker. The weather agencies' wind chill formula is built to take this difference into account.
Summary
"A 1 m/s wind makes it feel 1°C colder" is a good rule of thumb in light wind, up to about 5 metres per second. But the stronger the wind, the more slowly the wind chill keeps falling. At 0°C, even a 20 metres per second wind feels like only about −9°C. What decides the cold is how much of the warm air film on your skin the wind strips away, and the thinner that film gets, the harder it is to strip.
Wind takes away not temperature, but the blanket of air on your skin.
The first few metres per second of wind add the most cold.
For the full picture of how wind takes heat away, see Why can hypothermia happen even on days that aren't that cold?. For how layers of air keep out the cold, see Why are several thin layers warmer than one thick one?. And for the summer side of why wind feels cool, see Why does the wind from an electric fan feel cool?.
- With an electric fan switched off, hold your palm in front of it and note how your skin feels.
- Next, switch it to "low". Notice how big the chilly change is going from "off" to "low".
- Then step up to "medium" and "high", and compare: does each step feel like a smaller change than "off to low"?
If you put a dry thermometer in front of the fan, its reading hardly changes. This shows that wind isn't cooling the air. It only changes how fast heat escapes from your skin.
For those who want more ― terms, formulas and links to textbooksEach part is labelled by level, from junior-high science to university courses
- Junior highCovered in junior-high science
- High schoolCovered in high-school physics and earth science
- High school+Advanced high-school material, or textbook sidebars
- UniversityUniversity courses not taught in high school (heat transfer engineering, biometeorology)
- ResearchNot yet settled even in university teaching; researchers are still studying it
Junior highTerms: this phenomenon has names
- Perceived temperature: the cold or heat a person feels on their skin, expressed as a temperature. Wind, humidity and sunshine make it differ from the air temperature.
- Wind chill index (wind chill temperature): a perceived temperature that counts only the cold caused by wind. The best-known version is the formula North American weather agencies have used since 2001.
- Boundary layer: the thin, slow-moving layer of air clinging to a surface. Heat has to pass through this layer to escape.
Junior highHigh schoolChecking with the formula: wind chill at 0°C and 10 metres per second
We calculate the wind chill itself with the wind chill index formula that Environment Canada and the US National Weather Service have used since 2001. Choosing 0°C makes the air-temperature terms vanish, which simplifies the sum.
| In symbols | W ＝ 13.12 ＋ 0.6215 × T − 11.37 × V0.16 ＋ 0.3965 × T × V0.16 |
| In words | Wind chill ＝ the part set by air temperature, minus the "loss to wind", which is proportional to wind speed to the power 0.16 |
| Where it comes from | It computes the heat leaving facial skin as a balance between heat flowing from inside the body to the skin and heat flowing from the skin to the air, then converts that to the air temperature at which the same heat would escape in nearly still air (4.8 km/h) |
| W | Wind chill temperature, in °C |
| T | Air temperature, in °C (use at 10°C or below) |
| V | Wind speed at 10 metres height, in km/h (use at 4.8 km/h or above) |
| Air temperature | 0°C (the two terms containing T become 0) |
| Wind speed | 10 metres per second |
| Factor to convert m/s to km/h | 3.6 |
| 36 km/h to the power 0.16 | said to be about 1.774 |
| For 5 metres per second (18 km/h), to the power 0.16 | said to be about 1.588 |
| Convert the wind speed to km/h | 10 × 3.6 ＝ 36 |
| Loss to wind | 11.37 × 1.774 ≒ 20.17 |
| Wind chill at 10 metres per second (°C) | 13.12 − 20.17 ≒ −7.05 |
| Rule of thumb "1 m, 1°C" (°C) | 0 − 10 ＝ −10 |
| Loss to wind at 5 metres per second | 11.37 × 1.588 ≒ 18.06 |
| Wind chill at 5 metres per second (°C) | 13.12 − 18.06 ≒ −4.94 |
At 5 metres per second the formula gives about −4.9°C and the rule gives −5°C, nearly identical. At 10 metres per second the formula gives about −7.1°C and the rule −10°C, so the rule overestimates the cold by about 3°C. Doubling the wind speed raises the loss to wind by only about 1.1 times. That is what the small exponent 0.16 means.
High schoolHigh school+Why "to the power 0.16"?
High schoolHeat flows from hot places to cold places. The amount that flows is the temperature difference multiplied by how easily heat passes through (its conductance). Wind changes not the temperature difference but this "ease of flow".
High school+The ease with which heat passes from a surface into the wind is said to grow roughly as wind speed to the power 0.5 (forced convection). But on a human face, heat must also pass through skin tissue, a "wall that doesn't depend on wind". With two walls in series, the overall effect of wind speed is weakened further. Fitting a simple formula to the results of a model calculation gives the small exponent 0.16, so it is said.
UniversityForced convection and the heat transfer coefficient
In heat transfer engineering, how readily heat moves from a surface to a fluid is expressed by the heat transfer coefficient, estimated from a relation between the Nusselt number and the Reynolds number. For forced convection around a cylinder, the Nusselt number is said to be proportional to the Reynolds number to the power of about 0.5 to 0.6. The 2001 wind chill index was built from a model that combines this relation, treating the face as a cylinder, with the thermal resistance of skin tissue (Osczevski and Bluestein, 2005).
📖 Derivation of the formula and further reading: Japanese Wikipedia, "Taikan ondo" (perceived temperature) ／ Wikipedia "Wind chill" (English, formula and history)
ResearchWhat is still not well understood
- Differences between people. The formula models the face of an average adult. How much real cooling changes for children, older people, or different face sizes and amounts of body fat is said not to have been studied enough yet.
- Sunshine and moisture. The 2001 formula leaves out sunshine on a clear day and evaporation from wet skin. How to fold these into a single number is still debated.
- Relation to whole-body cold. The formula covers cooling of facial skin. How it connects to the cold felt by a clothed body, or to the fall in core body temperature, is studied with other models.
So what this article says is also "an explanation within what is known today". It is safest to think of wind chill as a conventional number for comparing cold.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Junior high | Science: weather observation (temperature and wind) | Wind speed, air temperature, and the idea of wind chill |
| High school | Physics: heat transfer | Heat flow is set by temperature difference and conductance |
| High school+ | Physics: how heat is transmitted (convection) | The difference between speed to the 0.5 and to the 0.16 |
| University | Heat transfer engineering, biometeorology | Forced convection, Nusselt number, thermal resistance of skin |
| Research | Biometeorology, ergonomics | Individual differences, handling of sunshine and moisture |
| ― | Link to daily life | Choosing winter clothes, reading forecast wind speeds |
Note: This article is a science explainer for general readers. The numbers given are rough guides to help you understand the mechanism. Wind chill does not account for sunshine, moisture, clothing or individual differences. In cold regions or in the mountains, follow weather information and the guidance of local authorities and mountain-safety organisations.