Wind Chill, Heat Index and Dew Point, Explained
After reading this you will know how the three standard "feels like" numbers are computed, when each one applies, and how to read them without fooling yourself about how a day will actually feel.
Two thermometers can read 30 °C and describe completely different afternoons. One is a dry day with a light breeze; the other is a still, humid day where your sweat will not evaporate. The air temperature is the same. What your body registers is not. Three formulas turn temperature, humidity and wind into numbers that track that experience: dew point, wind chill and heat index.
What the three numbers measure
Each number answers a different physical question, so it helps to keep them separate.
- Dew point
- The temperature to which the air would have to cool for its water vapour to start condensing. It is an absolute measure of how much moisture the air holds, unlike relative humidity, which depends on the current temperature.
- Wind chill
- How cold exposed skin feels when wind strips away the thin layer of warm air your body heats around itself. It only matters in the cold.
- Heat index
- How hot the air feels when high humidity slows the evaporation of sweat, your main cooling mechanism. It only matters in the heat.
Wind chill and heat index never apply at the same time. Between them sits a band of ordinary weather where the air temperature is the honest answer and no correction is needed.
When to use each one, and when not to
The formulas are empirical fits with defined ranges. Push them outside those ranges and they return numbers that look plausible but mean nothing.
The Environment Canada and US National Weather Service wind chill formula is defined for air temperatures at or below 10 °C with wind at or above 4.8 km/h. Below that wind speed there is no meaningful stripping of the boundary layer, and above 10 °C the cold-skin physics no longer dominates.
The Rothfusz heat index is defined for air temperatures at or above 27 °C. Below that, humidity has little effect on comfort and the regression coefficients were never fit there.
Dew point has no such gate. It is a real physical property of the air and is valid at any temperature.
If you feed 30 °C into a wind chill formula or 2 °C into a heat index formula, most calculators will still print a result. Ignore it. Outside the defined range the number is an extrapolation of a curve that was only measured elsewhere.
The formulas and the intuition behind them
Start with dew point, because it feeds your reading of everything else. A common and accurate approximation is the Magnus formula. First compute an intermediate term \gamma from temperature T (in °C) and relative humidity RH (in percent):
Here a = 17.27 and b = 237.7\,\text{°C} are the standard Magnus constants. The first term grows with temperature; the logarithm is negative whenever humidity is below 100 percent and pulls the dew point down. The dew point T_d then follows:
At 100 percent humidity the logarithm is zero, so T_d = T: the air is already saturated and dew point equals air temperature. That is the sanity check to remember.
Wind chill uses air temperature T in °C and wind speed V in km/h:
The V^{0.16} exponent is the important part. Wind chill worsens fast for the first gusts, then flattens. Going from 0 to 20 km/h costs far more felt warmth than going from 40 to 60 km/h. The two terms in V^{0.16} combine so that colder air makes wind bite harder.
The heat index is a longer regression in temperature and humidity. In Fahrenheit (the form it was fit in) with T_F and R = relative humidity in percent:
You do not need to memorise the coefficients. The shape is what matters: at fixed temperature the index rises steeply with humidity, and the cross terms make that rise accelerate as it gets hotter. To use it in Celsius, convert to Fahrenheit first, apply the formula, then convert the result back.
A worked example with the demo data
The demo button uses 30 °C, 70 % humidity and 10 km/h wind. Reproduce all three numbers by hand.
Dew point, wind chill and heat index at 30 °C, 70 %, 10 km/h
- Dew point term: \gamma = \frac{17.27 \times 30}{237.7 + 30} + \ln(0.70) = \frac{518.1}{267.7} - 0.3567 = 1.935 - 0.357 = 1.578.
- Dew point: T_d = \frac{237.7 \times 1.578}{17.27 - 1.578} = \frac{375.1}{15.69} = 23.9\,\text{°C}.
- Wind chill check: air is
30 °C, well above the10 °Ccutoff. Wind chill does not apply. No result. - Heat index: air is
30 °C=86 °F, above the27 °Cgate, so the formula applies. Plug T_F = 86 and R = 70 into the regression. - The regression returns roughly
100.5 °F, which is (100.5 - 32) \times \tfrac{5}{9} = 38.0\,\text{°C}.
So the honest thermometer says 30 °C, but it feels like about 38 °C, and the dew point of 23.9 °C is above the oppressive threshold of 21 °C. The high dew point is exactly why the heat index climbs so far above the air temperature.
Reading and interpreting the results
Dew point is the fastest read on mugginess. Use these rough bands, which hold at any air temperature:
| Dew point (°C) | How it feels |
|---|---|
| Below 10 | Dry, comfortable |
| 10 to 16 | Pleasant |
| 16 to 18 | Getting sticky |
| 18 to 21 | Humid, uncomfortable |
| Above 21 | Oppressive, sweat will not evaporate |
Relative humidity alone misleads you because it moves with temperature. Air at 70 % and 10 °C has a dew point near 5 °C and feels crisp. Air at 70 % and 30 °C, the demo case, has a dew point near 24 °C and feels tropical. Same percentage, opposite experience. The chart below shows how sharply the heat index rises with humidity once the air is warm.
Common mistakes
The most frequent error is applying a formula outside its range, covered above. Three more trip people up regularly.
Confusing wind speed conventions. The wind chill formula here takes km/h. The US version takes mph and has different coefficients. Mixing them gives a number that is wrong by several degrees. A 20 mph wind is 32.2 km/h, not 20 km/h.
Reading the heat index as a hard limit. A heat index of 38 °C is a comfort and health guide for a typical adult in shade. Direct sun can add 8 °C or more to the felt value, and the formula assumes light wind. It is not a fixed physical constant.
Treating relative humidity as mugginess. As shown, 70 % means nothing on its own. Convert to dew point before deciding how a day will feel.
When you want one number to compare two days, use dew point. It does not depend on the current temperature, so 18 °C dew point is equally sticky whether the air is 24 °C or 34 °C.
Related tools
These calculators use the same first-principles approach to everyday physics. The Free Fall Calculator and the Projectile Motion Calculator handle motion under gravity. The Wavelength ↔ Frequency Converter covers waves. For structures and machines, see the Beam Deflection Calculator and the Gear Ratio Calculator.
Frequently asked questions
Why does the tool sometimes show no wind chill or no heat index?
Because those formulas are only valid inside defined ranges. Wind chill needs air at or below 10 °C and wind at or above 4.8 km/h. Heat index needs air at or above 27 °C. In between, the air temperature itself is the best answer and no correction is printed.
Can wind chill and heat index apply at the same time?
No. One needs cold air, the other needs hot air. Their valid ranges do not overlap, so at most one correction ever fires for a given reading.
Is dew point the same as relative humidity?
No. Relative humidity is the fraction of the maximum moisture the air can hold at its current temperature, so it changes as the air warms or cools even with the same water present. Dew point is the actual moisture content expressed as a temperature and does not move when the air temperature changes.
Why is the felt temperature so much higher than the air temperature on humid days?
Your body cools by evaporating sweat. High humidity slows that evaporation, so heat builds up. The heat index estimates the still-air, shaded temperature that would feel the same at low humidity. In the demo case, 30 °C at 70 % feels like about 38 °C.
Does the heat index account for direct sunlight?
No. The standard formula assumes shade and light wind. Full sun can add roughly 8 °C to the felt value, so treat the shaded index as a floor on a sunny day.
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