Wind chill, heat index and dew point calculator

How to calculate wind chill and heat index

At 50 °F (10 °C) or colder, with wind of at least 3 mph (4.8 km/h), the feels-like temperature is the US National Weather Service (NWS) wind chill. From 80 °F (26.7 °C) up it is the NWS heat index; in between, it is the air temperature. Air at 0 °F in a 15 mph wind feels like −19.4 °F (−28.6 °C).

Dew point sits alongside both: the temperature at which the air would become saturated, a direct measure of how much moisture it holds.

Wind chill formula (NWS, 2001)

The NWS and Environment and Climate Change Canada adopted the current index in 2001. In °F and mph:

WC = 35.74 + 0.6215T − 35.75V^0.16 + 0.4275TV^0.16

T is the air temperature and V the wind speed. For 30 °F in a 20 mph wind:

1. V^0.16 = 20^0.16 = 1.61497.
2. 35.74 + 0.6215 × 30 = 54.385.
3. 35.75 × 1.61497 = 57.7352, which is subtracted.
4. 0.4275 × 30 × 1.61497 = 20.7120, which is added.
5. 54.385 − 57.7352 + 20.7120 = 17.4 °F, or −8.1 °C.

Canada publishes the same index in metric units, with T in °C and V in km/h:

WC = 13.12 + 0.6215T − 11.37V^0.16 + 0.3965TV^0.16

Across the NWS chart, −45 to 40 °F and 5 to 60 mph, the two versions agree within 0.1 °C. For 5 °C in a 20 km/h wind, both give 1.1 °C.

Wind chill measures how fast exposed skin loses heat. Wind speeds up cooling but cannot take an object below the air temperature: in 5 °C air the wind chill may read 1.1 °C, yet a water pipe cools only toward 5 °C.

Heat index formula (NWS)

The NWS Weather Prediction Center works in two stages, with T in °F and RH in percent. First it applies Steadman's simple formula, HI = 0.5 × [T + 61 + 1.2(T − 68) + 0.094RH].

If the average of that result and T is 80 °F or more, it switches to the Rothfusz regression:

HI = −42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²

Two corrections follow. Below 13% humidity at 80–112 °F, subtract [(13 − RH) ÷ 4] × √[(17 − |T − 95|) ÷ 17]. Above 85% humidity at 80–87 °F, add [(RH − 85) ÷ 10] × [(87 − T) ÷ 5].

At 90 °F and 60% humidity the simple formula gives 91.52 °F. The average with 90 °F is 90.76, so the regression applies and gives 99.7 °F (37.6 °C); the NWS chart rounds it to 100 °F.

Heat index describes shade with a light wind. Values beyond the NWS chart, 80–110 °F, are extrapolations, and the fit is weakest below about 40% humidity.

Dew point formula (Magnus)

With T in °C, the Magnus formula with the Alduchov–Eskridge constants 17.625 and 243.04 °C gives:

γ = ln(RH ÷ 100) + 17.625T ÷ (243.04 + T), then Td = 243.04γ ÷ (17.625 − γ)

At 25 °C and 60%: γ = −0.51083 + 1.64388 = 1.13305, and Td = 243.04 × 1.13305 ÷ 16.49195 = 16.7 °C (62.1 °F). At 100% humidity the dew point equals the air temperature.

Dew point tracks moisture better than relative humidity, which moves whenever the temperature does. Air with a 16.7 °C dew point reads 81% humidity at 20 °C, 60% at 25 °C and 45% at 30 °C.

The NWS La Crosse office calls a dew point of 55 °F (12.8 °C) or lower dry and comfortable, 55–65 °F sticky, and 65 °F (18.3 °C) or higher oppressive.

Below 0 °C the formula gives the dew point over liquid water; the frost point over ice is slightly higher.

Wind chill and heat index examples

The two 50 °F rows show the wind cutoff. At 3 mph the formula applies and gives 49.7 °F; at 2.99 mph it no longer applies, so the air temperature stands.

The last row's 12.4274 mph is 20 km/h. Wind has no term in the heat index, and humidity has none in the wind chill.

Frostbite times and heat danger levels

Environment and Climate Change Canada gives these risks for exposed skin by wind chill:

• Above −10 °C: low risk of frostbite.
• −10 °C to −27 °C: moderate risk; hypothermia with long exposure.
• From −28 °C: skin can freeze in 10 to 30 minutes.
• From −40 °C: 5 to 10 minutes.
• From −48 °C: 2 to 5 minutes.
• From −55 °C: under 2 minutes.

Air at −10 °C in a 40 km/h wind has a wind chill of −20.7 °C, in the moderate band.

The NWS heat index levels start at 80 °F (26.7 °C) for caution, 90 °F (32.2 °C) for extreme caution, 103 °F (39.4 °C) for danger and 125 °F (51.7 °C) for extreme danger.

Air at 35 °C and 50% humidity has a heat index of 40.7 °C (105.2 °F), in the danger band.

Common mistakes

• Mixing wind units. 20 mph is 32.2 km/h. Entering a forecast's 20 km/h as 20 mph turns the wind chill of 5 °C air from 1.1 °C into −0.1 °C.
• Using a wind reading taken at face height. The formula expects the 10 m (33 ft) wind from a weather report.
• Reading heat index as the temperature in the sun. It is a shade value; the NWS notes that full sunshine can add up to 15 °F (8.3 °C).
• Comparing with Canadian forecasts. Canada reports wind chill only at 0 °C or colder with wind of 5 km/h or more, and in summer it publishes the humidex, a separate formula whose numbers differ from the heat index for the same weather.
• Judging mugginess by relative humidity. Air at 10 °C and 90% has a dew point of 8.4 °C, dry and comfortable; air at 30 °C and 50% has a dew point of 18.4 °C, oppressive.

Related calculators

For pressure, air density and the boiling point of water at height, use the air pressure at altitude calculator. To convert a single reading between scales, use the temperature converter.