Equivalent Wind Chill Temperatures

This is the new chart

To determine wind chill, find the outside air temperature on the top line, then read down the column to the measured wind speed (MPH - Miles Per Hour.) For example: When the outside air temperature is 0 degrees F, and the wind speed is 20 MPH the rate of heat loss is equivalent to -39 degrees F when there is no wind (zero up to 4 mph.)

The area shown in green corresponds to Little Danger. The area shown in yellow corresponds to Increasing Danger where flesh may freeze within 1 minute. The area show in red corresponds to great danger where flesh may freeze within 30 seconds.

Calculating Windchill Values

Two of the more common formulations for windchill were developed by Siple (1945) and Court (1948). Court modified Siple's formulation only slightly, using "certain observed values" that were apparently ignored by Siple. Both formulations have the same algebraic structure, but with different constants; both provide an equation for heat loss (H) from an exposed surface. Selection of a "baseline" condition of windspeed and temperature allows solving for a windchill temperature at different conditions.

H = ( A + B * sqrt(S) + C * S ) dT

where:
H == Heat Loss, kg cals/m²/hr
dT == temperature difference (°C), between assumed
skin temperature (33°C) and ambient temperature
S == windspeed, m/s

and the constants, A, B, and C are:

Siple Court
A 10.45 9.00
B 10.00 10.90
C -1.00 -1.00
In a practical sense, with the following definitions, use the following formulas for calculating windchill (Siple's and Court's formulas, rearranging terms and substituting for unit conversions):

Twc == windchill temperature
T == ambient temperature
S == windspeed

For °C and m/s (baseline conditions of 33°C and 1.8 m/s):

Siple: Twc = 33 + ( T - 33 ) ( .474 + .454 sqrt(S) - .0454 S )

Court: Twc = 33 + ( T - 33 ) ( .550 + .417 sqrt(S) - .0454 S )

for S >= 1.79 m/s
T < 33 °C
For °F and mph (baseline conditions of 91.4°F and 4 mph):

Siple: Twc = 91.4 + ( T - 91.4 ) ( .474 + .304 sqrt(S) - .0203 S )

Court: Twc = 91.4 + ( T - 91.4 ) ( .550 + .279 sqrt(S) - .0203 S )

for S >= 4 mph
T < 91.4 °F

Test (Siple): S=20mph, T=20 °F ---> Twc = -10.5 °F
And finally, for folks who prefer °F and knots (baseline conditions of 91.4°F and 3.47 knots):

Siple: Twc = 91.4 + ( T - 91.4 ) ( .474 + .326 sqrt(S) - .0234 S )

Court: Twc = 91.4 + ( T - 91.4 ) ( .550 + .299 sqrt(S) - .0234 S )

for S >= ~3.5 knots (note: 1 mph = .869 knots)
T < 91.4 °F

Some notes:
There is nothing "exact" about windchill: it is an approximation or estimate. Other indices of "physiological" or "perceptual" temperature exist.
There's some uncertainty concerning the "baseline" values to be used. However, the stated values are likely close enough, and since windchill is only a crude estimate, ...

References:
Bair, Frank E., ed., 1992: The Weather Almanac, 6th edition. Gale Research, Inc., pp 140-143.
Court, A., 1948: Windchill. Bull. Amer. Meteor. Soc., 29, 487-493.

Siple, P.A., and C.F. Passel, 1945: Measurements of dry atmospheric cooling in subfreezing temperatures. Proc. Amer. Phil. Soc., 89, 177-199.

Steadman, R.G., 1971: Indices of windchill of clothed persons. J. Appl. Meteor., 10, 674-683.

Document Creation: Bob Rilling, / NCAR Atmospheric Technology Division
Created: 12-Feb-1996
Last Modified: 12-Feb-1996

What is Windchill?

Windchill is strictly a comparison. The "baseline" for the comparison is conceptually an unclothed individual moving through calm air at about 4 mph (a pretty brisk walking pace!). The comparison works like this:

The wind is blowing at 20 mph and the temperature is 20 deg F. If I were out naked, how would this make me feel? The answer (from the formula!) is that you'd feel like you were naked, and walking briskly through calm air at approximately -11 deg F. You might also feel pretty silly for having forgotten your coat and pants! The goal of the windchill temperature is to relate (perhaps extreme) conditions to something we have all likely experienced, namely: briskly walking naked through calm air at certain carefully calibrated temperatures! [If naked, would you walk anything but briskly?].
More seriously: the windchill described here was developed around the time of World War II, partly to provide an easily calculated index for battlefield planning. It was formulated to determine risk factors when operating outdoors under various conditions, and gives a very rough idea (in easily assimilated terms) of potential problems caused by the combination of wind with cold.
Note that windchill described here is not dependent on relative humidity, both by definition and the observed fact that humidity has very little effect on cooling, particularly at low temperatures. Further, it is implied that if there is no motion, there is no cooling (thus the comparison to a reference windspeed of 4 mph); additionally, the original work was done on a can (or plastic container) of water, with the assumption that there was general extensibility to exposed skin.

There is nothing "exact" about windchill: it is an approximation or estimate. Other indices of "physiological" or "perceptual" temperature exist.

For reference see:
Bair, Frank E., ed., 1992: The Weather Almanac, 6th edition. Gale Research, Inc., pp 140-143.
Court, A., 1948: Windchill. Bull. Amer. Meteor. Soc., 29, 487-493.

Siple, P.A., and C.F. Passel, 1945: Measurements of dry atmospheric cooling in subfreezing temperatures. Proc. Amer. Phil. Soc., 89, 177-199.

Steadman, R.G., 1971: Indices of windchill of clothed persons. J. Appl. Meteor., 10, 674-683.