Wind speed and wind direction describe the atmospheric movement. It is recommended to calculate the average wind speed and direction as average of wind events (see: Guide to Climatological Practices WMO-No. 100, 2011, World Meteorological Organization, Geneva, ISBN 978-92-63-10100-6, Chapter 4, p. 9). A wind event is a vector with the length of the wind speed and the angle of the wind direction in a polar coordinate system. The average of several wind events is the average of the abscissa and ordinate values of the respective Cartesian coordinates.



Therefore we need a formula to convert polar coordinates into Cartesian coordinates and vice versa.

x = r · cos α
y = r · sin α
r = √(x² + y²)
y≠0   =>   α = arctan x/y
x=0 and y=0   =>   α = 0
x>0 and y=0   =>   α = π/2 or 90°
x<0 and y=0   =>   α = 3π/2 or 270°
a (measured in radian) = α · 180/π (measured in degree)
a (measured in degree) = α · π/180 (measured in radian)

If there are N wind events then the average wind speed and wind direction are the components of the wind vector of the average of the x values and the average of the y values.

x = 1/N · ∑_n=1..N x_n ,  y = 1/N � ∑_n=1..N yn

An example with MS Excel shows how it works. In the table on the left side there are the hourly events. The measurements are the values in the yellow cells. The values are converted into the x- and y-values, see columns D and E. The last two columns F and G are for monitoring purposes only. In the cells on the right the hourly values of the x- and y-values are calculated (see D27 and E27). The results reflect in cells B27 and C27. On the right side is a visualization of hourly values (blue) and daily average (green).



The average vector indicates the transport of air masses. It represents a measure of the actual covered path of air particles. An alternative is the arithmetical averaging of the speed measurements. This indicates the energy of the wind. For the wind direction an alternative average value is the median. It indicates the most frequent direction of the wind.