In many atmospheric diffusion problems, a description of the steadiness of the wind direction is desired. For intervals of approximately an hour the mean wind direction is usually well defined and constant, but for longer intervals this may not be so, and a description of the variability of the mean direction with time is needed. It is proposed that the constancy of the wind, defined as the mean vector wind divided by the mean scalar wind V̄/V̄, can be used for simple classification purposes. A value of unity designates that the wind direction has not changed over the averaging period and a value of zero suggests a completely symmetrical distribution. In this paper, a trigonometric transformation is used to linearize the variation of constancy with the mean angular range of direction. This function, called the “steadiness” S, is then computed for various time intervals, and by use of extreme-value theory the recurrence interval of various mean wind direction ranges can be predicted. This provides an important probability statement for air pollution evaluations. Five years of data at Brookhaven National Laboratory have been analyzed for the following hourly intervals; 2, 4, 12, 24, 48, 96, 192, 384 and 720. The recurrence intervals of S with their associated meteorological conditions are presented for these periods and compared with similar studies of data from other stations.