A theoretical calculation is made of &sgr;(h), the standard deviation of vertical wind shears, in terms of the turbulence energy dissipation rate &egr; and Brunt-V¿is¿l¿ frequency &ohgr;B. This calculation provides a theoretical basis for the empirical power law relation &sgr;(h)=A hm obtained by rocket and balloon wind soundings; it also provides a scaling of &sgr;(h) with atmospheric conditions. The intervals h ranging from about 50m to 1000m are determined by buoyancy subrange turbulence, and smaller shear intervals are determined by inertial subrange turbulence. The theoretical &sgr;(h) allows &egr; to be predicted from vertical wind soundings in the troposphere and stratosphere. The predicted value of &egr; in the troposphere agrees with the value obtained by Kung. However, the predicted stratospheric value of &egr; is larger than obtained by Lilly et al. from HICAT flights. This discrepancy in stratospheric &egr; is attributed to non-turbulent, low frequency, short scale, quasi-horizontal motions of the stratosphere; motions that contribute to vertical wind soundings but not to gust measurements by horizontal HICAT flights.