A method has been developed to find the absolute spectral level of high frequency far field sound of a rotor in terms of random load fluctuations on the rotor blades. The analysis deals with frequencies where the radiated sound spectrum is smooth, i.e., above 300 to 400 Hz for a typical helicopter. This is in constrast to the low frequency regions where the spectrum is continuous but peaked near bladed passing harmonics. We first show that the smooth, broadband part of the spectrum corresponds to load fluctuations which are uncorrelated between blade passages. Then the spectral intensities from the individual blades are additive. A point load approximation with spanwise loading corrections is used and the blade loading spectrum is specifically derived for upwash fluctuations due to inflow turbulence. Analytic approximations are made to simplify the evaluation of certain integrals and series. The method is compared to the more general method of Homicz and George, where practical, and to published experimental data. The agreement between the two theories is excellent. The comparison to the experiments is good although it is not clear how to estimate the increase in intensity of atmospheric turbulence as it is distorted while being drawn into the rotor. The results indicate that atmospheric turbulence is perhaps the major contribution to broadband noise in hover. The approach is also applicable to other load fluctuation mechanisms.