The far-field body wave radiation from a class of circular rupture models is investigated as a function of takeoff angle, rupture velocity, and stopping behavior. In particular, the variation of spectral shape, pulse shape, and energy flux over the focal sphere is quantified. These results provide two new methods for estimating the source dimension, the first through the inversion of a characteristic frequency, and the second using the rise time of the displacement pulse shape. The class of kinematic rupture models which has been constructed also allows a direct estimate of the dynamic stress drop using the velocity pulse shape: as an example, this technique is applied to an SMA1 recording of a high stress drop Aleutian earthquake, Finally, the introduction of a new spectral parameter, the integral of the square of the ground velocity, is shown to considerably simplify calculation of the total radiated energy. Together with a re-evaluation of corner frequency and spectral falloff, these new results constitute a spectral theory for circular seismic sources which includes directivity and is valid for a range of subsonic rupture velocities.