The characteristic angle-beta concept provides a simple semiempirical method for determination of dose distributions in electron arc therapy. Initially, the method required a set of measured radial depth dose distributions for each electron beam energy used for arc therapy. In this paper, we report an extension of the angle-beta concept that enables the determination of arc therapy depth doses for an arbitrary electron energy from the known set of depth dose data at a reference energy. Depth dose distributions of stationary and arc electron beams have been studied in the energy range from 9 to 18 MeV. The stationary electron beams used for electron arc therapy were collimated by photon collimators only, no secondary collimation was used in our experiments. For stationary electron beams and for arc electron beams with a given characteristic angle beta, the depths of dose maximum as well as the depths of a given percentage depth dose beyond the depth of dose maximum are linearly proportional to the mean incident electron energy. This simple geometrical and dosimetric relationship increases the potential usefulness of the angle-beta concept in clinical electron arc therapy.