Electromagnetic contributions to the observed rest mass mo of the electron are calculated based on a wave picture of the macroscopically resting electron. The polarization of the vacuum is included in the calculation, assuming the permeability and permittivity of the vacuum, outside the electron, to depend on the distance to the electron. An analysis of the inner energy transport of the electron yields for the fine-structure constant α the relation α-1 = π4 surd2 (mm/mo), where mm is the mechanical part of mo. With the value calculated for mo/mm, an improved theoretical value for α is deduced. The new result α-1 = 137,0360266(8) is compared with the results of experimental determinations. It is found to be in agreement with Samuel's computation of the anomalous magnetic moment of the electron, but to disagree with that of Kinoshita.