In this paper an analytically derived dispersion relation for the Buneman instability in spherically confined plasmas is presented. The calculations are based on plasmas with spherical symmetry in which the dependence of the dispersion relation is, thus, only radial. This article is supposed to give a solution for said dispersion relation as this has not been done for such a peculiar geometry. On the other hand, new research on electrostatic confinement fusion schemes shows that there are physical effects that are strongly connected with such instabilities in spherical plasma devices and have, hence, to be taken into account in order to get a proper scientific understanding of the underlying mechanisms.