  Extra-dimensional theories contain a number of almost degenerate states at
each Kaluza-Klein level. If extra dimensional momentum is at least
approximately conserved then the phenomenology of such nearly degenerate states
depends crucially on the mass splittings between KK modes. We calculate the
complete one-loop radiative corrections to KK masses in general 5 and 6
dimensional theories. We apply our formulae to the example of universal extra
dimensions and show that the radiative corrections are essential to any
meaningful study of the phenomenology. Our calculations demonstrate that
Feynman diagrams with loops wrapping the extra dimensions are well-defined and
cut-off independent even though higher dimensional theories are not
renormalizable.
