A simple derivation is given of the Fermi formula for the contact hyperfine interaction energy between the magnetic moment of a nucleus and that of the surrounding electrons. Considerably fewer mathematical and more physical arguments are used than in previous derivations. It is shown that the contact hyperfine field at the nucleus is necessarily equal to the magnetic induction in the interior of a sphere possessing a uniform electronic magnetization. The simplifications achieved in the present derivation do not seem to result in a loss of rigor, and they do not require the introduction of essentially new assumptions.