We systematically examine corrections to the gravitational inverse square
law, which are due to compactified extra dimensions. We find the induced
Yukawa-type potentials for which we calculate the strength \alpha and range. In
general the range of the Yukawa correction is given by the wavelength of the
lightest Kaluza-Klein state and its strength, relative to the standard
gravitational potential, by the corresponding degeneracy. In particular, when n
extra dimensions are compactified on an n-torus, we find that the strength of
the potential is \alpha=2n, whereas the compactification on an n-sphere gives
\alpha= n+1. For Calabi-Yau compactifications the strength can be at most
\alpha=20.Comment: 8 pages, latex, 1 figure; v2: References added and some
clarifications in sec. 3 are made; v3: Physics Letters B versio
