  We present a c-function for spherically symmetric, static and asymptotically
flat solutions in theories of four-dimensional gravity coupled to gauge fields
and moduli. The c-function is valid for both extremal and non-extremal black
holes. It monotonically decreases from infinity and in the static region
acquires its minimum value at the horizon, where it equals the entropy of the
black hole. Higher dimensional cases, involving $p$-form gauge fields, and
other generalisations are also discussed.
