We present ab-initio calculations of the electronic structure of small Fe clusters (1-9 atoms) on Ni(001), Ni(111), Cu(001) and Cu(111) surfaces. Emphasis is given on the spin moments, and their dependence on cluster size and shape. We derive a simple quantitative rule, which relates the moment of each Fe atom linearly to its coordination number. Thus, for an arbitrary Fe cluster the spin moment of the cluster and of the individual Fe atoms can be readily found if the positions of the atoms are known.