The structures of EF-hand calcium binding proteins may be classified into two distinct groups: extended and compact structures. In this paper we studied 20 different structures of calcium binding proteins using the fractal analysis. Nine structures show extended shapes, one is semi-compact and the other 10 have compact shapes. Our study reveals different fractal characteristics for protein backbones belonging to different structural classes and these observations may be correlated to the physicochemical forces governing the protein folding.