The orientation dependence of electromechanical properties of relaxor based ferroelectric single crystals Pb(Zn1/3Nb2/3)O-3-(6-7)%PbTiO3 and Pb(Mg1/3Nb2/3)O-3-33%PbTiO3 has been calculated by coordinate transformation. Different from previous studies, the optimum cutting orientations have been predicted in terms of their piezoelectric responses in the corresponding crystal planes. The calculation results indicated that the anisotropic piezoelectric effects of [001] (c) and [011] (c) poled multi-domain crystals mainly come from the intrinsic contribution. However, the strong dielectric anisotropy of [001] (c) poled multi-domain crystals mainly comes from extrinsic domain and domain wall contributions. For [011] (c) poled multi-domain crystals, the intrinsic orientation effect enhances the dielectric anisotropy.