In our previous paper [Feng et al., Acta Mater.55, 2929 (2007)], an analytical model is proposed to estimate the stress field around an elastoplastic indentation/contact, matching nicely with the finite element analysis. The model is related to an embedded center of dilatation (ECD) in a half-space. In this paper, we focus on determining the ECD strength B* and the ECD depth ξ. By matching an expanding cavity model and the ECD model, we find that B* ≈ Yc3/6 and ξ ≈ 0.4c, where Y is the yield strength and c is the plastic zone radius. We provide a method to predict Y, c, and thereby B* as well as ξ through nanoindentation data, and we also demonstrate that pileup is the physical reason for the existence of the upper limit for the ratio of hardness to Y. Thus, our ECD model is completed by combining our previous paper (the analytical expression) and this paper (the essential parameters).