The most important material for shielding is concrete in nuclear facilities which performance can be improved by addition some Nanoparticles (NP) at the various concentrations. Nanoparticles, which have a distinctive potential for bio-radiation and shielding of nuclear reactors, are used in many areas due to their special characteristics, which lead to an improvement in the mechanical properties and the pore structure of the concrete shield. The aim of this research was to initiate a novel coefficient (n), experiment to theory density ratio for integrated NP at different nanoparticle concentrations (xnano), established upon purely mathematical viewpoints and some appropriate physical objectives.