An alternative method to determine the critical cooling rate of materials has been developed by explaining the size and cooling rate dependences of physical properties of metallic nanoparticles through the scaling theory. This method has been applied to silver and copper nanoparticles which have been obtained by molecular dynamics simulations. The results reveal that our values for critical rate are close for each studied physical quantity. Thus, by taking the average among them, we obtain 6.2(8) × 1012 K/s for silver and 8.9(5) × 1012 K/s for copper. We have also found the threshold size of nanoparticle behavior is independent of the cooling rate.