Measurements of the fractional momentum loss (\(S_{\rm loss}\equiv{\delta}p_T/p_T\)) of high-transverse-momentum-identified hadrons in heavy ion collisions are presented. Using \(\pi^0\) in Au\(+\)Au and Cu\(+\)Cu collisions at \(\sqrt{s_{_{NN}}}=62.4\) and 200 GeV measured by the PHENIX experiment at the Relativistic Heavy Ion Collider and and charged hadrons in Pb\(+\)Pb collisions measured by the ALICE experiment at the Large Hadron Collider, we studied the scaling properties of \(S_{\rm loss}\) as a function of a number of variables: the number of participants, \(N_{\rm part}\), the number of quark participants, \(N_{\rm qp}\), the charged-particle density, \(dN_{\rm ch}/d\eta\), and the Bjorken energy density times the equilibration time, \(\varepsilon_{\rm Bj}\tau_{0}\). We find that the \(p_T\) where \(S_{\rm loss}\) has its maximum, varies both with centrality and collision energy. Above the maximum, \(S_{\rm loss}\) tends to follow a power-law function with all four scaling variables. The data at \(\sqrt{s_{_{NN}}}\)=200 GeV and 2.76 TeV, for sufficiently high particle densities, have a common scaling of \(S_{\rm loss}\) with \(dN_{\rm ch}/d\eta\) and \(\varepsilon_{\rm Bj}\tau_{0}\), lending insight on the physics of parton energy loss.