It has been reported in many experimental and simulation studies that small solutes – dissolved in supercooled water (or supercooled liquid in general) – violates the Stokes-Einstein equation (SE), a hydrodynamic relation connecting the self-diffusion coefficient of the solute, the viscosity of the solvent, the radius of the solute, and the temperature of the system. However, with the increase in the solute’s size, the validity of the SE equation is gradually attained. It is generally believed that the presence of translational jump occurrence of the small solute in supercooled water is responsible for the SE breakdown. However, a quantitative estimation of the jump contribution for the self-diffusion of a solute is still lacking. Here, we have performed molecular dynamics (MD) simulations for four different nonpolar solutes (with increasing solute size), separately dissolved in water. By adopting a recent technique for direct identification of translational jump occurrence of the solute molecule, we have successfully calculated the jump-diffusion coefficient of the solute and its contribution to the total selfdiffusion of the solute molecule in liquid water both at room temperature and supercooled regime. As the solute size decreases, the contribution of jump-diffusion increases at the supercooled regime. We have also separated the jump-diffusion from the total diffusion of the solute to obtain the residual diffusion, which better follows the SE equation. This is direct evidence for the increased importance of translational jump-diffusion for the observed breakdown of the SE relation for small solutes at the supercooled regime. These new findings can assist in comprehending many experimental results where the breakdown of the SE equation is observed.