Diffusion is the molecular transport of one substance relative to another in a single phase. It can result from changes in temperature, pressure, concentrations or external force fields. The diffusivity or diffusivity coefficient is the proportionality constant between the diffusion flux and diffusion potential. The diffusivities for binary gases and liquids can be calculated in several ways according to their conditions. For this project, the diffusivities for gas systems according to the Chapman-Enskog equation were calculated as well as the diffusivities for binary gas mixtures at low pressures and low densities and binary liquid mixtures, as seen in the Matlab codes and sample calculations.