The radius and the origin of a mean earth ellipsoid have been determined using geoid heights derived from SEASAT-1 radar altimetric observations of the ocean surface and potential coefficients. While assuming that the altimetric geoid is the best available, adjustments are made to the geoid derived from potential coefficients so that the geoid differences are minimized. This adjustment is then applied to the ellipsoid which best fits the geoid derived from potential coefficients. Solutions using two different sets of altimetric geoid heights and geoid heights based on the DOD WGS 72 and GEM10B potential coefficients gave a mean ellipsoid with radius a=6378134.9 m and origin shifts less than 1 m in the x and y components and approximately -2.5 m in the z component. A description of the geoid height data used in the solutions for the ellipsoid parameters, results of the solutions, and a summary are presented.