Radius of gyration of a uniform sphere ($R_g^2=3R^2/5$)

For a uniform solid sphere of radius $R$, the squared radius of gyration about its centre is the mass-weighted mean of $r^2$:Thus its volume is $(4\pi /3)(5/3{)}^{3/2}{R}_g^3$, about $9.01R_g^3$. A nonuniform object or a different shape need not obey this conversion. This distinction matters when estimating molecular number density from scattering measurements of a radius of gyration.