We combine DensePak integral field unit and TAURUS Fabry-Perot observations of 13 nuclear rings to show an interconnection between the kinematic properties of the rings and their resonant origin. The nuclear rings have regular and symmetric kinematics, and lack strong non-circular motions. This symmetry, coupled with a direct relationship between the position angles and ellipticities of the rings and those of their host galaxies, indicates that the rings are in the same plane as the disk and are circular. From the rotation curves derived, we have estimated the compactness (v 2/r) up to the turnover radius, which is where the nuclear rings reside. We find that there is evidence of a correlation between compactness and ring width and size. Radially wide rings are less compact, and thus have lower mass concentration. The compactness increases as the ring width decreases. We also find that the nuclear ring size is dependent on the bar strength, with weaker bars allowing rings of any size to form.