A new method is presented to describe deformations of an N-membered planar ring (N-ring) molecule in terms of deformation vectors that can be expressed by a set of 2N-3 deformation amplitudes and phase angles. The deformation coordinates are directly derived from the normal vibrational modes of the N-ring and referenced to a regular polygon (N-gon) of unit length. They extend the conceptual approach of the Cremer-Pople puckering coordinates (J. Am. Chem. Soc. 1975, 97, 1354) to the planar ring and make it possible to calculate, e.g., a planar ring of special deformation on a Jahn-Teller surface. It is demonstrated that the 2N-3 deformation parameters are perfectly suited to describe the pseudorotation of a bond through the ring as it is found in cyclic Jahn-Teller systems. In general, an N-membered planar ring can undergo N-2 different bond pseudorotations provided the energetics of such a process is feasible. The Jahn-Teller distortions observed in ring compounds correspond either directly to the basic pseudorotation modes or to linear combinations of them. Any deformed ring molecule can be characterized in terms of the new ring deformation coordinates, which help to identify specific electronic effects. The usefulness of the ring deformation coordinates is demonstrated by calculating the Jahn-Teller surfaces for bond pseudorotation in the case of the cyclopropyl radical cation and cyclobutadiene as well as the ring deformation surfaces of disulfur dinitride and its dianion employing multireference averaged quadratic coupled cluster (MR-AQCC) theory, equation-of-motion coupled cluster theory in form of EOMIP-CCSD, and single determinant coupled cluster theory in form of CCSD(T).