A new approach for the problem of quantum ring and quantum dot spectra is proposed. The exact separation of variables [1] for the problem allows us to study the variations of the spectra for a broad range of geometries while keeping an advantage of high computational efficiency. Our approach is illustrated by the calculations of a single particle spectrum of a quantum ring for varying geometry of the quantum ring. The spectrum can resemble or deviate from the one-dimentional ring spectrum according to the choice of the ring geometry