Here we address a theoretical study of concentric GaAs–(Ga, Al)As double quantum rings, under a magnetic field applied perpendicularly to the ring plane. Electron–hole transition energies are calculated as a function of the system geometry confinement, following a single-particle picture, neglecting interaction effects. We adopted an effective-mass approximation, within a hard potential model calculation, exactly solved by using confluent hypergeometric functions. A huge dependence on the barrier width value and on the external ring width of the Ga1−xAlxAs coupled rings is found for the transition energy values. The results show a high competition between geometric and magnetic-field confinement, leading to an increase of the electron–hole energies with the magnetic field, and a reducing behavior as the outer ring width is assumed to be larger. Our results are in quite good agreement with the experimental data by Mano et al (2005 Nano Lett. 5 425).