The dominance ratio, or more precisely the closeness to unity of the dominance ratio, is an important characteristic of large reactors. It allows the prior determination of the minimum number of source iterations required in deterministic calculations of the power spatial distribution. In this work a relatively simple approach to evaluating the dominance ratio is proposed. It essentially makes use of the symmetry of the core. The dependence of the dominance ratio on the neutron flux spatial distribution is demonstrated. Numerical results are presented for three symmetric model problems with few-group isotropic cross sections and for full-scale VVER-1000 reactor models. Also, a strategy for evaluating the dominance ratio for some nonsymmetrical assemblies is proposed and tested on a well-known fuel storage facility.