The 'Bayesian inference of electron microscopy' (BioEM) framework makes it possible to determine the stoichiometry of protein complexes using 3D coarse-grained models and a relatively small number of cryo-electron microscopy images as input. We applied the method to determine the most probable rotor ring stoichiometry of the archaeal Na+ ATP synthase from Pyrococcus furiosus, a multisubunit complex able to produce ATP under extreme conditions. Archaeal ATP synthases consist of a catalytic A1 part and a membrane-embedded AO portion. The AO portion is composed of a rotor ring and the a-subunit. The rotor ring of P. furiosus ATP synthase is composed of 16-kDa c-subunits, each consisting of four helices forming a bundle, with only one Na+-binding site per bundle. This ring was proposed to be decameric from LILBID-MS analysis of the entire ATP synthase. By contrast, the BioEM posterior favors a c9 ring stoichiometry. With BioEM, we ranked coarse-grained models of the whole complex with different ring geometry, using 6400 unprocessed particle images of the A1AO complex collected in vitreous ice. BioEM makes it possible to probabilistically establish the domain stoichiometry using low-resolution information and comparably few particle images.