The nature of ultraluminous X-ray sources (ULXs) – off-nuclear extragalactic sources with luminosity, assumed isotropic, ≳1039 erg s−1 – is still debated. One possibility is that ULXs are stellar black holes (BHs) accreting beyond the Eddington limit. This view has been recently reinforced by the discovery of ultrafast outflows at ∼0.1–0.2c in the high-resolution spectra of a handful of ULXs, as predicted by models of supercritical accretion discs. Under the assumption that ULXs are powered by super-Eddington accretion on to BHs, we use the properties of the observed outflows to self-consistently constrain their masses and accretion rates. We find masses ≲100 M⊙ and typical accretion rates ∼10−5 M⊙ yr−1, i.e. ≈10 times larger than the Eddington limit calculated with a radiative efficiency of 0.1. However, the emitted luminosity is only ≈10 per cent beyond the Eddington luminosity, because most of the energy released in the inner part of the accretion disc is used to accelerate the wind, which implies radiative efficiency ∼0.01. Our results are consistent with a formation model where ULXs are BH remnants of massive stars evolved in low-metallicity environments.