ABSTRACT We use the observed jet boundary transition from parabolic to conical shape, which was previously discovered to be a possible common property in active galactic nuclei, to estimate various parameters for black holes, jets and the ambient medium. We previously explained the geometry transition as a consequence of a change in the jet properties: a transition from a magnetically dominated to an equipartition regime. This interpretation allows us to estimate the black hole spin, the black hole mass and the ambient pressure amplitude, using the observed jet shape break position and the jet width at the transition point, for 11 active galactic nuclei. The black hole spin values obtained using our method are consistent with the lower estimates for sources with redshift z < 2 from spin evolution modelling. We find that the method of black hole mass determination based on the relationship between the broad-line region size and its luminosity may underestimate the masses of sources with large jet viewing angles. We propose a new method for the determination of the black hole mass, obtaining masses in the interval 108–1010 M⊙. The range of values of the ambient pressure amplitude points to the uniform medium conditions for the sources in our sample, with a tentative indication of higher pressure around Fanaroff–Riley II sources.