The results and an analysis of experimental studies of the distribution of the average relative magnetic induction in the cross section along the longitudinal axis of a hollow cylindrical ferromagnetic core of a round section magnetized by a homogeneous constant magnetic field are presented. A new formula is presented for calculations that take into consideration the thickness of the wall of the core and the dependence of the magnetic characteristics of its material on the size of the magnetizing field. A comparison has been made of the results of calculations and experiments for hollow cores of different geometries and the various magnetic characteristics of a material in a wide range of changes in the magnetizing field. The scope of the formula is shown.