Abstract <p>Formulas for calculating the strength of the reaction field inside and outside a uniformly magnetized magnet in the form of a cylinder of finite dimensions are obtained. A Fortran program has been written that implements the methodology proposed on the basis of these formulas. The possibilities of applying this method to solve the geometric inverse problem of magnetostatics for magnetics or for through and internal cavities of the corresponding shape are discussed. The obtained formulas have been tested for their compliance with physical laws, as well as with known formulas for both specific cases of the considered configuration and the limit cases of the studied geometric shape of the magnet.</p>