A model is presented which relates the experimentally determined critical current density to the irreversible magnetization of a "hard" superconductor. The internal field distribution in long cylinders and tubes in longitudinal applied fields is calculated from the critical current density data. The distribution of the induction B is related to the field distribution by the use of the ideal (reversible) type II magnetization curve. To illustrate the use of the model, critical current density and magnetization measurements have been performed on a niobium specimen in both highly annealed and strained states. Magnetization measurements were also made on niobium tubes of various wall thicknesses. The shape of the magnetization curves are correctly predicted. Details of the magnetization curve near Hc2 for the strained specimen, which were not predicted by previous models, have been partially verified.