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A model is presented which gives cross sections (differential in the ejected secondary electron energy) for the ionization of atoms and molecules in proton or electron collisions. The model is in the form of an analytical equation which holds for all primary and secondary energies and for any target gas for which certain parameters are known. The accuracy is estimated to be 15-20%. The model is based on the classical binary encounter model modified to agree with the Bethe theory at high energies and, for proton impact, with the molecular promotion model at low energies. For multi-shell targets, the partial cross sections for the shells, are added. The model equation may be integrated to yield such quantities as the total ionization cross section, the stopping cross section due to ionization, and the average secondary electron energy. For proton impact the integrations must be done numerically or by using approximations. For electron impact the equation is simpler and may easily be analytically integrated.