Ionization of atoms is the first step in many analytical procedures. The cross section for ionizing a particular atomic shell is essential for calculating the magnitude of analytical signals. Calculations using atomic wave functions for various shells of all elements relevant for X-ray microanalysis over a range of electron energies up to 400 keV were performed. The calculations for high energies above threshold can be considerably simplified by using the mathematical form of the Bethe ridge that dominates the scattering in this region. Corrections for exchange at low energies above threshold are incorporated in these calculations. A selection of results showing the effects of different approximations on ionization cross sections for K, L, and M shells is presented.