A method for calculating impact ionization coefficients by solving the Boltzmann transport equation is presented. The distribution function is taken to be expressible as a Legendre polynomial expansion, which is substituted into a Boltzmann equation that incorporates the effects of nonparabolic band structure, deformation‐potential phonon scattering, and impact ionization. The resulting Boltzmann equation can be expressed in a linear form, and solved using sparse‐matrix difference‐differential methods. Ionization coefficients are obtained directly from the distribution function. Calculated values for the ionization coefficients agree very well with experiment for electrons in silicon.