Abstract The optimum design of magnet structures requires that every part of the magnets work at a point on the demagnetization curve which is as near to (BH)max as possible. CTA is a program for the computation of magnetic fields in axisymmetric systems. It has some defects in its search for magnet working points, and furthermore, for a complex structure it cannot provide a sole result to judge how much magnetic energy is contributed by the magnets. In this paper the authors introduce average magnetic energy product to serve as a criterion for the judgment of the work state of magnets. For every magnet structure the improved CTA can present a unique average magnetic energy product and a map of the energy product distribution.