The equivalence relation for the calculation of resonance capture employs a modified rod radius to account for inaccuracies in the Wigner rational approximation of the probability of escape from the rod. In this paper we extend older work to derive a correction to the mean chord length which depends on the peak resonance cross section, the potential scattering, and the rod radius. Such a formula represents a useful compromise between use of the less accurate but computationally convenient equivalence relation and accurate but computationally complex methods. By fitting the radius modifier over a wide range of values, the following representation is found: