Summary: \textit{A. P. Calderón} [Semin. Numer. Anal. Appl. Continuum Physics, 65- 73 (1980; MR 81k:35160)] determined a method to approximate the conductivity \(\sigma\) of a conducting body in \(R^ n\) (for \(n\geq 2)\) based on measurements of boundary data. The approximation is good in the \(L_{\infty}\) norm provided that the conductivity is a small perturbation from a constant. We calculate the approximation exactly for the case of homogeneous concentric conducting disks in \(R^ 2\) with different conductivities. Here, the difference in the conductivities is the perturbation. We show that the approximation yields precise information about the spatial variation of \(\sigma\), even when the perturbation is large. This ability to distinguish spatial regions with different conductivities is important for clinical monitoring applications.