Wall correction factors, which correct ion chamber response for photon attenuation and scatter, can differ by as much as 1.0% for spherical chambers depending on whether they are obtained experimentally by extrapolation measurements or by Monte Carlo simulation. This difference is not explained by experimental or calculational statistics which lie in the range 0.05%–0.2%. In this paper it is demonstrated that linear extrapolation of experimental data for spherical chambers is inappropriate, owing to the curvature of the chamber walls. A simple nonlinear theory is constructed that resolves the difference. The Monte Carlo calculations and the nonlinear theory are compared with extrapolation measurements for the NIST (formerly NBS) spherical chambers. It is concluded that wall correction factors should be obtained by Monte Carlo calculation for spherical chambers and that linear-extrapolation techniques should be regarded with suspicion for all chambers.