Inverse square correction factors for wide-angle free-air chambers (WAFACs) and free-air chambers (FACs) for cylindrical, conical and square-prism detectors are required for determining the on-axis air kerma from measurements or Monte Carlo calculations made with these different shaped detectors. Values of air kerma measured with these detectors use an effective volume technique related to the inverse square correction factors. This paper presents these factors in a consistent framework and the relationships between them are made clear. Using Monte Carlo simulations, the various corrections and techniques are shown to be accurate within a statistical precision of about 0.04% or better with the exception of the published correction for square prism detectors which is shown to hold only for thin detectors which have an opening angle corresponding to the NIST and NRCC WAFAC primary standards. A more accurate correction for square prism detectors is presented which properly averages 1/d rather than d where d is the distance away from the source.