Researchers have attempted to evaluate the likelihood of hip fracture as a function of an engineering concept called the moment of inertia, as applied to the cross-sectional area of hip bones. While the premise is sound, the results have been disappointing. Although several authors have acknowledged that errors may arise in the current methods investigators employ to determine the cross section moment of inertia (CSMI), none have looked critically at the sources, or even the magnitude, of those errors. This paper evaluates the nature of the error that can be introduced by the use of one-dimensional bone mineral density scans to estimate the CSMI and quantifies its impact on predictive calculations. In addition, this paper presents an improved method for approximating the mechanical section properties of highly complex cross sections. The factors affecting the accuracy of the proposed method are tested, and its error rate is also quantified. The method employs a two-dimensional analysis of digital images of the subject cross section and does not require extensive user expertise or investment in expensive finite element analysis programs to implement. The limited file space necessary to install the required code means that standard smart phones could be used to directly evaluate the most complex cross section in the field.