Many studies have examined the structure and properties of the Force Concept Inventory (FCI); however, far less research has investigated the Force and Motion Conceptual Evaluation (FMCE). This study applied Multidimensional Item Response Theory (MIRT) to a sample of N = 4528 FMCE post-test responses. Exploratory factor analysis showed that 5, 9, and 10-factor models optimized some fit statistics. The FMCE uses extensive blocking of items into groups with a common stem; these blocks factored together in most models. A confirmatory analysis, which constrained the MIRT models to a theoretical model constructed from expert solutions, produced a model requiring only 8 principles, fundamental reasoning steps. This was substantially fewer than the 19 principles identified in the FCI by a previous study. Correlation analysis also demonstrated that the two instruments were very dissimilar. The reduced number of principles and the repetition of items using a single principle allowed the extraction of eight single-principle subscales, seven with Cronbach's alpha greater than the 0.7 required for acceptable internal consistency. The differences between the FCI and the FMCE suggest that the two instruments could provide complementary, but different, information about student understanding of Newton's laws with the FCI measuring an integrated Newtonian force concept and the FMCE measuring details of that force concept.