Muscle forces are difficult to measure in vivo, so the force-generating capacity of muscles is commonly inferred from muscle architecture. It is often assumed, implicitly or explicity, that a muscle’s maximum force-generating capacity is proportional to physiological cross-sectional area (PCSA), and that a muscle’s operating range is proportional to mean optimal fascicle length. Here, we examined the effect of muscle architecture (PCSA and fascicle length) on muscle function (maximal isometric force and operating range) using a three-dimensional finite element model which accounts in a mechanically consistent way for muscle deformation and other complexities of muscle contraction. By varying architectural properties independently, it was shown that muscle force-generating capacity does not scale by the same factor as PCSA, and that operating range does not scale by the same factor as optimal fascicle length. For instance, 3-fold independent variation of mean optimal fascicle length caused the maximum isometric force-generating capacity of the muscle to vary from 83% to 105% of the force predicted by PCSA alone. Non-uniformities in fascicle length that develop as the muscle deforms during contraction reduce muscle force and operating range. Thus, a three-dimensional finite element model that satisfies fundamental physical constraints predicts that the maximum force-generating capacity of skeletal muscle depends on factors other than PCSA, and that operating range depends on factors other than optimal fascicle length. These findings have implications for how the force-generating properties of animal muscles are scaled to human muscles, and for how the functional capacity of muscles is predicted from muscle architecture.