Small animals are remarkably efficient climbers but comparatively poor runners, a well-established phenomenon in locomotor energetics that drives size-related differences in locomotor ecology yet remains poorly understood. Here, I derive the energy cost of legged locomotion from two complementary components of muscle metabolism, Activation-Relaxation and Cross-bridge cycling. A mathematical model incorporating these costs explains observed patterns of locomotor cost both within and between species, across a broad range of animals (insects to ungulates), for a wide range of substrate slopes including level running and vertical climbing. This ARC model unifies work- and force-based models for locomotor cost and integrates whole-organism locomotor cost with cellular muscle physiology, creating a predictive framework for investigating evolutionary and ecological pressures shaping limb design and ranging behaviour.