The time that animals spend travelling at various speeds and the tortuosity of their movement paths are two of the many things that affect space-use by animals. In this, high turn rates are predicted to be energetically costly, especially at high travel speeds, which implies that animals should modulate their speed according to path characteristics. When animals move so as to maximize distance and minimize metabolic energy expenditure, they travel most efficiently at the speed that gives them a minimum cost of transport (COT min), a well-defined point for animals that move entirely in fluid media. Theoretical considerations show though, that land animals should travel at their maximum speed to minimize COT, which they do not, instead travelling at walking pace. So, to what extent does COT min depend on speed and turn rate and how might this relate to movement paths? We measured oxygen consumption in humans walking along paths with varied tortuosity at defined speeds to demonstrate that the energetic costs of negotiating these paths increase disproportionately with both speed and angular velocity. This resulted in the COT min occurring at very low speeds, and these COT min speeds reduced with increased path tortuosity and angular velocity. Logged movement data from six free-ranging terrestrial species underpinned this because all individuals turned with greater angular velocity the slower their travel speeds across their full speed range. It seems, therefore, that land animals may strive to achieve minimum movement costs by reducing speed with increasing path variability, providing one of many possible explanations as to why speed is much lower than currently predicted based on lab measurements of mammalian locomotor performance.