It is widely accepted that metabolic rates scale across species approximately as the 3/4 power of mass in most if not all groups of organisms. Metabolic demand per unit mass thus decreases as body mass increases. Metabolic rates reflect both the ability of the organism's transport system to deliver metabolites to the tissues and the rate at which the tissues use them. We show that the ubiquitous 3/4 power law for interspecific metabolic scaling arises from simple, general geometric properties of transportation networks constrained to function in biological organisms. The 3/4 exponent and other observed scaling relationships follow when mass-specific metabolic demands match the changing delivery capacities of the network at different body sizes. Deviation from the 3/4 exponent suggests either inefficiency or compensating physiological mechanisms. Our conclusions are based on general arguments incorporating the minimum of biological detail and should therefore apply to the widest range of organisms.