It has been thought that the basal metabolic rate of organisms increases as body mass is raised to some power, p. But the value of p has proved controversial, with both 2/3 and 3/4 being proposed. It is found here that the relationship between mass and metabolic rate does not follow a pure power law at all, and requires a quadratic term to account for curvature. Taking temperature and phylogeny into account, this explains why different data sets have produced different exponents when a power law has been fitted