The origin of variation in animal growth rate and body size is not well understood but central to ecological and evolutionary processes. We develop a relationship that predicts the change in relative body size variation within a cohort will be approximately equal to the relative change in mean per unit size growth rate, when only size-dependent factors affect growth. When modeling cohort growth, relative size variation decreased, remained unchanged, or increased, as a function of growth rate-size scaling relationships, in a predictable manner. We use the approximation to predict how environmental factors (e.g., resource level) affect body size variation, and verified these predictions numerically for a flexible growth model using a wide range of parameter values. We also explore and discuss the assumptions underlying the approximation. We find that factors that similarly affect mean growth rate may differently affect size variation, and competition may increase body size variation without changing size-independent relationships. We discuss implications of our results to the choice of growth equations used in models where body size variation is an important variable or output.