The purpose of this paper was to show how dimensional analysis and biological similarity theory can be used to define and derive extensive (size-dependent) and intensive (size-independent) variables. The method was then used to analyze the peak rate of oxygen consumption (V.O2peak) data of children, adolescents, and adults to determine if size-independent increases in V.O2peak occur during growth and development. The results indicated growth and development is accompanied by a substantial increase in size-independent V.O2peak, which was associated with improvements in size-independent peak heart rate ( HR(peak)). When differences in fat free mass (FFM) were considered, size-independent HR(peak) was similar in boys and girls within each age-group, but was greater in men than in women. In contrast, when differences in FFM were accounted for, size-independent peak oxygen pulse (O2P(peak)) was independent of age, although males tended to have greater values than females at all ages. Because O2P(peak) is proportional to the product of stroke volume ( SV) and arterial mixed-venous oxygen difference (a-vO2peak), when differences in FFM were considered, the size-independent nature of O2P(peak) indicated the combined effects changes in SV(peak) and (a-vO(2)peak) played a secondary role in improving aerobic capacity. In conclusion, during normal growth and development improvement in HR(peak), not stroke volume and arterial mixed-venous oxygen difference, appears to increase aerobic capacity.