The purpose of the study was to mathematically model the regression of percent of maximal oxygen consumption (% VO2 max) on relative (% of max) heart rate (HR). The 26 subjects (Ss) were classified based on activity levels into high, medium, and low-fitness. Each S performed a series of treadmill walks and runs ranging from 30 to 100% of max VO2. Percent of VO2 max and relative HR were determined during each exercise bout. The data were subjected to a trend analysis utilizing multiple regression techniques. The associated Rs were: linear 0.966, quadratic 0.971, cubic 0.971, and quartic 0.977. The second and fourth order terms statistically accounted for more of the variability than their predecessors, but these differences were not of practical significance. There were no statistically significant differences among the fitness subgroup regression slopes or intercepts for any of the sets of regression equations. The bivariate equation was Y = 1.369-X-40.99 (Y = % VO2 max and X=relative HR) with a standard error of the estimate of 5.67 % VO2 max.