The aim of this study was first to determine if level, uphill, and downhill energy cost of running (ECR) values were correlated at different slopes and for different running speeds, and second, to determine the influence of lower limb strength on ECR. Twenty-nine healthy subjects completed a randomized series of 4-min running bouts on an instrumented treadmill to determine their cardiorespiratory and mechanical (i.e., ground reaction forces) responses at different constant speeds (8, 10, 12, and 14 km·h ^-1 ) and different slopes (-20, -10, -5, 0, +5, +10, +15, and +20%). The subjects also performed a knee extensor (KE) strength assessment. Oxygen and energy costs of running values were correlated between all slopes by pooling all running speeds (all r ² ≥ 0.27; p ≤ 0.021), except between the steepest uphill vs. level and the steepest downhill slope (i.e., +20% vs. 0% and -20% slopes; both p ≥ 0.214). When pooled across all running speeds, the ECR was inversely correlated with KE isometric maximal torque for the level and downhill running conditions (all r ² ≥ 0.24; p ≤ 0.049) except for the steepest downhill slope (-20%), but not for any uphill slopes. The optimal downhill grade (i.e., lowest oxygen cost) varied between running speeds and ranged from -14% and -20% (all p < 0.001). The present results suggest that compared to level and shallow slopes, on steep slopes ~±20%, running energetics are determined by different factors (i.e., reduced bouncing mechanism, greater muscle strength for negative slopes, and cardiopulmonary fitness for positive slopes). On shallow negative slopes and during level running, ECR is related to KE strength.