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Background  Since walking is a daily activity not to require the maximal effort in healthy populations, a very few universal bio-parameters and/or methods have been defined to evaluate individual walking characteristics in those populations. A concept of “economy” is a potential candidate; however, walking economy highly depends on speed, so direct comparisons of economy values are difficult between studies. We investigated whether the vertical component of net walking “efficiency” (Eff vert ; %) is constant across speed. In that case, direct comparisons of Eff vert  will be possible between studies or individuals at any voluntary speed.    Methods  Thirty young male participants walked at eight speeds on the level or ± 5% gradients, providing vertical speeds ( v  vert ). Differences in energy expenditure between level and uphill or downhill gradients (ΔEE) were calculated. The metabolic rate for vertical component (MR vert ) was calculated by multiplying ΔEE with body mass (BM). The mechanical power output for vertical component (P mech ) was calculated by multiplying BM, gravitational acceleration, and  v  vert . Eff vert  was obtained from the ratio of P mech  to MR vert  at each  v  vert . Delta efficiency (Delta-E; %) was also calculated from the inverse slope of the regression line representing the relationship of P mech  to MR vert .    Results  Upward Eff vert  was nearly constant at around 35% and downward Eff vert  ranged widely (49–80%). No significant differences were observed between upward Delta-E (35.5 ± 8.8%) and Eff vert  at any speeds, but not between downward Delta-E (44.9 ± 12.8%) and Eff vert .    Conclusions  Upward ΔEE could be proportional to  v  vert . Upward, but not downward, Eff vert  should be useful not only for healthy populations but also for clinical patients to evaluate individual gait characteristics, because it requires only two metabolic measurements on the level and uphill gradients without kinematic information at any voluntary speed.    Trial registration  UMIN000017690 (R000020501; registered May 26th, 2015, before the first trial) and UMIN000031456 (R000035911; registered Feb. 23rd, 2018, before the first trial).

On the simple calculation of walking efficiency without kinematic information for its convenient use