When vision is excluded humans are still able to walk back to a starting point or to a previously seen target. This performance may be mediated by path integration, based on information about movement with respect to the ground or to inertial space, that is, on substratal or inertial idiothetic cues. We intend to unravel whether, and how accurately, these two inputs act and interact on the translatory component of this navigation performance. Subjects were asked 1) to reproduce a path they had walked, and 2) to indicate the location of a target they had seen before being blindfolded by (i) walking there, (ii) treading a motor-driven conveyor belt until they imagine they are there, and (iii) reporting, while being driven in a trolley, when they seem to pass the target. The estimation of path length turns out to vary as a function of walking velocity, step length, and step rate. The estimate becomes virtually veridical when subjects walk at their normal pace, but it overshoots at lower and undershoots at higher values of these variables. Veridicality at near normal speeds is also found with passive transport (iii), but with a reverse dependence on velocity. It is concluded that in these paradigms path control and perception are mediated by an open-loop performance of the underlying path integration system, calibrated in such a way as to yield veridical estimates during normal walking. Either inertial or substratal idiothetic information is sufficient for this performance. However, the quantitative relations found argue in favor of the hypothesis that substratal idiothetic information predominates when both are available. In spite of its limitations the capability shown here may serve as an essential constituent of navigation by path integration in humans.