How does the magnitude of the exploration force influence the precision of haptic perceptual estimates? To address this question, we examined the perceptual precision for moment of inertia (i.e., an object's "angular mass") under different force conditions, using the Weber fraction to quantify perceptual precision. Participants rotated a rod around a fixed axis and judged its moment of inertia in a two-alternative forced-choice task. We instructed different levels of exploration force, thereby manipulating the magnitude of both the exploration force and the angular acceleration. These are the two signals that are needed by the nervous system to estimate moment of inertia. Importantly, one can assume that the absolute noise on both signals increases with an increase in the signals' magnitudes, while the relative noise (i.e., noise/signal) decreases with an increase in signal magnitude. We examined how the perceptual precision for moment of inertia was affected by this neural noise. In a first experiment we found that a low exploration force caused a higher Weber fraction (22%) than a high exploration force (13%), which suggested that the perceptual precision was constrained by the relative noise. This hypothesis was supported by the result of a second experiment, in which we found that the relationship between exploration force and Weber fraction had a similar shape as the theoretical relationship between signal magnitude and relative noise. The present study thus demonstrated that the amount of force used to explore an object can profoundly influence the precision by which its properties are perceived. © 2012 Debats et al.