Perceiving the length of a rod by dynamic touch is tied to the inertia tensor Iij, a quantification of its resistance to rotational acceleration. Perception of the portion extending in front of the grasp has previously been ascribed to decomposing one component of Iij by attention. The tensorial nature of dynamic touch suggests that this ability must be anchored wholly in the tensor. Three experiments show that perceived partial length is a function of two components of the tensor, one tied primarily to magnitude and the other tied primarily to direction, whereas perceived whole length is a function of a magnitude component alone. Dynamic touch is characterized in terms of a haptic perceptual instrument that softly assembles to exploit Iij differently depending on the intention, producing 1:1 maps that are appropriately scaled for each intention.