Rodents move their whiskers to locate objects in space. Here we used psychophysical methods to show that head-fixed mice can localize objects along the axis of a single whisker, the radial dimension, with one-millimeter precision. High-speed videography allowed us to estimate the forces and bending moments at the base of the whisker, which underlie radial distance measurement. Mice judged radial object location based on multiple touches. Both the number of touches (1-17) and the forces exerted by the pole on the whisker (up to 573 μN; typical peak amplitude, 100 μN) varied greatly across trials. We manipulated the bending moment and lateral force pressing the whisker against the sides of the follicle and the axial force pushing the whisker into the follicle by varying the compliance of the object during behavior. The behavioral responses suggest that mice use multiple variables (bending moment, axial force, lateral force) to extract radial object localization. Characterization of whisker mechanics revealed that whisker bending stiffness decreases gradually with distance from the face over five orders of magnitude. As a result, the relative amplitudes of different stress variables change dramatically with radial object distance. Our data suggest that mice use distance-dependent whisker mechanics to estimate radial object location using an algorithm that does not rely on precise control of whisking, is robust to variability in whisker forces, and is independent of object compliance and object movement. More generally, our data imply that mice can measure the amplitudes of forces in the sensory follicles for tactile sensation.