Abstract: A tool holder that allows floating to accommodate radial displacement including: a shank, having a bore at one end, the bore being perpendicular to the longitudinal axis of the shank; a mounting head, with cavities at both ends at least one bore extending radially to each cavity from the outside surface of the mounting head, wherein the shank extends into the cavity at one end of the mounting head; a tool mounts in the other cavity of the mounting head; a pin connecting the shank and the mounting head, with a sliding fit through the bore of mounting head, and a clearance fit through the shank, wherein the clearance fit and clearance between the shank and the cavity member allows a floating freedom of slightly greater than twice the anticipated eccentricity between the centerline of the shank and the centerline of a workpiece hole; and a device for securely engaging the tool in the cavity at the first end of the mounting head.