PURPOSE: To apply a greater torque in one direction compared to the other direction by providing the respective sides of an active head as two half-sides, the active zones of which are asymmetrical with respect to each other relative to the axial mid-plane in a tool for tightening/slackening a threaded member with an active head having a polygonal cross-section.

CONSTITUTION: The head of this tool having the center 0 of a cross section has a roughly polgonal cross-section, and the side 1 has a recessed circular-arc 4 constituting a part of a filler surface with a comparatively small radius r1 centering about a point A on the radius 2, and the other side has a radius r2(>r1), a projecting circular arc 5 centering about a point B of an outer contour tangentially joied to the circular arc 4 and a straight section 6 intersecting perpendicularly to a bisector 7 of each radius 2, 3 and tangentially joined to the circular arc 5. Further, it has a projecting circular arc 8 with a radius R2 far larger than the radius r2 and tangentially joined to the section 6, and a recessed circular-arc 9 centering about a point C on the radius 3 or near the radius and tagentially joined to the circular arc 4 together with the circular arc 8 on the adjacent side of the contour.