In technology, a common helical surface is a right closed helicoid (auger). It is formed by a helical movement of a horizontal segment, provided that the axis of the auger crosses at one of its ends. The formation of the surface of an open helicoid is similar but the segment must intersect the axis and be located at a constant distance from it. It is known from differential geometry that the helical surface can be transformed by bending to the surface of rotation. This fact is taken as the basis for calculating the geometric shape of a flat workpiece. The surface of the open helicoid is non-disjointed, so the shape of the workpiece must be found in such a way as to minimize plastic deformations during surface formation. Parametric equations of continuous flexion of the turn of an open helicoid into the section of a single-cavity hyperboloid of rotation have been derived. Continuous bending can be represented as a gradual deformation of the turn while reducing its step. The meridian of hyperboloid rotation is the corresponding area of hyperbola. The hyperboloid section is proposed to be approximated by the surface of the truncated cone. This approximation will be more accurate in the area of the hyperbole where it asymptotically approaches the segment of the right line. After selecting a cone, it becomes possible to determine its size and build its exact sweep since the cone is a unfolding surface. The sweep is constructed in the form of a flat ring with a cut sector and will be the desired flat workpiece to form a turn of the auger from it. Most accurately, the surface of the turn of the open helicoid can be made by stamping the workpiece of the resulting form. For small-scale production of the helical surface of an open helicoid, it is advisable to weld flat rings together and, during installation, stretch along the shaft while twisting around its axis. The accuracy of the obtained surface will depend on the accuracy of the approximation of the hyperboloid section of rotation with a truncated cone, which is the topic of this work.