A round steel rod having a carbon content between 0.30 and 0.60% is processed by a cold working process to form a flat wire for forming a ring gear. The cold working process forms a semifinished flat wire by at least one cold rolling or cold roller drawing step and at least one two-way or four-way rolling step. The semifinished flat wire is processed by die drawing using a drawing die to obtain a finished flat wire in a last stage of the cold working process. The cold working process reduces the round steel rod at a total area reduction of 65% or below.