A thread structure in accordance to one or more embodiments includes a thread extending helically along a portion of a bit body in spaced thread turns, the thread having a crest extending between a first flank and a second flank and a root extending between the thread turns, the root having a curvature defined by a portion of an ellipse tangentially adjoining the first and second flank at respective flank transition points, the ellipse having a major axis extending parallel to the axis and a minor axis extending perpendicular to the major axis and through a root bottom.