A thread forming tap has a full thread portion and a leading portion contiguous with the full thread portion and reducing in diameter toward its tip. The full thread and leading portions are provided with external thread on which lobes and recesses are alternately formed. When δ represents an angle around a tool center line toward a thread forming side, the shape of the lobe varies along a quadratic curve relative to angle δ so that relief amount increases toward inflection point angle δ. However, in a rough plastic deformation section where angle δ is greater than inflection point angle θ and exceeds the working region, the shape varies along an Archimedean curve with clearance angle α1 so that the relief amount increases linearly relative to angle δ, and a margin section is substantially zero or within a range where angle δ is less than or equal to 1°.