The cylindrical calibration head (1) for the drilling of a shaft (4), comprising three flutes (20, 21, 22) arranged evenly around the circumference so that they are spaced one from the next by an angle of 120 DEG with respect to a rotation with respect to the axis of the calibration head, the flutes allowing for the removal of chips and the passage of lubricant during drilling, each of the flutes comprising a machining insert of which the position in the flute can be adjusted using an adjusting cartridge.