A machine to bend pipes that includes: a plate that is configured and arranged to move along an X-axis; a bending head connected to the plate, where the bending head is capable of moving along a Z-axis and is equipped with at least one bending arm and at least one bending die; and at least one calendering jig, which is located at a position that is before the bending die, with respect to a feeding direction of the pipe. The calendering jig includes at least two first rolls used to lock the pipe and at least one second roll that is configured and arranged for determining the calendering radius of the pipe, wherein the at least one second roll is anchored to the plate. The bending head is configured and arranged to move in the Z direction with respect to both the plate and the second roll.