Pipe cutter with calibrator and reamer/deburrer for the edges of the cut pipe, characterized in that : a) in the body of the pipe cutter there is at least one calibrator , between which and the very body of the pipe cutter is delimited a cavity that can accommodate the end of a pipe (t) positioned in said calibrator ; each calibrator having at its end a mouth that varies between a minimum diameter (d1) at its base and a maximum diameter (d) that corresponds to the calibre of the worked pipe (t) ; b) it comprises, in the body of the pipe cutter, at least one deburrer , disposed so that it is longitudinal to the body and made up of one or more parts (S) provided with at least two convergent edges, at least one of them constituting a blade reaching said cavity ; said parts (S) are in a single deburrer , are of different widths (S1), (S2), (S3) corresponding to the various diameters of the pipes (t) to be deburred, and can be placed in any angular position with respect to the main axis of the pipe cutter, and the blades situated in its various parts (S) have a chamfered cutting zone; in which deburrer, simultaneously, a blade in a contiguous part (S) deburrs/reams the outside of the cut edge of the pipe (t); c) each calibrator is a body exhibiting symmetry of revolution that is aligned with at least one blade ; such that by inserting the pipe (t) in the corresponding calibrator and rotating it, first the cut edge of the pipe (t) is calibrated to give it a diameter equal to that of the remaining inner diameter of the pipe (t) and then, when the calibrated edge advances in the corresponding cavity , the blades simultaneously deburr and ream said edge. a) in the body of the pipe cutter there is at least one calibrator , between which and the very body of the pipe cutter is delimited a cavity that can accommodate the end of a pipe (t) positioned in said calibrator ; each calibrator having at its end a mouth that varies between a minimum diameter (d1) at its base and a maximum diameter (d) that corresponds to the calibre of the worked pipe (t) ; b) it comprises, in the body of the pipe cutter, at least one deburrer , disposed so that it is longitudinal to the body and made up of one or more parts (S) provided with at least two convergent edges, at least one of them constituting a blade reaching said cavity ; said parts (S) are in a single deburrer , are of different widths (S1), (S2), (S3) corresponding to the various diameters of the pipes (t) to be deburred, and can be placed in any angular position with respect to the main axis of the pipe cutter, and the blades situated in its various parts (S) have a chamfered cutting zone; in which deburrer, simultaneously, a blade in a contiguous part (S) deburrs/reams the outside of the cut edge of the pipe (t); c) each calibrator is a body exhibiting symmetry of revolution that is aligned with at least one blade ; such that by inserting the pipe (t) in the corresponding calibrator and rotating it, first the cut edge of the pipe (t) is calibrated to give it a diameter equal to that of the remaining inner diameter of the pipe (t) and then, when the calibrated edge advances in the corresponding cavity , the blades simultaneously deburr and ream said edge. <EOS>