True Position Calculator

True position states where a feature such as a hole must lie relative to a datum reference frame, and it bounds the deviation with a circular or cylindrical tolerance zone rather than a rectangular one. Because the zone is specified as a diameter, the reported value is twice the radial distance from the theoretically exact location: TP = 2 x sqrt(dX squared + dY squared). A hole 0.080 mm off in X and 0.120 mm off in Y sits 0.144 mm from nominal and therefore reports a true position of 0.288 mm, which passes a 0.4 mm zone with about 72 percent of the tolerance consumed. The round zone matches how a fastener actually fits a clearance hole, where only the total radial offset matters and its direction is irrelevant. Replacing a plus or minus 0.005 inch coordinate zone with the circular zone that circumscribes it, 0.0141 inch in diameter, adds roughly 57 percent more usable area without permitting any deviation the square zone forbade. Two qualifications matter. First, this calculation assumes regardless of feature size; if the drawing carries the maximum material condition modifier, bonus tolerance equal to the departure of the actual size from MMC is added to the stated zone before comparison. Second, the deviations must be measured in the datum reference frame the drawing establishes, not from a convenient part edge, so the result depends entirely on how the part was aligned on the coordinate measuring machine. Hole perpendicularity matters too, since a tilted deep hole reports different positions at its entry and exit planes.

The circular tolerance zone is widely credited to Stanley Parker, an engineer at the Royal Torpedo Factory in Alexandria, Scotland, who around 1938 to 1940 noticed that parts rejected by rectangular coordinate limits assembled perfectly well. He argued that a hole location should be bounded by a round zone about the true position, since a fastener does not care in which direction the error lies, and set out the reasoning in wartime and post-war British writing on drawing practice. Britain subsequently incorporated positional tolerancing into its BS 308 engineering drawing standards. In the United States the method entered practice through military standardization, with MIL-STD-8 issued in 1949 covering dimensioning and tolerancing symbols, followed by successive civil standards: USASI Y14.5 in 1966, ANSI Y14.5-1973, ANSI Y14.5M-1982, ASME Y14.5M-1994, and ASME Y14.5-2009 and 2018, which progressively formalized datum reference frames, the maximum and least material condition modifiers, and composite position tolerancing. ISO built a parallel system around ISO 1101 for geometrical tolerancing of form, orientation, location, and run-out. Routine verification of true position became practical only as coordinate measuring machines spread through industry from the 1970s onward, because evaluating a diametral zone with hard gauging and hand measurement is far more awkward than checking two independent coordinate dimensions.