How this instrument works
True position, as defined by ASME Y14.5, is a geometric dimensioning and tolerancing (GD&T) measure of how far a hole, boss or other feature has drifted from its theoretically exact location — the position a drawing specifies before any real-world manufacturing variation is accounted for. It's reported as a single diametral number, meaning it describes a circular tolerance zone the feature's actual center must fall within, not a simple linear distance in one direction.
A feature's actual location typically deviates from its theoretical position in two directions at once — some amount in X, some amount in Y — and those two deviations combine geometrically, not by simple addition, since they're perpendicular to each other. The straight-line (radial) distance from the theoretical position to the actual position comes from the Pythagorean theorem: the square root of the sum of the X deviation squared and the Y deviation squared. True position doubles that radial distance, because the tolerance is specified as a diameter — a circle the same radial distance in every direction — not a radius.
This diametral convention is what makes true position different from simply reporting the radial deviation directly: a true position tolerance of, say, 0.010 inches on a drawing means the feature's actual center must fall within a circle 0.010 inches across, centered on the theoretical position — so the permitted radial deviation is actually half of the stated tolerance value, 0.005 inches in that example. Inspectors compute the true position value from measured X and Y deviations and compare it directly against the tolerance called out on the drawing to determine pass or fail.
- Enter the measured horizontal deviation into X deviation from true position (in) — how far off in the X direction the inspected feature landed from its theoretical location.
- Enter the measured vertical deviation into Y deviation from true position (in) — how far off in the Y direction.
- Read True position (diametral) for the single number to compare directly against the drawing's true position tolerance callout.
- Enter deviations as signed or unsigned values — the formula squares both, so direction doesn't affect the result, only magnitude does.
Worked example — 0.003-inch X and 0.004-inch Y deviation
Enter 0.003 into X deviation from true position (in) and 0.004 into Y deviation from true position (in). True position (diametral) reads 0.010000 in.
By hand: (0.003, 0.004, 0.005) is a scaled 3-4-5 Pythagorean triple, so √(0.003² + 0.004²) = √(0.000009 + 0.000016) = √0.000025 = 0.005 in exactly by the Pythagorean theorem, giving a radial deviation of 0.005 in. Doubling that for the diametral convention gives TP = 2 × 0.005 = 0.010 in — a feature that would pass a true position tolerance of 0.010 in or larger, right at the boundary of that particular callout.
Questions
Why does true position double the radial deviation instead of reporting it directly?
Because ASME Y14.5 specifies true position as a diametral tolerance — the feature's actual center must fall within a circular zone of a given diameter, not a given radius, centered on the theoretical position. Doubling the radial deviation converts that straight-line distance into the equivalent diameter, matching the convention used on every true position callout on a GD&T drawing.
How do I know if a feature passes or fails its true position tolerance?
Compare the calculated true position value directly against the tolerance called out on the drawing (inside the feature control frame) — if the calculated value is less than or equal to the tolerance, the feature passes; if it exceeds the tolerance, it fails. A true position value of 0.010 in against a drawing tolerance of 0.010 in passes right at the boundary; against a tolerance of 0.008 in it would fail.
Does the sign of the X or Y deviation matter?
No — the formula squares both deviations before adding them, and squaring eliminates any sign, so a deviation of +0.003 in and −0.003 in produce the identical true position result. Direction relative to the theoretical position doesn't affect the true position value itself, only the magnitude of the offset in each direction does.
What's the difference between true position and simply measuring how far off a hole is?
A simple 'how far off' measurement is typically a single linear or radial distance in one direction or combined radially, while true position specifically follows the ASME Y14.5 diametral convention — doubling the radial deviation — and is meant to be compared against a feature control frame's stated tolerance on a formal engineering drawing. Reporting a raw radial deviation instead of the doubled diametral figure would make a part look like it's failing a tolerance it actually passes, or vice versa.
Can true position be used for features other than round holes?
Yes — true position applies to any feature with a defined theoretical location, including bosses, pins, slots and patterns of features, not just round holes. The X and Y deviation figures come from measuring that feature's actual center (or centerline, for a slot) against its theoretical location, then applying the identical diametral formula regardless of the feature's shape.