True position calculator.
Enter the X and Y deviation from your inspection report to get true position, with a pass or fail against the drawing.
Enter the measurement
Why the answer is doubled
A positional callout describes a cylinder. The number in the feature control frame is that cylinder’s diameter, and the axis of the feature has to lie inside it. What an inspection produces is a distance from the theoretically exact point to the actual one, and that distance is a radius.
So the comparison only works once the radius is doubled. A hole 0.004 out in X and 0.003 out in Y is 0.005 from where it should be. That makes a 0.010 diameter zone, which sits exactly on a 0.010 tolerance. Reporting 0.005 against 0.010 makes the part look twice as good as it is, and it is the single most common error in positional inspection.
When the holes sit on a circle instead of a rectangular grid, the drawing rarely gives you the nominal X and Y to measure against. Coordinates for any hole count and start angle works them out, and those are the numbers each deviation is measured from.
| ΔX | ΔY | Radial distance | True position | Against 0.010 |
|---|---|---|---|---|
| 0.0010 | 0.0010 | 0.0014 | 0.0028 | Within tolerance |
| 0.0020 | 0.0020 | 0.0028 | 0.0057 | Within tolerance |
| 0.0030 | 0.0040 | 0.0050 | 0.0100 | Within tolerance |
| 0.0040 | 0.0040 | 0.0057 | 0.0113 | Outside tolerance |
| 0.0050 | 0.0050 | 0.0071 | 0.0141 | Outside tolerance |
| 0.0060 | 0.0080 | 0.0100 | 0.0200 | Outside tolerance |
Questions inspectors ask about true position
How do you calculate true position?
True position deviation is twice the straight line distance from where the feature should be to where it is. Take the deviation in X and the deviation in Y, square each, add them, take the square root, and double the result. You double it because a positional tolerance defines a cylindrical zone whose diameter is the stated tolerance, and the distance you measured is a radius.
Why is true position doubled?
True position is doubled because the tolerance is a diameter and the measurement is a radius. A positional callout of 0.010 describes a cylinder 0.010 across, centered on the theoretically exact location, and the feature axis must lie inside it. A feature 0.004 away from true in X and 0.003 in Y is 0.005 from center, which is 0.010 across, so it sits exactly on the boundary. Forgetting the two is the most common error in positional inspection, and it makes every part look twice as good as it is.
What is bonus tolerance at MMC?
Bonus tolerance is the extra positional allowance a feature earns as it moves away from maximum material condition. When a positional tolerance carries the circled M modifier, the stated tolerance applies at maximum material condition, which for a hole is its smallest allowed size. As the hole gets larger, the difference is added to the positional tolerance as bonus. A 0.250 minimum hole measured at 0.256 has departed 0.006, so a 0.010 positional tolerance becomes 0.016. The part works just as well, because the extra clearance in the hole absorbs the extra positional error.
What is the difference between MMC and LMC bonus?
Maximum material condition is the state with the most material, meaning the smallest hole or the largest pin, and least material condition is the opposite. Bonus is always the absolute departure from whichever condition the modifier names, so for a hole at MMC the bonus grows as the hole grows, and for a hole at LMC the bonus grows as the hole shrinks. MMC is used for assembly fits and is by far the more common. LMC is used to protect wall thickness or edge distance.
What is regardless of feature size?
Regardless of feature size means no bonus applies. Without a modifier, a positional tolerance is regardless of feature size by default under the current standard, so the stated tolerance is the whole allowance whatever size the feature came out. Choose that setting on this page when the drawing carries no circled modifier.
Can true position be converted to plus and minus coordinates?
Only approximately, and the conversion goes wrong in both directions. A positional tolerance of 0.014 is often quoted as roughly plus or minus 0.005 in X and Y, because the square that fits inside the round tolerance zone has sides of the diameter divided by the square root of two. That inscribed square is smaller than the real zone, so converting rejects parts that are good. Converting the other way accepts parts that are bad. Inspect against the callout on the drawing.
Who made it, and what it does not do
This tool was written by Shopfloor Agency's lead engineer, who holds a bachelor’s degree in mechanical engineering and builds websites for US manufacturers. It runs entirely in your browser.
The arithmetic is exact and matches the definition in ASME Y14.5. It cannot establish your datums, and that is where most real positional disputes start. Two inspectors measuring the same part from different datum interpretations will get different deviations, and no calculator settles that. It also assumes a two axis positional callout, so a composite frame, or a pattern controlled at two levels, needs each level evaluated separately.
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