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True position calculator: position from X/Y deviation, with MMC bonus

Enter the nominal and the measured location of a hole or pin and the position tolerance from the feature control frame. The calculator gives the true position as a diameter, says whether it is in tolerance and, with Ⓜ, adds the bonus tolerance from the actual size. It runs in your browser; nothing is sent anywhere.

Location

Tolerance

Material condition

Use one unit for every field – millimetres or inches. Decimal point or comma both work.

Worked example

A Ø8 hole is dimensioned at X 40, Y 25 with a position tolerance of Ø0.1 at MMC. The CMM reports X 40.03 and Y 24.96, and the hole measures 8.04 against a size tolerance of 8.0 to 8.1.

  1. Deviation: ΔX = +0.03, ΔY = −0.04. Distance from nominal: √(0.03² + 0.04²) = 0.05.
  2. True position: Ø = 2 × 0.05 = Ø0.10. Without a modifier that is exactly at the limit – still in tolerance, with nothing to spare.
  3. With Ⓜ: the hole is 0.04 larger than its smallest limit (MMC 8.0), so the bonus is 0.04 and the allowed position is Ø0.14. The hole is in tolerance with 0.04 left.

These are the values preset in the calculator above.

Bonus tolerance at MMC and LMC

The maximum material condition (MMC) is the size at which a feature has the most material: the smallest hole, the largest pin. A position tolerance with Ⓜ applies at that size. As the feature moves away from MMC – the hole gets larger, the pin smaller – the assembly gains clearance, and the position tolerance may grow by the same amount. That extra is the bonus tolerance. With Ⓛ (least material condition) it runs the other way and protects wall thickness instead of assembly; without a modifier (RFS, regardless of feature size) there is no bonus.

From ± coordinates to position

Older drawings give hole locations with ± tolerances in X and Y: a square zone. Position uses a circle. The circle through the corners of a ±a square has the diameter 2√2 × a ≈ 2.828 × a, so ±0.05 becomes Ø0.141 – 57 % more area than the square, which is one reason position tolerancing exists. The circle inside the square is Ø2a.

Frequently asked questions

How is true position calculated?

True position is twice the distance between the measured and the nominal location: Ø = 2 × √(ΔX² + ΔY²). A hole 0.03 mm off in X and 0.04 mm off in Y is 0.05 mm away from nominal, so its position is Ø0.10.

What is the bonus tolerance at MMC?

If the position tolerance carries the maximum material modifier (Ⓜ), the zone grows by as much as the feature departs from its maximum material size: a hole by how much larger it is than its smallest limit, a pin by how much smaller it is than its largest limit.

How do I convert a ± coordinate tolerance to position?

A square zone of ±a in X and Y has a diagonal of 2√2 × a. The circle through its corners is Ø2.828 × a: ±0.05 corresponds to Ø0.141. The circle inscribed in the square is Ø2a, so ±0.05 is at least Ø0.10.

The size limits of a hole like »Ø8 H7« come from ISO 286: see the ISO 286 tolerance charts, for example H7. What a first article inspection report and a PPAP package contain: What is PPAP?