True position calculator
True position is twice the radial distance from nominal: TP = 2·√(ΔX² + ΔY²). A hole measured 0.05 mm off in X and 0.03 mm off in Y sits at a true position of Ø0.117 mm. Enter your measured deviations, and — if the callout carries Ⓜ or Ⓛ — the actual feature size, and the calculator adds the bonus tolerance the departure from MMC/LMC earns before giving a pass/fail against the frame.
Measured deviations
Largest pin that enters the hole, not a 2-point size
IN TOLERANCE
- Actual position
- Allowed (tol + bonus)
- Bonus tolerance
- Max bonus |MMC − LMC|
How it’s calculated
Position = 2·√(ΔX² + ΔY²[ + ΔZ²]). At MMC or LMC, bonus = departure from the stated material-condition boundary, and allowed = stated tolerance + bonus (ASME Y14.5-2018 5.9.4.2, 5.9.6.2). The size is the unrelated actual mating envelope at MMC (the largest perfect pin that enters a hole, the smallest perfect ring over a shaft; 3.29) and the unrelated actual minimum material envelope at LMC (3.30), not a two-point caliper or bore-gauge size, which overstates the bonus when the feature has form error. The bonus is largest at the other limit of size, so it can never exceed |MMC − LMC|; a size past either limit is a size reject. Limits are absolute (5.4): a position equal to the allowed diameter passes. The same arithmetic applies to ISO 2692 Ⓜ/Ⓛ; the reciprocity requirement Ⓡ and datum feature shift at MMB are not included.
Where does bonus tolerance come from?
At maximum material condition, a hole at its smallest allowed size gets exactly the stated tolerance. As the hole is made larger (toward least material), the extra clearance becomes usable position tolerance — the bonus equals the departure from MMC. That is why an out-of-position hole can still pass: the frame's Ø0.25 Ⓜ may effectively be Ø0.31 for the hole as made.