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GD&T true position, explained

In Hebrew: מיקום אמיתי ב־GD&T

True position tolerances where a feature such as a hole may sit, as a round zone around its exact location. A hole passes when twice its distance from that location is no larger than the stated diameter, plus any bonus earned at MMC.

True position (GD&T) calculator

Pre-filled with the worked example below. Change any value.

Actual position
0.2Ø mm
Allowed position
0.3Ø mm

Within position tolerance.

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Why a round zone

Plus-or-minus coordinates give a square zone: ±0.1 in x and ±0.1 in y. But a hole 0.14 off along the diagonal is no worse for assembly than one 0.14 off along an axis, and the square rejects one while accepting the other. Position replaces the square with the circle that passes through its corners, a zone about 57 per cent larger, and every part it adds was a functionally good part the square was scrapping.

The location is defined by basic dimensions, shown in boxes on the drawing, measured from datums A, B and C. Basic dimensions carry no tolerance of their own; all the allowed variation lives in the feature control frame.

Bonus tolerance at MMC

The symbol Ⓜ after the tolerance means the stated value applies when the hole is at its maximum material condition, its smallest allowed size. A hole made larger leaves more room for the mating pin, so it may also sit further off. The extra allowance, the bonus, equals how far the hole departs from MMC. That is how a functional gauge works: a fixed pin either goes in or it does not.

For a shaft or pin, MMC is the largest size, and the bonus is the MMC size minus the measured size.

A worked number

A hole is toleranced Ø10.0 to 10.2 mm, position Ø0.2 at MMC. It measures Ø10.1, and its centre is 0.06 mm off in x and 0.08 mm off in y. The actual position is 2 × √(0.06² + 0.08²) = 2 × 0.1 = Ø0.2. The bonus is 10.1 − 10.0 = 0.1, so the allowed position is Ø0.3. The hole passes.

Move it to 0.09 and 0.09: about Ø0.25 actual position, still inside Ø0.3, but outside a ±0.07 square that someone tightened "to be safe".

Common mistakes

  • Comparing the radial offset, √(Δx² + Δy²), with the diametral tolerance. Position is a diameter, so double it.
  • Taking bonus when the frame has no Ⓜ. Without it, the tolerance is fixed regardless of size.
  • Computing the bonus for a pin the same way as for a hole. For a pin, the bonus grows as it gets smaller.

Mechanical engineering, explained