True position is twice the radial deviation
The square root is the radius of the deviation — how far the real center sits from the basic (theoretically exact) location. GD&T states the tolerance zone as a diameter, so you double it. The result is compared against the callout: the feature passes when TP is less than or equal to the specified tolerance (plus any bonus).
- Worked example. Δx = 0.03 mm, Δy = 0.04 mm → √(0.0009 + 0.0016) = 0.05 mm radius → TP = 0.10 mm.
- Three axes. Add the Z term the same way: TP = 2 × √(Δx² + Δy² + Δz²).
A round zone, not a square one
Plus/minus dimensioning boxes the feature into a square zone, which quietly allows about 41 percent more deviation into the corners than along the axes. A position callout defines a round zone of uniform diameter, so the tolerance is the same in every direction.
A ±0.05 mm square zone lets a feature stray 0.071 mm toward a corner, while a ∅0.10 mm position zone caps it at 0.050 mm in any direction — tighter where it counts, uniform everywhere.
Deviation to true position, at a glance
| Δx | Δy | Radius | True position |
|---|---|---|---|
| 0.03 | 0.04 | 0.050 | 0.100 |
| 0.05 | 0.05 | 0.071 | 0.141 |
| 0.10 | 0.00 | 0.100 | 0.200 |
| 0.02 | 0.02 | 0.028 | 0.057 |
Values in mm. Note the last case: a feature off by 0.02 mm on both axes still uses 0.057 mm of a diameter tolerance, because true position is a diameter.
Common questions
How do I calculate true position from X and Y measurements?
Find how far the feature is off in each axis (measured minus nominal), square both, add them, take the square root, then multiply by 2. For a 0.03 mm X error and 0.04 mm Y error: sqrt(0.03^2 + 0.04^2) = 0.05, times 2 is a 0.10 mm true position.
Why multiply by 2?
The square root of the squared errors is the radius of the deviation, the straight-line distance from the true spot to the measured spot. GD&T states position tolerance as a diameter, not a radius, so you double it. Forgetting the 2 is the most common mistake.
What is bonus tolerance?
When the callout uses MMC or LMC, a feature made away from that limit earns extra position tolerance equal to that size difference. A hole with MMC 9.9 mm made at 10.0 mm gains 0.1 mm of bonus, so a 0.05 mm callout allows up to 0.15 mm.
