# What is the true position?

True position calculator for GD&T: the position deviation 2 × √(dx² + dy²) of a hole or pin from its basic location, with the bonus tolerance at MMC and a pass or fail against the position tolerance.

- Page: https://www.acalculator.org/physics/true-position-calculator
- JSON spec: https://www.acalculator.org/physics/true-position-calculator.json
- Version: 8e6a733e70ce

## Default answer

Example with the default inputs (Basic X 1 in, Basic Y 1 in, Measured X 1.003 in, Measured Y 0.996 in, Position tolerance 0.01 in, Material condition RFS): The true position is 0.01 in: Pass against an allowed 0.01 in.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| bx | Basic X | The X coordinate of the true (basic) position on the drawing. |
| by | Basic Y | The Y coordinate of the true (basic) position on the drawing. |
| mx | Measured X | The X coordinate of the measured centre of the feature. |
| my | Measured Y | The Y coordinate of the measured centre of the feature. |
| tol | Position tolerance | The diameter of the position tolerance zone in the feature control frame. |
| mc | Material condition | RFS (no modifier), or MMC (Ⓜ) on a hole or on a pin, which adds a bonus tolerance. |
| mmc | MMC size | The maximum material size: the smallest hole or the largest pin the size limits allow. |
| size | Measured size | The measured diameter of the hole or pin. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| position | True position | The position deviation as a diameter: 2 × √(dx² + dy²). |
| verdict | Result | Pass when the true position is at most the allowed tolerance. |
| allowed | Allowed tolerance | The position tolerance plus any bonus tolerance. |
| bonus | Bonus tolerance | At MMC: the measured size − MMC size for a hole, MMC size − measured size for a pin. |
| margin | Margin | Allowed tolerance − true position; negative when the feature fails. |
| dx | X deviation (dx) | Measured X − basic X. |
| dy | Y deviation (dy) | Measured Y − basic Y. |
| radial | Radial distance | The distance from the basic position to the measured centre: √(dx² + dy²). |

## Method

dx = measured X − basic X; dy = measured Y − basic Y; true position = 2 × √(dx² + dy²). Allowed = tolerance + bonus, with bonus = measured − MMC size (hole) or MMC size − measured (pin) at MMC, and 0 at RFS. Pass when true position ≤ allowed.

## Assumptions

- A 2D position of a round feature with a diameter (⌀) tolerance zone; the datums set the basic X and Y.
- The measured size is within the size limits; a hole below MMC or a pin above MMC has no answer.

## Worked examples

1. bx = 0.0254, by = 0.0254, mx = 0.025476, my = 0.025298, tol = 0.000254, mc = rfs gives position = 0.000254, verdict = Pass, margin = 0, radial = 0.000127. Source: GD&T Basics, True Position – Position Tolerance (position = 2 × √(dx² + dy²); bonus tolerance = measured hole size − MMC hole size), https://www.gdandtbasics.com/true-position/ (retrieved 2026-10-05).
2. bx = 0.0254, by = 0.0254, mx = 0.025476, my = 0.025298, tol = 0.000203, mc = hole, mmc = 0.00635, size = 0.006452 gives position = 0.000254, bonus = 0.000102, allowed = 0.000305, verdict = Pass. Source: GD&T Basics, True Position – Position Tolerance (position = 2 × √(dx² + dy²); bonus tolerance = measured hole size − MMC hole size), https://www.gdandtbasics.com/true-position/ (retrieved 2026-10-05).
3. bx = 0.05, by = 0.02, mx = 0.0501, my = 0.0201, tol = 0.0002, mc = pin, mmc = 0.01, size = 0.00995 gives position = 0.000283, bonus = 0.00005, allowed = 0.00025, verdict = Fail. Source: GD&T Basics, True Position – Position Tolerance (position = 2 × √(dx² + dy²); bonus tolerance = measured hole size − MMC hole size), https://www.gdandtbasics.com/true-position/ (retrieved 2026-10-05) (for a pin the bonus is MMC − measured size).

## FAQ

### How do you calculate true position?

Find how far the measured centre is from the basic position in X and Y, then double the straight-line distance: true position = 2 × √(dx² + dy²). With dx = 0.003 in and dy = −0.004 in, it is 2 × 0.005 = 0.010 in.

### Why is true position multiplied by 2?

The position tolerance is the diameter of a circle centred on the basic position. √(dx² + dy²) is a radius, so doubling it gives a diameter you can compare with the tolerance directly.

### What is bonus tolerance?

When the position tolerance has the MMC modifier (Ⓜ), the feature gains extra tolerance as it departs from its maximum material size. For a hole the bonus is measured size − MMC size; for a pin it is MMC size − measured size.

### What is MMC for a hole and for a pin?

Maximum material condition is the size with the most material left on the part: the smallest allowed hole, or the largest allowed pin.

### Does a true position equal to the tolerance pass?

Yes. The feature passes when its true position is at most the allowed tolerance, so a position equal to the tolerance is on the edge of the zone and passes.

### What does RFS mean?

Regardless of feature size: no material modifier, so there is no bonus and the tolerance stays the same at any size within the limits.

## Sources

- GD&T Basics, True Position – Position Tolerance: position = 2 × √(dx² + dy²) and bonus tolerance from the departure from MMC, retrieved 2026-10-05. https://www.gdandtbasics.com/true-position/
- NIST Special Publication 811 (2008), Appendix B.8: 1 in = 25.4 mm exactly, retrieved 2026-10-05. https://www.nist.gov/pml/special-publication-811