True Position Calculator (GD&T position from X/Y deviation, with MMC bonus)

Understanding the true position calculator — concept and principle

In geometric dimensioning and tolerancing (GD&T), a position tolerance controls how far a hole, pin or other feature may sit from its exact (nominal) location. This calculator turns measured X and Y deviations into the diametral true position, adds any bonus tolerance from a maximum material condition (MMC) modifier and reports pass or fail with the remaining margin.

The hole sits exactly on its Ø0.1 limit, but the MMC bonus widens the zone to Ø0.15.

How it is calculated

Δx = measured X − nominal X; Δy = measured Y − nominal Y

True position = 2 × √(Δx² + Δy²)

Bonus: hole at MMC = actual size − MMC size; pin at MMC = MMC size − actual size; RFS = 0

Allowed = drawing tolerance + bonus; pass if true position ≤ allowed

All values in mm; the position tolerance is a diameter (Ø).

The principle

A diametral tolerance zone is a cylinder centred on the nominal location. The feature's axis may lie anywhere inside it. The radial distance from nominal is √(Δx² + Δy²), and since the zone is specified by diameter, the comparable number is twice that. With an MMC modifier, the tolerance applies when the feature is at its tightest-fit size (smallest hole or largest pin). As the feature moves away from that size, there is more clearance for assembly, so the position zone may grow by the same amount. That extra allowance is the bonus.

Worked example

Default inputs: nominal (25, 40), measured (25.03, 39.96), tolerance Ø0.1, hole at MMC, actual size 10.05, MMC size 10.00.

Δx = 0.03 mm, Δy = −0.04 mm.
Radial offset = √(0.03² + 0.04²) = 0.05 mm.
True position = 2 × 0.05 = 0.1 mm.
Bonus = 10.05 − 10.00 = 0.05 mm; allowed = 0.1 + 0.05 = 0.15 mm.
0.1 ≤ 0.15, so Pass — within the position tolerance, with a margin of 0.05 mm.

Each point is the calculator re-run with only “Nominal Y (mm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Nominal Y (mm)	True position (diameter, mm)
10	59.92
20	39.92
30	19.9201
40	0.1
50	20.0801
60	40.08
80	80.08

How to read the result

A positive margin means the feature is acceptable for this check; a negative one means it is out of position. Without the MMC bonus, this hole would sit exactly on its 0.1 limit, which shows how much the bonus can matter. Converting a ± coordinate tolerance into a diametral zone typically gives about 57 % more area, which is one reason GD&T position is widely used.

Common mistakes

Comparing the radial offset (not doubled) with the diameter tolerance.
Applying a bonus when the drawing has no MMC modifier.
Measuring from the wrong datum reference frame.
Using a size outside the size tolerance; a feature out of size fails regardless of position.

Keep in mind: This is a 2-D check on one cross-section. Datums, projected tolerance zones, orientation along the depth and the full rules of ASME Y14.5 or ISO GPS must be applied as the drawing specifies.

Frequently asked questions

Why is the offset doubled?

The position tolerance is a diameter, so the measured radial offset is doubled to compare like with like.

What does MMC mean?

Maximum material condition: the size at which the part has the most material, the smallest hole or largest pin.

What is RFS?

Regardless of feature size: no bonus applies, whatever the actual size.

Can a part fail position but still assemble?

Sometimes, but it is still nonconforming to the drawing.

Sources: ASME Y14.5, Dimensioning and Tolerancing (position tolerance and material condition modifiers)

Checked 9 Nov 2026. Diametral position tolerance zone (position = 2√(Δx² + Δy²)) and MMC bonus tolerance as defined in ASME Y14.5 geometric dimensioning and tolerancing: standard formula.

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