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True Position Calculator —
Position Tolerance, MMC Bonus, and Coordinate-to-Position Conversion

By C&W Engineering Team
Enter how far a hole or pin measured from its basic location in X and Y, and get the true position value the way a CMM reports it. Add the feature's size limits and its measured size, and the calculator applies the MMC or LMC bonus tolerance, tells you whether the feature passes, and draws the tolerance zone with the measured point inside it. A second panel converts a ± coordinate tolerance to the equivalent position zone and back.[1]
True position and bonus tolerance
X and Y are the measured deviations of the feature's axis from its basic (theoretically exact) location. The position tolerance is the diameter in the feature control frame. Bonus applies only when the frame carries an M or L modifier; at RFS the zone is fixed.
Coordinate tolerance ↔ position tolerance
A ± coordinate tolerance is a square zone; a position tolerance is a round one. The round zone that just contains the square is 2.83 × the ± value, and the largest square that fits inside a round zone is ± 0.354 × its diameter. Enter either side.
The round zone has 57% more area than the square it replaces, which is the practical reason position tolerancing gives the shop more usable tolerance for the same functional requirement.

What True Position Means

A position tolerance in a feature control frame defines a cylindrical zone, centred on the basic location, within which the axis of the feature must lie. "True position" is the shorthand for how far the actual axis is from that basic location, expressed as a diameter so that it compares directly with the zone size on the drawing. If the axis is off by Δx in one direction and Δy in the other, the radial error is √(Δx² + Δy²) and the true position is twice that:[1]

Formula
True position (diameter) = 2 × √(Δx² + Δy²). A feature passes when this value is no larger than the tolerance zone diameter plus any bonus.

The factor of two is the source of most disagreements between a machinist's coordinate check and a CMM report. A hole that measures 0.003 off in X and 0.002 off in Y feels like it is "within 0.003," but its true position is 0.0072, and against a Ø0.010 zone it has used 72% of the tolerance.

Bonus Tolerance at MMC

When the feature control frame carries the M modifier, the stated position tolerance applies only when the feature is at its maximum material condition: the smallest hole or the largest pin. As the feature departs from MMC toward its other size limit, the location can be off by that same amount more and the mating part will still assemble, so the position tolerance grows by the departure. That growth is the bonus tolerance.[1][2]

FeatureMMC sizeBonus at MMC
Hole or slot (internal)Minimum size limitMeasured size − minimum size
Pin or boss (external)Maximum size limitMaximum size − measured size

The L modifier works the other way, protecting a minimum wall or edge distance: the tolerance applies at least material condition and grows as the feature approaches MMC. With no modifier (regardless of feature size, RFS) the zone is fixed at the stated diameter no matter what size the feature measures. The calculator applies all three.

What the calculator does not do is datum shift: when a datum feature is itself referenced at MMC, the datum can float by its own departure and the whole pattern gains a further allowance. That needs the datum feature's size and modifier, and is left to a full GD&T analysis.

Worked Example

A Ø0.250 through hole, size limits 0.250 to 0.255, is located with a position tolerance of Ø0.010 at MMC. The CMM reports the axis 0.0045 off in X and 0.0030 off in Y, and the hole measures 0.253.

StepValue
True position = 2 × √(0.0045² + 0.0030²)2 × 0.00541 = 0.0108
Against the stated zone alone (RFS)0.0108 > 0.010: fails
Bonus = measured size − MMC size = 0.253 − 0.2500.003
Allowed = 0.010 + 0.0030.013
Against the bonused zone (MMC)0.0108 ≤ 0.013: passes, 83% of the tolerance used

The same hole drilled at the bottom of its size limit, 0.250, would have no bonus and would be rejected. That is the practical meaning of MMC: a hole cut a little larger buys location tolerance, exactly as much as the mating pin needs.

Converting Coordinate Tolerances

Older drawings locate holes with ± dimensions, which define a square tolerance zone. A position tolerance defines a circle. The circle that passes through the corners of a ±t square has a diameter of 2√2 × t, about 2.83t; going the other way, the largest square that fits inside a Ø z circle is ±0.354z. Converting a ±0.005 coordinate callout to Ø0.014 position keeps every previously acceptable hole acceptable and adds the corners of the circle, 57% more area, which is why the conversion is a free gift to manufacturing.[1][3]

In plain terms
True position is "how far off, doubled." Bonus is "how much bigger than the smallest allowed hole, added on." A CMM does both in one line; this page lets you check that line by hand.

GD&T inspected on a CMM and reported

C&W measures position, bonus, and datum shift on calibrated CMMs and delivers AS9102 first-article reports with the numbers behind every pass.

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Sources & References
[1]ASME Y14.5-2018, Dimensioning and Tolerancing: tolerances of position, material condition modifiers (MMC, LMC, RFS), bonus tolerance, and the conversion between coordinate and position tolerancing.
[2]ASME Y14.5.1-2019, Mathematical Definition of Dimensioning and Tolerancing Principles: the actual-value definition of position as the smallest zone containing the feature axis.
[3]Machinery's Handbook, 31st ed., Geometric Dimensioning and Tolerancing section: position tolerance, conversion of coordinate tolerances, and functional gaging.