True Position Tolerance: Understanding Bonus Tolerance and MMC/LMC

True position with material condition modifiers is one of the most powerful — and most misunderstood — tools in GD&T: correctly applying MMC bonus tolerance can dramatically increase manufacturing yield without sacrificing functional assembly requirements.

Position tolerance (⊕) controls where a feature of size is located relative to its true (theoretically exact) position, defined by basic dimensions from a datum reference frame. When combined with material condition modifiers — MMC (Maximum Material Condition) or LMC (Least Material Condition) — position callouts become dynamic: the permissible location tolerance grows as the actual feature size departs from the modifier condition. This is bonus tolerance, and understanding it is essential for engineers who want to write functional tolerances that maximize producibility while ensuring assemblability.

Position Callout Anatomy

A typical position feature control frame for a hole reads:

| ⊕ | ∅0.2 Ⓜ | A | B | C |

Breaking this down:

• ⊕ — true position geometric characteristic symbol
• ∅ — the tolerance zone is cylindrical (an axis must fall within a cylinder)
• 0.2 — the stated (minimum) position tolerance diameter, in millimeters
• Ⓜ — MMC modifier: the 0.2 applies when the hole is at MMC (smallest size); bonus tolerance is allowed as size grows
• A | B | C — primary, secondary, and tertiary datum references that establish the DRF from which true position is measured

The true position itself is defined by basic dimensions (numbers in rectangular boxes) from the datum reference frame — for example, 45 (boxed) from datum B and 30 (boxed) from datum C. Basic dimensions are theoretically exact; their tolerance is not the title block general tolerance but is instead entirely governed by the position feature control frame.

Maximum Material Condition (MMC) Defined

MMC is the condition where a feature of size contains the most material:

• For a hole (internal feature): MMC = smallest allowable hole diameter (the hole has most material when it is smallest)
• For a pin or shaft (external feature): MMC = largest allowable diameter (the pin has most material when it is largest)

MMC represents the worst case for assembly clearance — the smallest hole paired with the most offset position means the fastener is least likely to fit. This is why the stated (tightest) position tolerance applies at MMC: it is the condition that most threatens assemblability.

Bonus Tolerance: The Core Concept

When the Ⓜ modifier is applied, the position tolerance zone is not fixed — it grows as the actual mating size (AMS) of the feature departs from MMC toward LMC. The additional tolerance available is called bonus tolerance:

Bonus tolerance = |Actual Mating Size − MMC size|

Total allowable position tolerance = Stated position tolerance + Bonus tolerance

This makes physical sense: a larger hole can accept a more offset fastener (the extra diameter of the hole compensates for positional deviation). The bonus tolerance is always positive or zero — it can never reduce below the stated tolerance.

Worked Example: Bolt Hole Position with MMC

Consider a hole specified as ∅10.0 +0.3/0.0 (so MMC = ∅10.0, LMC = ∅10.3) with position | ⊕ | ∅0.2 Ⓜ | A | B | C |.

Actual Hole Dia (mm)	Departure from MMC (mm)	Stated Tolerance (mm)	Bonus Tolerance (mm)	Total Allowed Position Tolerance ∅ (mm)
10.0 (MMC)	0.0	0.2	0.0	0.2
10.1	0.1	0.2	0.1	0.3
10.2	0.2	0.2	0.2	0.4
10.3 (LMC)	0.3	0.2	0.3	0.5

A hole at actual ∅10.2 has a total allowed position tolerance of ∅0.4 — double the stated value. If the inspector measures the hole axis at ∅0.35 from true position, the part passes (0.35 < 0.4) even though the actual deviation exceeds the stated 0.2. Without the MMC modifier (RFS condition), that same part would fail.

This is the productivity power of MMC: parts that are functionally acceptable (the fastener will assemble) are not rejected solely because a tight fixed tolerance is exceeded. The functional requirement — the fastener goes in — is the actual design intent.

Least Material Condition (LMC)

LMC is the opposite of MMC:

• For a hole: LMC = largest allowable diameter
• For a pin: LMC = smallest allowable diameter

When the Ⓛ modifier is applied, the stated position tolerance applies at LMC, and bonus tolerance accrues as the feature size moves toward MMC. LMC modifier is used when the concern is material breakout or minimum wall thickness — for example, ensuring a hole does not break through a thin wall even when shifted from true position.

Example application: A hole ∅8.0 +0.2/0.0 near the edge of a casting with wall thickness requirement. | ⊕ | ∅0.3 Ⓛ | A | B | C | ensures the tightest position control when the hole is at its largest (LMC, most wall material removed), providing the most protection against wall breakout at that condition.

Regardless of Feature Size (RFS)

RFS means the stated geometric tolerance applies regardless of the actual mating size — no bonus tolerance is available. In ASME Y14.5-2018, RFS is the default condition when no modifier symbol appears. ISO 1101 also uses RFS as default (referred to as “regardless of feature size” or using the symbol Ⓢ to make it explicit).

When to use RFS for position:

• Press-fit pins where the location accuracy requirement is independent of pin size
• Precision locating features where the geometric accuracy is the true functional requirement, not assembly clearance
• When using concentricity or symmetry style control (though modern practice prefers position even for these)
• Datum features in feature control frames (datums are always RFS unless modified)

Virtual Condition and Functional Gauging

The concept of virtual condition (VC) underpins functional gauge design for MMC position:

For a hole at MMC: VC = MMC diameter − stated position tolerance = smallest the gauge pin can be

In the worked example: VC = 10.0 − 0.2 = ∅9.8 mm. A GO gauge pin of ∅9.8 mm, located at true position, will fit into any hole that simultaneously satisfies both the size and position requirements. This is the basis of functional gauging — a simple pass/fail test that inherently applies bonus tolerance without any calculation.

For an external feature (pin) at MMC: VC = MMC diameter + stated position tolerance. The functional receiver gauge has a hole of VC size at the true position; if the pin passes through the gauge, both size and position are acceptable.

Verifying Position with a CMM

CMM verification of true position follows these steps:

• Step 1: Establish the datum reference frame (A, B, C) by probing datum features and aligning the CMM coordinate system
• Step 2: Probe the feature of interest (e.g., bore) — measure at least 4 points to calculate the actual cylinder axis
• Step 3: Extract actual size (for MMC calculation) — smallest diameter of the bore from the CMM fit
• Step 4: Calculate actual position deviation — distance from the measured feature axis to the true position axis: position error = 2 × √((Δx)² + (Δy)²) for a cylindrical zone
• Step 5: Calculate total allowed tolerance: stated tolerance + bonus (if MMC/LMC modifier applies)
• Step 6: Compare actual position error to total allowed tolerance: pass if actual ≤ allowed

When to Use MMC vs LMC vs RFS

Modifier	Use When	Typical Application
MMC Ⓜ	Assembly clearance is the functional concern	Bolt hole patterns, clearance holes, floating fastener assemblies
LMC Ⓛ	Wall thickness or material breakout is the concern	Holes near edges, thin-wall castings, coaxial features with minimum wall
RFS (no modifier)	Geometric accuracy is the concern regardless of size	Press fits, precision locating pins, datum features

Zero Positional Tolerance at MMC

An advanced but elegant technique is zero position at MMC: | ⊕ | ∅0 Ⓜ | A | B | C |. Here, the stated tolerance is zero — at MMC, the hole axis must be exactly at true position. But since MMC is the theoretical limit, any real hole departs from MMC by at least its size tolerance, immediately gaining bonus tolerance equal to that departure.

This approach transfers all the tolerance to the size tolerance, making the size limits directly represent the functional limit. The virtual condition equals the MMC size exactly. Zero-position-at-MMC is popular in fixed fastener assemblies and in tolerance stack analysis because it simplifies calculations and makes the functional gauge size obvious.

Conclusion

True position with MMC or LMC modifiers is not a relaxation of standards — it is a mathematically rigorous representation of functional assembly requirements that eliminates unnecessary rejections of parts that would assemble and function correctly. By understanding how bonus tolerance is calculated, how virtual condition governs functional gauge design, and when to apply each modifier, engineers can write position tolerances that maximize manufacturing yield while providing genuine functional guarantees. Position with MMC is among the most important tools in a GD&T practitioner’s toolkit.