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2.3 Material Condition Concepts: MMC, LMC, & RFS Calculations
ASME GDTP Technologist Y14.5-2009
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1 Chapter 1: Scope, Certification Logistics, Fundamental Rules & General Dimensioning
1.1 ASME GDTP Technologist Exam Scope, Prometric Logistics, & Certification Rules 1.2 Fundamental Rules of ASME Y14.5-2009 (Rules a through p) 1.3 Engineering Drawing Standards, Drawing Units, & Basic vs. Toleranced Dimensions 1.4 Dimensioning Features: Diameters, Radii, Chamfers, Countersinks, Counterbores, Spotfaces, Keyseats & Slots 1.5 Application of Dimensions & Location of Features: Lines, Leaders, Reference Dimensions, Rectangular vs. Polar Coordinates
2 Chapter 2: Features, Limits of Size, & Material Condition Principles
2.1 Features, Features of Size, & Limits of Size 2.2 Rule #1 (Taylor Principle / Envelope Rule), Its Exceptions & Overrides 2.3 Material Condition Concepts: MMC, LMC, & RFS Calculations
3 Chapter 3: General Tolerancing & Symbology
3.1 Direct Tolerancing, Limit Dimensioning, & Angular Tolerancing 3.2 The 14 Geometric Characteristic Symbols, Feature Control Frames, & Special Modifiers 3.3 Screw Threads, Gears & Splines, Angular Surfaces, Tapers & Statistical Tolerancing 3.4 Feature Control Frame Placement, Combined Frames, Tolerance Zone Definition & Tabulated Tolerances
4 Chapter 4: Datum Reference Frames & Degrees of Freedom
4.1 Theoretical Datums, Datum Feature Simulators, & Physical Datum Features 4.2 Degrees of Freedom Constraint & The 3-2-1 Datum Precedence System 4.3 Planar, Cylindrical, & Width Datum Feature Establishment
5 Chapter 5: Advanced Datum Applications: Targets, Boundary Modifiers, Customized Frames & Restrained Condition
5.1 Datum Target Points, Lines, Areas, & Movable Datum Simulators 5.2 Material Boundary Modifiers (RMB, MMB, LMB) & Datum Shift Calculations 5.3 Functional Datum Feature Selection, Multiple Datum Reference Frames & Simultaneous vs. Separate Requirements 5.4 Rotational Constraint About a Datum Axis or Point & Customized Datum Reference Frames 5.5 Irregular & Complex Datum Features, Mathematically Defined Surfaces, Restrained Condition & Datum Feature Controls
6 Chapter 6: Form Tolerances
6.1 Flatness & Straightness Controls for Surfaces & Features of Size 6.2 Circularity & Cylindricity Controls, Differences, & Inspection
7 Chapter 7: Orientation Tolerances
7.1 Parallelism Controls for Planar Surfaces & Cylindrical Features of Size 7.2 Perpendicularity & Angularity Tolerances with Basic Angles & Tangent Plane
8 Chapter 8: Location: Position Fundamentals & Calculations
8.1 Position Tolerancing Fundamentals, True Position, & Coordinate Conversions 8.2 Bonus Tolerance & Virtual Condition Calculations for Internal & External Features 8.3 Projected Tolerance Zones (Ⓟ Modifier) & Fixed vs. Floating Fastener Formulas 8.4 Zero Positional and Orientation Tolerancing at MMC and at LMC 8.5 Surface vs. Axis Interpretation of Position & the Boundary Concept for Slots, Tabs & Noncircular Features
9 Chapter 9: Location: Patterns, Composite Controls, Coaxial & Symmetrical Relationships, and Functional Gaging
9.1 Hole & Slot Patterns, Multi-Segment Frames, & Composite Position Tolerancing 9.2 Functional Gaging Principles & Inspection Verification of Position 9.3 Coaxial Holes, Counterbored Holes, Non-Parallel Axes, Spherical Features & Bidirectional Position 9.4 Concentricity & Symmetry Tolerances Under ASME Y14.5-2009 9.5 LMC Applied to Position: Wall Thickness, Breakout Protection & Boundary Calculations
10 Chapter 10: Profile Tolerances
10.1 Profile of a Line & Profile of a Surface Fundamentals & Basic Geometry 10.2 Bilateral, Unilateral, & Unequally Disposed Profile Boundaries (Ⓤ Modifier) 10.3 Composite Profile Tolerances vs. Multiple Single-Segment Profile Controls 10.4 Profile Verification, Coplanarity Controls, & Non-Rigid Parts 10.5 Profile Applications: Conicity, Extruded and Irregular Shapes, and Profile-Controlled Datum Features 10.6 Modifier Rules for Profile & Combined Controls (Profile with Position, Orientation and Runout)
11 Chapter 11: Runout Tolerances & Comparative Control Analysis
11.1 Circular Runout vs. Total Runout Interpretation & Dial Indicator Verification 11.2 Comparative Analysis: Runout vs. Form, Orientation, & Concentricity Controls
2.3 Material Condition Concepts: MMC, LMC, & RFS Calculations
Key Takeaways Explain This Topic AI
Maximum Material Condition (MMC) is the state where a feature of size contains the maximum volume of material within its specified limits: minimum hole/slot diameter, and maximum pin/shaft diameter.
Least Material Condition (LMC) is the state where a feature of size contains the minimum volume of material within its specified limits: maximum hole/slot diameter, and minimum pin/shaft diameter.
Regardless of Feature Size (RFS) is the universal default under ASME Y14.5-2009 Rule #2; geometric tolerances apply uniformly across all produced sizes without bonus tolerance unless an MMC or LMC modifier is explicitly specified.
Bonus tolerance is earned when a feature departs from its specified material condition boundary toward the opposite limit: Bonus Tolerance = |Actual Size - Specified Material Condition Limit|.
Engineering design intent dictates modifier selection: MMC guarantees clearance and assembly, LMC preserves minimum wall thickness and structural strength, and RFS maintains precise alignment and dynamic rotational balance.
Last updated: September 2026
Material Condition Concepts: MMC, LMC, & RFS Calculations
Quick Summary: ASME Y14.5-2009 defines three material condition principles that govern how size variations affect geometric tolerances: Maximum Material Condition (MMC) (maximum part volume: minimum hole, maximum shaft), Least Material Condition (LMC) (minimum part volume: maximum hole, minimum shaft), and Regardless of Feature Size (RFS) (geometric tolerance applies identically at every manufactured size). Under Rule #2 , RFS is the mandatory drawing default for all geometric controls unless an MMC ( Ⓜ ) or LMC ( Ⓛ ) symbol is explicitly stated. Calculating bonus tolerance provides critical manufacturing flexibility while preserving functional assembly or wall thickness.
1. The Three Material Condition Principles
In geometric dimensioning and tolerancing, material conditions describe the state of a feature of size relative to its allowable dimensional boundaries.
Maximum Material Condition (MMC) (ASME Y14.5-2009, Section 1.3.38): The condition in which a feature of size contains the maximum amount of material within the stated limits of size.
For external features (pins, shafts, bosses, tabs): MMC is the upper limit of size (maximum allowable diameter or thickness).
For internal features (holes, bores, slots, keyways): MMC is the lower limit of size (minimum allowable diameter or width).
Least Material Condition (LMC) (ASME Y14.5-2009, Section 1.3.39): The condition in which a feature of size contains the minimum amount of material within the stated limits of size.
For external features : LMC is the lower limit of size (minimum allowable diameter or thickness).
For internal features : LMC is the upper limit of size (maximum allowable diameter or width).
Regardless of Feature Size (RFS) (ASME Y14.5-2009, Section 1.3.48): Indicates that a geometric tolerance or datum reference applies at any increment of size of the feature within its limits of size.
2. ASME Y14.5-2009 Rule #2: The Universal RFS Default
A pivotal rule tested on the ASME GDTP Technologist exam is Rule #2 (Section 2.8) , which governs the application of material condition modifiers:
"RFS applies, with respect to the individual tolerance, and datum reference, where no modifying symbol is specified. MMC, LMC, MMB, or LMB must be specified on the drawing where it is required." (ASME Y14.5-2009, Section 2.8)
Historical Evolution of Rule #2
ANSI Y14.5M-1982 : Tolerances of position defaulted to MMC, whereas form, orientation, and runout defaulted to RFS. This created frequent confusion among drafters and inspectors.
ASME Y14.5M-1994 and Y14.5-2009 : The standard eliminated dual defaults. RFS is now the universal default for all 14 geometric characteristics . If a feature control frame contains no circled modifier symbol, the tolerance applies strictly at RFS.
Obsolete Symbol : In legacy drawings, a circled "S" ( Ⓢ ) was used to indicate RFS. This symbol was officially eliminated in 1994 and is prohibited on modern ASME Y14.5 drawings. RFS is indicated solely by the absence of an MMC or LMC modifier.
3. Mathematical Formulations and Bonus Tolerance Calculations
When an MMC ( Ⓜ ) or LMC ( Ⓛ ) modifier is applied to a geometric tolerance, the stated tolerance in the feature control frame applies strictly when the feature is produced at that designated boundary. When the manufactured feature departs from that boundary, additional geometric tolerance—known as bonus tolerance —is earned.
Master Calculation Formulas
Feature Category Material Condition Size Limit Formulation Bonus Tolerance Formula
External Feature (Shaft, Pin, Boss, Tab) MMC Upper Limit of Size ( D max D_{\text{max}} D max ) Bonus = MMC − Actual Mating Size \text{Bonus} = \text{MMC} - \text{Actual Mating Size} Bonus = MMC − Actual Mating Size
LMC Lower Limit of Size ( D min D_{\text{min}} D min ) Bonus = Actual Mating Size − LMC \text{Bonus} = \text{Actual Mating Size} - \text{LMC} Bonus = Actual Mating Size − LMC
RFS Entire Size Range ( D min D_{\text{min}} D min to D max D_{\text{max}} D max ) Bonus = 0.00 \text{Bonus} = 0.00 Bonus = 0.00 (No bonus permitted)
Internal Feature (Hole, Bore, Cavity, Slot) MMC Lower Limit of Size ( D min D_{\text{min}} D min ) Bonus = Actual Mating Size − MMC \text{Bonus} = \text{Actual Mating Size} - \text{MMC} Bonus = Actual Mating Size − MMC
LMC Upper Limit of Size ( D max D_{\text{max}} D max ) Bonus = LMC − Actual Mating Size \text{Bonus} = \text{LMC} - \text{Actual Mating Size} Bonus = LMC − Actual Mating Size
RFS Entire Size Range ( D min D_{\text{min}} D min to D max D_{\text{max}} D max ) Bonus = 0.00 \text{Bonus} = 0.00 Bonus = 0.00 (No bonus permitted)
The Total Permissible Tolerance Formula Total Permissible Tolerance = Stated Geometric Tolerance + Bonus Tolerance \text{Total Permissible Tolerance} = \text{Stated Geometric Tolerance} + \text{Bonus Tolerance} Total Permissible Tolerance = Stated Geometric Tolerance + Bonus Tolerance
- 4. Step-by-Step Engineering Worked Examples
- Example 1: Internal Clearance Hole at MMC
An engineering drawing specifies an internal mounting hole as ∅ 10.0 0 − 0.00 + 0.20 mm \varnothing 10.00^{+0.20}_{-0.00}\text{ mm} ∅ 10.0 0 − 0.00 + 0.20 mm with a position tolerance of ∅ 0.25 mm \varnothing 0.25\text{ mm} ∅ 0.25 mm at MMC to Datums A, B, and C.
Limits of Size : MMC = 10.00 mm \text{MMC} = 10.00\text{ mm} MMC = 10.00 mm , LMC = 10.20 mm \text{LMC} = 10.20\text{ mm} LMC = 10.20 mm .
Stated Position Tolerance : 0.25 mm 0.25\text{ mm} 0.25 mm .
Evaluating across the manufacturing spectrum:
Produced Hole Size (AME) Departure from MMC Bonus Tolerance Stated Tolerance Total Allowable Position Tolerance
10.00 mm 10.00\text{ mm} 10.00 mm (MMC) 0.00 mm 0.00\text{ mm} 0.00 mm 0.00 mm 0.00\text{ mm} 0.00 mm 0.25 mm 0.25\text{ mm} 0.25 mm ∅ 0.25 mm \varnothing 0.25\text{ mm} ∅ 0.25 mm
10.05 mm 10.05\text{ mm} 10.05 mm 0.05 mm 0.05\text{ mm} 0.05 mm 0.05 mm 0.05\text{ mm} 0.05 mm 0.25 mm 0.25\text{ mm} 0.25 mm ∅ 0.30 mm \varnothing 0.30\text{ mm} ∅ 0.30 mm
10.10 mm 10.10\text{ mm} 10.10 mm 0.10 mm 0.10\text{ mm} 0.10 mm 0.10 mm 0.10\text{ mm} 0.10 mm 0.25 mm 0.25\text{ mm} 0.25 mm ∅ 0.35 mm \varnothing 0.35\text{ mm} ∅ 0.35 mm
10.15 mm 10.15\text{ mm} 10.15 mm 0.15 mm 0.15\text{ mm} 0.15 mm 0.15 mm 0.15\text{ mm} 0.15 mm 0.25 mm 0.25\text{ mm} 0.25 mm ∅ 0.40 mm \varnothing 0.40\text{ mm} ∅ 0.40 mm
10.20 mm 10.20\text{ mm} 10.20 mm (LMC) 0.20 mm 0.20\text{ mm} 0.20 mm 0.20 mm 0.20\text{ mm} 0.20 mm 0.25 mm 0.25\text{ mm} 0.25 mm ∅ 0.45 mm \varnothing 0.45\text{ mm} ∅ 0.45 mm
Notice that when the hole is machined at its maximum allowable diameter ( 10.20 mm 10.20\text{ mm} 10.20 mm ), the allowable positional error nearly doubles from 0.25 mm 0.25\text{ mm} 0.25 mm to 0.45 mm 0.45\text{ mm} 0.45 mm . This extra tolerance reduces manufacturing scrap without compromising assembly.
Example 2: External Dowel Pin at MMC
A locating pin is specified as ∅ 16.00 ± 0.10 mm \varnothing 16.00 \pm 0.10\text{ mm} ∅ 16.00 ± 0.10 mm with a perpendicularity tolerance of 0.05 mm 0.05\text{ mm} 0.05 mm at MMC to Datum A.
Limits of Size : MMC = 16.10 mm \text{MMC} = 16.10\text{ mm} MMC = 16.10 mm , LMC = 15.90 mm \text{LMC} = 15.90\text{ mm} LMC = 15.90 mm .
Produced Pin Diameter : 15.95 mm 15.95\text{ mm} 15.95 mm .
Departure from MMC : 16.10 − 15.95 = 0.15 mm 16.10 - 15.95 = 0.15\text{ mm} 16.10 − 15.95 = 0.15 mm (Bonus Tolerance).
Total Allowable Perpendicularity Tolerance : 0.05 + 0.15 = 0.20 mm 0.05 + 0.15 = 0.20\text{ mm} 0.05 + 0.15 = 0.20 mm .
Example 3: Internal Fluid Passage at LMC
An aircraft hydraulic manifold features a high-pressure port drilled through an exterior boss. The boss outer boundary is critical, and wall thinning risks rupture under 3,000 psi. The hole is specified as ∅ 8.00 ± 0.20 mm \varnothing 8.00 \pm 0.20\text{ mm} ∅ 8.00 ± 0.20 mm with a position tolerance of ∅ 0.10 mm \varnothing 0.10\text{ mm} ∅ 0.10 mm at LMC to Datums A and B.
Limits of Size : MMC = 7.80 mm \text{MMC} = 7.80\text{ mm} MMC = 7.80 mm , LMC = 8.20 mm \text{LMC} = 8.20\text{ mm} LMC = 8.20 mm .
Critical Design Intent : When the hole is drilled at its largest allowable diameter ( 8.20 mm 8.20\text{ mm} 8.20 mm , LMC), the tube wall is at its thinnest permissible baseline. At LMC, the positional tolerance remains strictly 0.10 mm 0.10\text{ mm} 0.10 mm (zero bonus).
Manufactured Condition : Suppose the hole is drilled at ∅ 7.90 mm \varnothing 7.90\text{ mm} ∅ 7.90 mm (leaving extra material on the wall).
Departure from LMC : 8.20 − 7.90 = 0.30 mm 8.20 - 7.90 = 0.30\text{ mm} 8.20 − 7.90 = 0.30 mm (Bonus Tolerance).
Total Allowable Position Tolerance : 0.10 + 0.30 = 0.40 mm 0.10 + 0.30 = 0.40\text{ mm} 0.10 + 0.30 = 0.40 mm .
Because the extra metal in the smaller hole preserves the minimum required wall thickness, the hole axis can shift by an additional 0.30 mm 0.30\text{ mm} 0.30 mm without endangering structural integrity.
5. Functional Design Rationale: Selecting MMC, LMC, or RFS
Selecting the proper material condition modifier is an engineering design decision based on part function, assembly requirements, and inspection economics:
Design Objective Modifier Applied Functional Justification Primary Inspection Method
Clearance & Assembly MMC ( Ⓜ ) Guarantees parts will assemble even in worst-case dimensional and geometric combinations. Allows bonus tolerance as size departs toward LMC. Functional fixed hard gages (Go plug gages, ring gages, multi-pin receiver fixtures).
Minimum Wall Thickness & Strength LMC ( Ⓛ ) Preserves minimum material between a hole and part edge, or between adjacent passages. Prevents breakout, wall collapse, or machining breakthrough. Coordinate Measuring Machines (CMMs), optical vision systems, ultrasonic thickness gages.
Rotational Balance & Precision Alignment RFS (Default) Prevents axis shift across feature size variations. Critical for high-speed rotating turbine shafts, precision press fits, and gear tooth mesh alignment. Dial test indicators, air gages, precision runout centers, multi-axis CMM scanning.
6. Common Exam Traps & Technologist Watchouts
Trap 1: The "Bigger Number = MMC" Fallacy. Candidates frequently look at the upper numerical limit and assume it is MMC. For all internal features (holes, slots, bores), the smaller number is MMC because drilling less metal out of the block leaves maximum material in the part.
Trap 2: "Bonus Tolerance Can Salvage an Out-of-Spec Size." Bonus tolerance applies exclusively to geometric tolerances; it NEVER relaxes limits of size. If a hole specified as ∅ 10.00 − 10.20 mm \varnothing 10.00 - 10.20\text{ mm} ∅ 10.00 − 10.20 mm is drilled at ∅ 9.94 mm \varnothing 9.94\text{ mm} ∅ 9.94 mm , it is undersized and rejected, even if its location is mathematically flawless.
Trap 3: Forgetting the RFS Default. On exam questions showing a feature control frame without a circled M or L, candidates often instinctively compute bonus tolerance. Under Rule #2, absence of a modifier means RFS, and bonus tolerance is strictly zero.
Trap 4: Inverting Bonus Calculations at LMC. At LMC, bonus is earned as the feature departs from the LMC limit toward MMC . For an internal hole, bonus increases as the hole becomes smaller , not larger.