3.2 The 14 Geometric Characteristic Symbols, Feature Control Frames, & Special Modifiers

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

3.2 The 14 Geometric Characteristic Symbols, Feature Control Frames, & Special Modifiers

Key Takeaways Explain This Topic AI

The 14 geometric characteristic symbols are organized into five functional families: Form (never permits datums), Orientation (always requires datums), Location (requires datums), Profile (may or may not reference datums), and Runout (always requires a datum axis).

A Feature Control Frame is read strictly left to right across up to five compartments: Compartment 1 dictates the geometric symbol; Compartment 2 defines tolerance magnitude, zone shape (⌀), and feature modifiers; and Compartments 3 through 5 define primary, secondary, and tertiary datums with material boundary modifiers.

Material condition modifiers Ⓜ (MMC) and Ⓛ (LMC) can only be applied to features of size; when placed in datum compartments, they represent Maximum Material Boundary (MMB) and Least Material Boundary (LMB), authorizing datum shift.

ASME Y14.5-2009 introduced essential special modifiers including Unequally Disposed Profile (Ⓤ), Continuous Feature (<CF>), and Independency (Ⓘ), eliminating the need for ambiguous drawing notes.

Projected tolerance zones (Ⓟ) project the tolerance boundary outside the feature by the mating engagement height, preventing fastener tilt in tapped or press-fit holes from interfering with mating clearance holes.

Last updated: September 2026

3.2 The 14 Geometric Characteristic Symbols, Feature Control Frames, & Special Modifiers

Quick Summary: The universal language of Geometric Dimensioning and Tolerancing (GD&T) under ASME Y14.5-2009 is built upon 14 geometric characteristic symbols organized into five distinct functional families: Form , Orientation , Location , Profile , and Runout . Every geometric specification is conveyed through a standardized Feature Control Frame (FCF) containing up to five compartments read strictly from left to right. Mastery of this symbology, the syntax of datum references, and the legal applications of specialized modifiers—such as MMC/MMB , LMC/LMB , Projected Tolerance Zone (Ⓟ) , Unequally Disposed Profile (Ⓤ) , and Tangent Plane (Ⓣ) —is the single most heavily tested subject area on the ASME GDTP Technologist examination.

1. Taxonomy of the 14 Geometric Characteristic Symbols

ASME Y14.5-2009 organizes all geometric controls into five families based on the geometric attribute being controlled and whether datum reference frames are required.

The 14 Symbols Master Classification Table

Family Geometric Characteristic Symbol Datum Requirement Typical Tolerance Zone Shape
Form Straightness — NEVER Permitted Two parallel lines, two parallel planes, or cylindrical zone
Flatness ⏢ NEVER Permitted Two parallel planes
Circularity ○ NEVER Permitted Two concentric circles (radial distance in 2D plane)
Cylindricity ⌭ NEVER Permitted Two concentric cylinders (radial distance in 3D space)
Orientation Perpendicularity ⟂ ALWAYS Required Two parallel planes or cylindrical zone at 90° to datum
Parallelism // ALWAYS Required Two parallel planes or cylindrical zone parallel to datum
Angularity ∠ ALWAYS Required Two parallel planes or cylindrical zone at basic angle to datum
Location Position ⌖ Standard Practice Cylindrical zone or two parallel planes
Concentricity ◎ ALWAYS Required Cylindrical zone centered on datum axis (median points)
Symmetry ⌯ ALWAYS Required Two parallel planes centered on datum center plane (median points)
Profile Profile of a Line ⌒ Optional Two uniform boundary lines (2D cross-section)
Profile of a Surface ⌓ Optional Two uniform boundary envelopes (3D surface)
Runout Circular Runout ↗ ALWAYS Required Two concentric circles along 2D rotational paths
Total Runout ⌰ ALWAYS Required Two coaxial cylinders enclosing 3D surface during rotation
2. In-Depth Analysis of the Five Symbol Families
1. Form Tolerances (Straightness, Flatness, Circularity, Cylindricity)

Core Function : Form controls shape against a feature's own geometry; it determines how much a feature may deviate from a theoretically perfect geometric form.

The Golden Rule of Form : Form controls NEVER reference datums under any circumstance. Form is an intrinsic, standalone property of a feature. Attempting to add a datum reference to a form control frame (e.g., | Flatness | 0.1 | A | ) is an immediate syntax violation on the GDTP exam.

Envelope Rule Integration : In accordance with Rule #1 , form tolerances applied to a surface must always be smaller than the feature's size tolerance.

2. Orientation Tolerances (Perpendicularity, Parallelism, Angularity)

Core Function : Orientation controls the tilt or angular relationship of a surface, center plane, or axis relative to one or more datum planes or axes.

Datum Requirement : Orientation controls ALWAYS require at least one datum reference. An orientation callout without a datum is invalid.

Orientation vs. Location : Orientation controls control tilt, but they never control location . Parallelism ensures a face does not angle relative to datum A, but it does not establish how far that face sits from datum A.

3. Location Tolerances (Position, Concentricity, Symmetry)

Core Function : Location controls establish the permissible variation in the placement of features of size relative to an established Datum Reference Frame (DRF).

Position (⌖) : The workhorse of GD&T. Controls the location and orientation of centerlines, axes, and center planes relative to basic dimensions and datums.

Concentricity (◎) & Symmetry (⌯) : Specialty controls that govern the median points of diametrically opposed elements (for concentricity) or symmetrically opposed elements (for symmetry). Unlike position, they control median point derivation rather than axis/boundary envelopes and cannot carry material condition modifiers (they apply strictly RFS).

4. Profile Tolerances (Profile of a Line, Profile of a Surface)

Core Function : Profile defines a uniform three-dimensional boundary envelope along a true profile established by basic dimensions.

Datum Flexibility : Profile controls may or may not reference datums :

Without Datums : Profile acts purely as a form control (e.g., controlling the curvature of an aesthetic surface against itself).

With Datums : Profile can simultaneously control size , form , orientation , and location , making it the most versatile control in Y14.5.

5. Runout Tolerances (Circular Runout, Total Runout)

Core Function : Runout controls composite surface variations (eccentricity, out-of-roundness, waviness, taper) when a part is rotated 360° about a datum axis.

Datum Requirement : Runout ALWAYS requires a datum axis. Datums must be established by centers, cylindrical diameters, or coaxial bearing journals.

3. Feature Control Frame (FCF) Architecture & Reading Order

A Feature Control Frame (FCF) is a rectangular compartmented box that states the geometric requirements for a feature. It is read strictly from left to right across up to five distinct compartments. Architecture of a Feature Control Frame

+---------+------------------+----------+----------+----------+
| Comp 1 | Comp 2 | Comp 3 | Comp 4 | Comp 5 |
| Geometric| Tolerance Value | Primary |Secondary | Tertiary |
| Symbol | & Modifiers | Datum | Datum | Datum |
+---------+------------------+----------+----------+----------+
| ⌖ | ⌀ 0.25 Ⓜ Ⓟ 14 | A Ⓜ | B | C |
+---------+------------------+----------+----------+----------+
Detailed Breakdown of FCF Compartments

Compartment 1: Geometric Characteristic Symbol : Identifies which of the 14 characteristics is being controlled (e.g., Position, Flatness, Profile).

Compartment 2: Tolerance Compartment :

Zone Shape Prefix : The diameter symbol ( ∅ \varnothing ∅ ) precedes the numerical value if the tolerance zone is cylindrical or diametral. If the zone is bounded by two parallel planes (e.g., on a flat surface or width), the diameter symbol is omitted.

Tolerance Value : The numerical magnitude of the tolerance zone (e.g., 0.25 or .010 ).

Material Condition Modifier : Applicable only to features of size: M ◯ \textcircled{\tiny M} M ◯ for Maximum Material Condition, L ◯ \textcircled{\tiny L} L ◯ for Least Material Condition. Under Rule #2 , if no modifier is present, Regardless of Feature Size ( RFS ) automatically applies.

Special Zone Modifiers : Supplemental symbols such as Projected Tolerance Zone ( P ◯ \textcircled{\tiny P} P ◯ ), Unequally Disposed Profile ( U ◯ \textcircled{\tiny U} U ◯ ), Tangent Plane ( T ◯ \textcircled{\tiny T} T ◯ ), or Free State ( F ◯ \textcircled{\tiny F} F ◯ ).

Compartment 3: Primary Datum Reference : Identifies the primary datum feature letter (e.g., A ). Can carry a material boundary modifier ( M ◯ \textcircled{\tiny M} M ◯ for MMB, L ◯ \textcircled{\tiny L} L ◯ for LMB, or default RMB).

Compartment 4: Secondary Datum Reference : Constrains remaining degrees of freedom after the primary datum is established.

Compartment 5: Tertiary Datum Reference : Constrains the final rotational or translational degree of freedom.

Critical Rule: The sequence of datums represents the order of precedence . An FCF reading | A | B | C | is physically and mathematically different from | B | A | C | because the first datum contacts the simulator with highest priority, locking its respective degrees of freedom first.

4. Comprehensive Guide to Modifiers & Special Symbols

ASME Y14.5-2009 features a rich vocabulary of modifying symbols that clarify design intent and unlock manufacturing cost savings.

Master Modifiers Reference Table

Symbol / Notation Name FCF Compartment / Location Applicable Feature Type Standard Meaning & Mechanical Function

Ⓜ Maximum Material Condition (MMC) Comp 2 (Tolerance) Features of Size only Authorizes bonus tolerance as feature departs from MMC toward LMC.

Ⓜ Maximum Material Boundary (MMB) Comp 3, 4, 5 (Datums) Datum Features of Size Authorizes datum shift as datum feature departs from MMB.

Ⓛ Least Material Condition (LMC) Comp 2 (Tolerance) Features of Size only Preserves critical material (e.g., wall thickness); authorizes bonus tolerance as feature approaches MMC.

Ⓛ Least Material Boundary (LMB) Comp 3, 4, 5 (Datums) Datum Features of Size Authorizes datum shift relative to the least material boundary.

Ⓟ Projected Tolerance Zone Comp 2 (following tolerance) Threaded / press-fit holes Projects tolerance zone outside the hole by a specified height to account for fastener tilt.

Ⓤ Unequally Disposed Profile Comp 2 (following profile value) Profile surfaces First number = total zone width; second number = amount adding material (outside true profile).

Ⓣ Tangent Plane Comp 2 (following tolerance) Planar surfaces in orientation Controls a theoretical plane contacting the surface high points, ignoring local valley depressions.

Ⓕ Free State Comp 2 (following tolerance/modifier) Non-rigid features Specifies tolerance applies in unrestrained state without inspection clamping forces.

[I] Independency Symbol Beside size dimension Features of Size Exempts feature of size from Rule #1 (Taylor Principle); size and form vary independently.

<CF> Continuous Feature Beside dimension or above FCF Multiple interrupted features Treats multiple co-planar surfaces or co-axial diameters as a single continuous geometric feature.

ST Statistical Tolerance Comp 2 or adjacent to callout Any toleranced feature Indicates tolerance is based on statistical process capability rather than 100% boundary limits.

○ (bend) All-Around Symbol Circle on leader elbow Profile controls Indicates profile tolerance applies continuously around entire 2D perimeter shown in view.

◎ (bend) All-Over Symbol Double circle on leader elbow Profile controls Indicates profile tolerance applies across all 3D exterior and interior surfaces of the part.

↔ \leftrightarrow ↔ Between Symbol Beneath FCF (e.g., A ↔ B A \leftrightarrow B A ↔ B ) Profile controls Designates exact segment boundary between point A and point B where profile applies.

5. Detailed Review of High-Impact Modifiers
Projected Tolerance Zone (Ⓟ)

When a threaded hole or press-fit dowel hole receives a mating bolt or pin, any angular tilt of the hole inside the component becomes magnified as the fastener extends into the mating part. A standard positional tolerance zone applies only within the depth of the tapped hole. The projected tolerance zone symbol (Ⓟ) projects the cylindrical tolerance zone outside the hole face by a specified projection height (e.g., | ⌖ | ⌀ 0.25 Ⓜ Ⓟ 15 | A | B | C | ). This ensures that the fastener centerline remains within tolerance throughout the entire thickness of the mating component.

Unequally Disposed Profile (Ⓤ)

Introduced in ASME Y14.5-2009 Section 8.3.1.2 to eliminate confusing phantom-line callouts, the Ⓤ modifier specifies non-symmetric profile zones. In the callout | ⌓ | 1.0 Ⓤ 0.3 | A | B | :

The first value ( 1.0 ) defines the total width of the tolerance zone envelope.

The value following the Ⓤ symbol ( 0.3 ) defines the portion of the tolerance zone that adds material (disposed outward from the true profile).

The remaining balance ( 1.0 − 0.3 = 0.7 1.0 - 0.3 = 0.7 1.0 − 0.3 = 0.7 ) extends into the part material ( subtracting material ).

If the callout reads | ⌓ | 1.0 Ⓤ 0 | , the tolerance is completely unilateral inside the material. If it reads | ⌓ | 1.0 Ⓤ 1.0 | , it is completely unilateral adding material.

Tangent Plane (Ⓣ)

When applied to an orientation tolerance on a planar surface (e.g., | // | 0.2 Ⓣ | A | ), the tangent plane symbol (Ⓣ) dictates that the tolerance applies to a theoretical plane contacting the high points of the manufactured surface. This permits minor localized surface depressions, waviness, or pitting, so long as the plane established by the high contact points remains parallel to the datum.

6. Step-by-Step Methodology: How to Unpack Any Feature Control Frame

When confronted with an FCF on the GDTP Technologist exam, execute this rigorous five-step decoding protocol:

Step 1: Identify the Geometric Characteristic & Family : Look at Compartment 1. Is it Form, Orientation, Location, Profile, or Runout? Immediately verify datum legality: if it is a Form symbol and contains datums, it is an invalid callout.

Step 2: Decode the Tolerance Zone : Look at Compartment 2. Is there a diameter symbol ( ∅ \varnothing ∅ )? If yes, the zone is cylindrical (controlling an axis). If not, the zone is bounded by two parallel planes. Read the numerical tolerance value.

Step 3: Check for Feature Modifiers : Look for M ◯ \textcircled{\tiny M} M ◯ , L ◯ \textcircled{\tiny L} L ◯ , P ◯ \textcircled{\tiny P} P ◯ , U ◯ \textcircled{\tiny U} U ◯ , or T ◯ \textcircled{\tiny T} T ◯ in Compartment 2. If M ◯ \textcircled{\tiny M} M ◯ is present, calculate bonus tolerance as the feature departs from MMC. If omitted, enforce RFS per Rule #2.

Step 4: Establish the Datum Reference Frame : Parse Compartments 3, 4, and 5 in strict order of precedence (Primary → \to → Secondary → \to → Tertiary). Note any material boundary modifiers ( M ◯ \textcircled{\tiny M} M ◯ for MMB or L ◯ \textcircled{\tiny L} L ◯ for LMB) that authorize datum shift.

Step 5: Inspect Leader Attachment & Application : Check where the leader line points. If attached directly to a surface, it controls that surface. If attached to a size dimension, dimension line, or diameter callout, it controls a feature of size (its axis or median plane), making Rule #1 and material condition modifiers applicable.

7. Critical Exam Traps in Symbology & FCF Syntax

Form Controls with Datums : A frequent trick question. Straightness, Flatness, Circularity, and Cylindricity NEVER use datums.

Illegal Diameter Symbol (⌀) : Placing a diameter symbol in Compartment 2 for a planar surface or width feature (e.g., | // | ⌀ 0.2 | A | on a flat face) is an invalid callout. The diameter symbol is permitted only when the tolerance zone is cylindrical or spherical ( S ∅ S\varnothing S ∅ ).

MMC/LMC Modifiers on Planar Surfaces : Placing M ◯ \textcircled{\tiny M} M ◯ or L ◯ \textcircled{\tiny L} L ◯ in Compartment 2 when controlling a single planar surface is illegal. Planar surfaces have no size limits and cannot have a maximum material condition. (MMC is legal on flatness only when attached to a thickness dimension controlling a derived median plane).

Confusing Concentricity (◎) with Position (⌖) or Runout (↗) : Concentricity does not control axis runout or surface wobble; it controls the median points of diametrically opposed surface points. It cannot use M ◯ \textcircled{\tiny M} M ◯ .