7.1 Parallelism, Perpendicularity, and Angularity

ASME GDTP Senior Level Exam

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1 Introduction & Exam Overview

1.1 Current Exam Facts 1.2 Senior Level vs Technologist and Y14.5 Revisions 1.3 How to Use This Guide and Study Strategy 1.4 The Y14.5-2018 Senior Exam and What Changed from 2009

2 Dimensioning and Symbology

2.1 Y14.5 Dimensioning Rules, Limits, and Fits 2.2 Basic Dimensions and Their Role 2.3 Feature Control Frame Structure and Reading 2.4 GD&T Symbols, Modifiers, and Communication 2.5 Screw Threads, Gears, and Splines 2.6 Angular Surfaces, Tapers, Radii, and Special Tolerance Cases

3 Datum Referencing I: Selection and Precedence

3.1 Functional Datum Feature Selection 3.2 Datum Precedence and Degrees of Freedom 3.3 Datum Targets 3.4 Datum Feature Simulators

4 Datum Referencing II: Modifiers and Shift

4.1 Multiple Datum Features and Datum Reference Frames 4.2 RMB, MMB, and LMB on Datum Features 4.3 Datum Shift Behavior 4.4 Planar vs Datum Feature of Size

5 Datum Referencing III: Setup and Calculations

5.1 Inclined and Translated Datum Features 5.2 Inspection Setup and Datum Establishment 5.3 Datum Calculation Walkthrough 5.4 Customized Datum Reference Frames and Rotational Constraint 5.5 Free State, Restrained Condition, and Nonrigid Parts

6 Form Controls

6.1 Flatness and Straightness 6.2 Circularity and Cylindricity 6.3 Rule #1, Form, and Size

7 Orientation Controls

7.1 Parallelism, Perpendicularity, and Angularity 7.2 Orientation Zones and Material Modifiers 7.3 Avoiding Unnecessary Orientation and Over-Control

8 Location I: Position and Boundaries

8.1 Position Tolerancing and True Position 8.2 Virtual and Resultant Condition 8.3 Bonus Tolerance at MMC and LMC

9 Location II: Application and Modifiers

9.1 Selecting MMC, LMC, and RFS by Function 9.2 Fixed and Floating Fastener Formulas 9.3 Projected Tolerance Zones 9.4 Coordinate Conversion and Appendix B Position Calculations

10 Location III: Patterns and Allocation

10.1 Composite Position Tolerancing 10.2 Patterns, Simultaneous Requirements, and Multiple Segments 10.3 Slots, Tabs, and Tolerance Allocation 10.4 Coaxial Feature Controls, Concentricity, and Symmetry

11 Profile I: Fundamentals and Strategy

11.1 Profile of Line and Surface 11.2 Defining the True Profile 11.3 Datum-Referenced Profile Strategy 11.4 Equal and Unequal Disposition

12 Profile II: Scope and Verification

12.1 All-Around, All-Over, and Limited Scope 12.2 Composite Profile and Coplanarity 12.3 Castings, Weldments, Sheet Metal, and CMM Evaluation 12.4 Combined Controls and Profile as a Refinement

13 Runout Controls

13.1 Circular and Total Runout 13.2 Datum-Axis Simulation and Rotating Parts 13.3 Runout vs Position, Profile, and Form

14 Exam Strategy and Calculations

14.1 Virtual/Resultant Condition and Bonus Formulas 14.2 Datum Shift and Worst-Case Boundary Calculations 14.3 Functional Gaging and Verification 14.4 Test-Day Tactics, Common Traps, and Review

7.1 Parallelism, Perpendicularity, and Angularity

Key Takeaways Explain This Topic AI

Parallelism, perpendicularity, and angularity are the three orientation controls in ASME Y14.5-2009, and each must reference at least one datum — an orientation callout with no datum is invalid.

The tolerance zone for a surface is two parallel planes of width t; the zone for an axis is a cylinder of diameter t (the Ø symbol is required for an axis zone).

Orientation controls angle only, never location; locating a feature is the job of position or profile, and a perpendicularity callout alone does not position a hole.

Perpendicularity and parallelism angles (0° and 90°) are implied by default; angularity requires an explicitly stated basic angle, without which the callout is uninterpretable.

Because position already constrains orientation within its zone, a separate orientation callout refines — it does not duplicate — the orientation already held by position.

Last updated: August 2026

7.1 Parallelism, Perpendicularity, and Angularity

Quick Answer: Orientation controls in ASME Y14.5-2009 — parallelism, perpendicularity, and angularity — relate a feature to a datum reference frame and confine it within a zone of fixed orientation (parallel, 90°, or a basic angle). Unlike form controls, every orientation control must reference at least one datum. The zone for a surface is two parallel planes; the zone for an axis is a cylinder. Orientation controls angle only — location is the job of position or profile, not orientation.

The defining trait: orientation always references a datum

Parallelism , perpendicularity , and angularity are the three orientation controls in ASME Y14.5-2009. They differ in the angle they enforce — 0°, 90°, or a stated basic angle — but they share two traits that set them apart from form controls:

Each one relates the considered feature to at least one datum . A parallelism callout with no datum reference is invalid and uninterpretable.

Each one controls orientation only . They can refine the angle of a feature relative to a datum, but they cannot control the feature's location — that is the role of position or profile.

This is the conceptual boundary the Senior exam probes most: orientation tells a surface or axis which way to point; position or profile tells it where to sit.

Parallelism

Parallelism keeps a surface, axis, or center plane parallel to a datum. The default tolerance zone for a surface is two parallel planes separated by the tolerance value t , oriented parallel to the datum. Every point of the considered surface must lie inside that zone. For an axis, the zone is a cylinder of diameter t whose axis is parallel to the datum. The entire derived median line of the considered feature of size must lie inside the cylinder. Note the diameter symbol: an axis-parallelism callout without Ø is interpreted as a width zone applied to a center plane, not a cylindrical zone about an axis.

Perpendicularity

Perpendicularity holds a feature at 90° to a datum. For a surface, the zone is again two parallel planes separated by t, this time oriented perpendicular to the datum. For an axis, the zone is a cylinder of diameter t whose axis is perpendicular to the datum — the axis must lie entirely inside that cylinder. Because 90° is assumed by default in Y14.5-2009, no basic angle is shown on a perpendicularity callout, and none is needed.

Angularity

Angularity holds a feature at a basic angle other than 0° or 90° to a datum. The basic angle is stated on the drawing with a basic dimension (enclosed in a rectangular frame). The tolerance zone is two parallel planes (or a cylinder, for an axis) oriented at that basic angle to the datum. Without the basic angle the angularity callout is incomplete and uninterpretable — a common trap on Senior questions. The basic angle has no plus-or-minus tolerance of its own; the entire angular uncertainty is held inside the t-wide zone.

Worked example: perpendicularity of an axis

Consider a pin Ø10 ±0.1 with an axis-perpendicularity callout of Ø0.2 to datum A (the face the pin rises from), applied RFS. The cylindrical zone of Ø0.2 is oriented perpendicular to A. The pin's derived median line must lie entirely inside that cylinder. Two facts are worth highlighting:

The zone does not locate the axis — the pin can be anywhere on the face as long as it stands upright within Ø0.2. Location, if it matters, must come from position or a coordinate tolerance.

The Ø0.2 confines the axis, not the surface. Surface irregularity is a separate form/cylindricity concern.

Comparison of the three controls

Control Angle to datum Surface zone Axis zone Basic angle required?

• Parallelism 0° Two parallel planes, width t Cylinder Øt No (0° implied)
• Perpendicularity 90° Two parallel planes, width t Cylinder Øt No (90° implied)
• Angularity Basic angle Two parallel planes, width t Cylinder Øt Yes (basic dimension)
• The Senior-level trap: orientation is not location

A drawing that gives a hole a perpendicularity callout to datum A but no position control does not locate the hole — it only makes the hole stand up straight. If the hole's location matters, position (or profile of a surface) must be added. Conversely, a position callout to A already constrains perpendicularity to A within its cylindrical zone; adding a separate, looser perpendicularity to the same datum adds nothing, and a tighter one refines only the orientation. Recognizing which callout does which job is the heart of section 7.1 and a recurring theme of the Senior exam.