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8.2 Virtual and Resultant Condition

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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

8.2 Virtual and Resultant Condition

Key Takeaways Explain This Topic AI

Virtual condition (VC) is the worst-case mating boundary a feature can occupy; it is the boundary used for assembly clearance checks and functional gaging.

For an external feature (pin/boss) at MMC with a position tolerance t, VC = MMC + t; for an internal feature (hole) at MMC, VC = MMC − t.

Resultant condition (RC) is the worst-case boundary on the opposite end of the size range from virtual condition; it is used for minimum wall thickness and minimum material checks.

For a pin at MMC, RC = LMC − (t + bonus at LMC); for a hole at MMC, RC = LMC + (t + bonus at LMC), where bonus at LMC = (MMC − LMC) for the position calculation.

VC and RC bound the entire envelope of where the feature's surface can lie; any produced feature must have its surface inside the RC boundary and outside the VC boundary (for mating).

Last updated: August 2026

8.2 Virtual and Resultant Condition

Once position tolerancing and the material condition modifier are in place, two worst-case boundaries fall out of the math: virtual condition (VC) — the mating boundary used for assembly and functional gaging — and resultant condition (RC) — the boundary on the opposite side used for wall thickness and minimum material. Senior exam questions routinely ask you to compute both for a pin or a hole.

Virtual Condition (VC)

Virtual condition is the boundary generated by the collective effect of size and the position (or other geometric) tolerance at the stated material condition. It is the worst-case mating boundary : the boundary the feature can never violate while still being in-spec, and the boundary a mating part must clear.

The VC formulas depend on whether the feature is external (pin, boss, tab) or internal (hole, slot):

  • Feature At Virtual Condition
  • External (pin) MMC VC = MMC + t
  • Internal (hole) MMC VC = MMC − t
  • External (pin) LMC VC = LMC − t
  • Internal (hole) LMC VC = LMC + t

Where t is the position tolerance value in the FCF.

For an external feature at MMC , the pin at its largest (MMC) with the maximum allowed position error produces the largest mating boundary — that's the worst case for the hole it has to fit into, so the two worst-case effects add: VC = MMC + t.

For an internal feature at MMC , the hole at its smallest (MMC) with the maximum position error produces the smallest effective hole — the worst case for the pin that has to pass through it, so the position eats into the hole: VC = MMC − t.

Resultant Condition (RC)

Resultant condition is the boundary at the other end of the size range — the boundary generated by the feature at the opposite material condition plus the position tolerance (and any bonus available there). RC is used for minimum wall thickness , minimum material between features, and similar calculations.

For a feature controlled at MMC, the RC formulas are:

  • Feature Controlled at Resultant Condition
  • External (pin) MMC RC = LMC − (t + bonus_at_LMC)
  • Internal (hole) MMC RC = LMC + (t + bonus_at_LMC)

Where bonus_at_LMC is the bonus tolerance available when the feature is at LMC — for an MMC-controlled feature, bonus_at_LMC = |MMC − LMC| = the full size tolerance range.

Why VC and RC Are Different Boundaries

VC fixes the mating boundary — it is the worst case for assembly, computed from the small end of the size range plus the worst position. RC fixes the opposite boundary — it is the worst case for material left between the feature and an edge or another feature, computed from the large end of the size range plus the worst position plus the bonus available there.

A produced in-spec feature has its actual mating surface somewhere between RC and VC. For a pin, VC is the larger, outer boundary and RC the smaller, inner one, so the surface lies inside VC and outside RC . For a hole, VC is the smaller boundary and RC the larger one, so the surface lies outside VC and inside RC — the VC gage pin passes through, and the hole never opens beyond RC. Wall-thickness problems use RC; assembly problems use VC.

Using VC for Gaging and Assembly

Functional gaging is built on VC. A Go gage for a hole at MMC has a pin of diameter = VC; if the gage pin enters the hole, the hole's VC is respected (it can assemble). For a pin at MMC, the Go gage is a ring of bore = VC; if the pin passes the ring, the pin's VC is respected. Because VC is the worst-case mating boundary, designing the mating part to clear VC guarantees assembly.

Worked Example 1: Pin at MMC

Pin specified ⌀10.0 ± 0.2 with position ⌀0.3 at MMC to A | B | C.

MMC = 10.2 (largest pin), LMC = 9.8 (smallest pin), size tolerance range = 0.4.

Virtual condition = MMC + t = 10.2 + 0.3 = ⌀10.5 . This is the worst-case mating boundary; a hole must be at least 10.5 to guarantee the pin fits.

Bonus at LMC = MMC − LMC = 0.4. Effective position zone at LMC = 0.3 + 0.4 = 0.7.

Resultant condition = LMC − (t + bonus_at_LMC) = 9.8 − 0.7 = ⌀9.1 . This is the smallest the pin's effective boundary can be on the material side; use it for minimum wall thickness from the pin's outer surface to an edge.

Worked Example 2: Hole at MMC

Hole specified ⌀12.0 ± 0.1 with position ⌀0.2 at MMC to A | B | C.

MMC = 11.9 (smallest hole), LMC = 12.1 (largest hole), size tolerance range = 0.2.

Virtual condition = MMC − t = 11.9 − 0.2 = ⌀11.7 . This is the worst-case mating boundary; a pin must be at most 11.7 to guarantee it passes through.

Bonus at LMC = MMC − LMC magnitude = 0.2. Effective position zone at LMC = 0.2 + 0.2 = 0.4.

Resultant condition = LMC + (t + bonus_at_LMC) = 12.1 + 0.4 = ⌀12.5 . This is the largest the hole's effective boundary can be on the material side; use it for minimum wall thickness from the hole's inner surface to an edge or to a neighboring feature.

Formulas Table (MMC-controlled features)

  • Quantity External (pin) Internal (hole)
  • MMC Largest size Smallest size
  • LMC Smallest size Largest size
  • Virtual condition MMC + t MMC − t
  • Bonus at LMC MMC − LMC LMC − MMC (absolute)
  • Resultant condition LMC − (t + bonus_at_LMC) LMC + (t + bonus_at_LMC)
  • Senior-Level Trap: Wrong Sign on the Hole VC

The most common Senior exam mistake on VC is treating a hole like a pin. A hole's VC is smaller than its MMC , because the worst case for mating is the smallest effective hole — the position tolerance eats into it. If you add the position tolerance to a hole's MMC, you have computed the wrong boundary (you've moved toward RC instead of VC). Memorize: internal features subtract at MMC, external features add at MMC.