Study guide
14.1 Virtual/Resultant Condition and Bonus Formulas
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
14.1 Virtual/Resultant Condition and Bonus Formulas
Key Takeaways Explain This Topic AI
Virtual condition (VC) is the worst-case mating boundary: for an external feature of size (pin/tab) VC = MMC + position tolerance; for an internal feature (hole/slot) VC = MMC − position tolerance.
Resultant condition (RC) is the opposite worst-case boundary produced by size and geometry: external RC = LMC − (position tolerance + bonus); internal RC = LMC + (position tolerance + bonus).
Bonus tolerance = |actual size − MMC| and only applies when the modifier is MMC (or LMC, in which case use |actual − LMC|); RFS yields zero bonus.
Maximum bonus equals the size tolerance (MMC − LMC), so the largest total position tolerance at LMC equals the stated value plus the full size tolerance.
A functional GO gage is built at VC; the part must assemble to the gage at MMC, which is why VC is the single most-tested calculation on the Senior exam.
Last updated: August 2026
14.1 Virtual/Resultant Condition and Bonus Formulas
Quick Answer: The virtual condition (VC) is the worst-case mating boundary a feature can present to its mate: external VC = MMC + position tolerance , internal VC = MMC − position tolerance . The resultant condition (RC) is the opposite boundary: external RC = LMC − (position tol + bonus) , internal RC = LMC + (position tol + bonus) . Bonus = |actual size − MMC| and is only available when the position control is applied at MMC.
Why VC and RC matter
Every feature of size controlled with a position, profile, or orientation tolerance at MMC generates two extreme boundaries. The virtual condition is the boundary used for assembly verification (and for functional GO gaging); the resultant condition is the boundary used to check minimum wall thickness, edge distance, and the LMC-side limit. On the Senior exam, almost every location or datum-shift calculation reduces to evaluating VC, RC, or bonus, so the sign convention must be automatic.
The master formulas
- Boundary External FOS (pin/tab) Internal FOS (hole/slot)
- MMC Upper size limit (largest) Lower size limit (smallest)
- LMC Lower size limit (smallest) Upper size limit (largest)
- Virtual condition MMC + position tol MMC − position tol
- Resultant condition LMC − (position tol + bonus) LMC + (position tol + bonus)
- Bonus |actual − MMC| (grows as pin shrinks) |actual − MMC| (grows as hole grows)
- Max bonus MMC − LMC = size tolerance MMC − LMC = size tolerance
A useful mnemonic: external adds, internal subtracts for VC; the reverse sign appears on RC. The bonus is always the absolute departure from MMC and is zero at MMC and maximum at LMC .
Worked example — external pin
A pin is dimensioned Ø10 ± 0.2 with position Ø0.1 at MMC to datums A|B|C.
MMC = 10.2, LMC = 9.8, size tolerance = 0.4.
VC = MMC + pos tol = 10.2 + 0.1 = Ø10.3 (the mating hole must clear Ø10.3).
At an actual pin size of Ø10.0 : bonus = |10.0 − 10.2| = 0.2 , so total position tolerance = 0.1 + 0.2 = Ø0.3 .
RC (worst, at LMC with full bonus) = LMC − (pos tol + max bonus) = 9.8 − (0.1 + 0.4) = Ø9.3 (the smallest inner boundary the pin can leave in the part).
The pin's surface must always lie entirely between Ø9.3 (RC inner) and Ø10.3 (VC outer). Any measured pin inside that envelope passes.
Worked example — internal hole
A hole is dimensioned Ø10 ± 0.2 with position Ø0.1 at MMC to datums A|B|C.
MMC = 9.8 (smallest hole), LMC = 10.2 (largest hole), size tolerance = 0.4.
VC = MMC − pos tol = 9.8 − 0.1 = Ø9.7 (a mating pin Ø9.7 will assemble in the worst case — this is the GO gage pin).
At an actual hole size of Ø10.0 : bonus = |10.0 − 9.8| = 0.2 , total position tolerance = 0.1 + 0.2 = Ø0.3 .
RC (worst, at LMC with full bonus) = LMC + (pos tol + max bonus) = 10.2 + (0.1 + 0.4) = Ø10.7 (the largest outer boundary the hole can occupy — used for minimum wall checks).
Common traps
Sign error on RC. Candidates write RC = LMC ± pos tol without the bonus. RC always includes the maximum bonus (the full size tolerance) when evaluated at LMC.
Confusing bonus with datum shift. Bonus is per-feature and grows as that one feature departs from MMC. Datum shift moves the entire datum reference frame; it is not a per-feature bonus (covered in 14.2).
Applying bonus at RFS. If the position frame has no MMC modifier, the default per Y14.5-2009 is RFS , and bonus = 0 . You cannot add a bonus just because the feature has a size tolerance.
Mixing radial/diametral. Position zones are stated as diameters; bonus is also a diameter. When computing a wall-thickness limit, divide the relevant diameters by 2 to use radial values.
Using MMC for an LMC-controlled feature. When the modifier is LMC, swap the roles: bonus = |actual − LMC|, and the functional boundary is the LMC-derived one (often the inner boundary for a hole, used to guarantee minimum material / clearance for a casting).
Senior exam payoff
Roughly a third of the 150 Senior questions involve a calculation or boundary judgment. If you can compute VC, RC, and bonus in under 30 seconds for any feature of size, you have the arithmetic backbone for the Location (25%), Datum (30%), and many Profile (20%) questions. Practice with the table above until the signs are automatic.