GD&T Position Tolerancing Calculations — Questions and Answers

Question 1: A hole has a position tolerance of ⌀0.4 at MMC. The actual hole diameter is 10.3 mm and MMC is 10.0 mm. What is the total allowable position tolerance?

⌀0.4
⌀0.7 (Correct answer)
⌀0.3
⌀1.0

Correct answer: ⌀0.7

At MMC the tolerance is ⌀0.4; the hole is 0.3 mm larger than MMC, so bonus tolerance adds 0.3, giving ⌀0.7 total.

Question 2: For a pattern of four holes, the True Position is defined by basic dimensions from datum A (primary), B (secondary), and C (tertiary). Which datum controls orientation of the pattern?

Datum A (Correct answer)
Datum B
Datum C
All three equally

Correct answer: Datum A

The primary datum (A) controls orientation — it establishes the first degree of constraint, typically perpendicularity or parallelism.

Question 3: A shaft pin has a position tolerance of ⌀0.5 at LMC. The actual pin diameter is 12.0 mm and LMC is 12.3 mm. What bonus tolerance is available?

⌀0.0
⌀0.3 (Correct answer)
⌀0.8
⌀0.2

Correct answer: ⌀0.3

At LMC, bonus tolerance equals the amount the actual size departs from LMC: 12.3 − 12.0 = 0.3 mm added to the stated ⌀0.5.

Question 4: The formula for converting a Cartesian position deviation (Δx, Δy) to a diametral position error is:

Δx + Δy
√(Δx² + Δy²)
2√(Δx² + Δy²) (Correct answer)
(Δx² + Δy²)

Correct answer: 2√(Δx² + Δy²)

The diametral true-position error = 2 × √(Δx² + Δy²), because the cylindrical tolerance zone is centered on true position.

Question 5: A hole center is measured at X = 25.08 mm and Y = 15.06 mm. Basic dimensions are X = 25.00 and Y = 15.00. What is the diametral position error?

⌀0.14
⌀0.20
⌀0.10 (Correct answer)
⌀0.28

Correct answer: ⌀0.10

Δx = 0.08, Δy = 0.06; radial error = √(0.08² + 0.06²) = √(0.01) = 0.10; diametral = 2 × 0.05 = ⌀0.10.

Question 6: When RFS (Regardless of Feature Size) is applied to a position tolerance, bonus tolerance is:

Equal to the size tolerance
Half the size tolerance
Not applicable — no bonus is allowed (Correct answer)
Added automatically by the inspector

Correct answer: Not applicable — no bonus is allowed

RFS means the geometric tolerance applies at every actual feature size with no bonus; the tolerance value is fixed.

Question 7: A composite position callout has an upper segment of ⌀0.8 and a lower segment of ⌀0.2. What does the lower segment control?

Location of the pattern from the datums
Feature-to-feature spacing within the pattern (Correct answer)
Orientation only, not location
Profile of the hole surface

Correct answer: Feature-to-feature spacing within the pattern

The lower (FRTZF) segment of a composite callout controls feature-to-feature relationship (spacing/orientation) within the pattern, not its location from external datums.

Question 8: A hole is located at basic X = 40.00, Y = 30.00. The CMM measures the hole axis at X = 40.05, Y = 29.96. What is the diametral position error?

⌀0.064
⌀0.128 (Correct answer)
⌀0.090
⌀0.032

Correct answer: ⌀0.128

Δx = 0.05, Δy = 0.04; radial = √(0.0025 + 0.0016) = √0.0041 ≈ 0.064; diametral = 2 × 0.064 ≈ ⌀0.128.

Question 9: What does the term 'virtual condition' mean for an internal feature (hole) controlled with position at MMC?

MMC size plus the position tolerance
MMC size minus the position tolerance (Correct answer)
LMC size plus the position tolerance
The actual measured size of the hole

Correct answer: MMC size minus the position tolerance

For an internal feature, virtual condition = MMC size − position tolerance, representing the worst-case boundary for assembly.

Question 10: A pin (external feature) has MMC = 12.0 mm and a position tolerance of ⌀0.3. What is its virtual condition?

11.7 mm
12.3 mm (Correct answer)
12.0 mm
11.85 mm

Correct answer: 12.3 mm

For an external feature, virtual condition = MMC + position tolerance = 12.0 + 0.3 = 12.3 mm.

Question 11: Projected tolerance zone is specified because:

It eliminates the need for datum references
It controls the zone where a fastener extends outside the part, preventing interference at assembly (Correct answer)
It applies the tolerance regardless of feature size
It converts the zone from cylindrical to conical

Correct answer: It controls the zone where a fastener extends outside the part, preventing interference at assembly

A projected tolerance zone extends the positional control above the hole to where mating fasteners or studs will reside, preventing angular stack-up issues.

Question 12: If a position callout reads ⌀0.25 (M) with a projected tolerance of 15 mm, what does '15' represent?

The diameter of the tolerance zone
The depth of the hole
The minimum projection height above the part surface (Correct answer)
The number of features in the pattern

Correct answer: The minimum projection height above the part surface

The projected tolerance zone height (15 mm) specifies how far the cylindrical zone extends beyond the part surface to capture fastener axis deviation.

Question 13: A zero tolerance at MMC callout (⌀0.000 (M)) means:

The feature must be perfect regardless of size
The entire size tolerance becomes available as bonus position tolerance when at actual size (Correct answer)
No positional variation is permitted at any size
The feature must be measured at exactly MMC

Correct answer: The entire size tolerance becomes available as bonus position tolerance when at actual size

With ⌀0.000 at MMC, there is no fixed tolerance; all allowable variation comes exclusively from bonus tolerance as the feature departs from MMC.

Question 14: Which statement correctly describes the 'inner boundary' of a hole controlled with position at MMC?

LMC size plus position tolerance
MMC size minus position tolerance (Correct answer)
LMC size minus position tolerance
Actual size plus position tolerance

Correct answer: MMC size minus position tolerance

The inner boundary (worst-case minimum size) = MMC − position tolerance, which equals the virtual condition for an internal feature.

Question 15: In a 3D tolerance stack, three features contribute ±0.10, ±0.15, and ±0.20 positional deviations along the same axis. What is the worst-case total deviation?

±0.20
±0.45 (Correct answer)
±0.30
±0.25

Correct answer: ±0.45

Worst-case (arithmetic) stack = 0.10 + 0.15 + 0.20 = ±0.45 mm along that axis.

Question 16: Using RSS (Root Sum of Squares) for the same three deviations (±0.10, ±0.15, ±0.20), the statistical tolerance is approximately:

±0.45
±0.27 (Correct answer)
±0.35
±0.18

Correct answer: ±0.27

RSS = √(0.10² + 0.15² + 0.20²) = √(0.01 + 0.0225 + 0.04) = √0.0725 ≈ ±0.27 mm.

Question 17: A pattern of 6 holes must assemble with 6 clearance fasteners. MMC of holes = 10.0 mm, fastener MMC = 9.6 mm. Using the fixed fastener formula, the position tolerance is:

⌀0.2
⌀0.4 (Correct answer)
⌀0.8
⌀0.6

Correct answer: ⌀0.4

Fixed fastener tolerance = (MMC_hole − MMC_fastener) / 1 = 10.0 − 9.6 = 0.4; split between two mating parts gives ⌀0.2 each, but for a single part: ⌀0.4.

Question 18: For a floating fastener assembly, the position tolerance formula is:

T = H − F
T = (H − F) / 2 (Correct answer)
T = H + F
T = H / F

Correct answer: T = (H − F) / 2

Floating fastener formula: each part gets T = (H_MMC − F_MMC) / 2, splitting the clearance equally between both mating parts.

Question 19: A true position callout without any modifier defaults to which condition under ASME Y14.5-2018?

MMC
LMC
RFS (Correct answer)
Projected

Correct answer: RFS

Under ASME Y14.5-2018, RFS is the default implied condition when no modifier symbol (M or L) is shown.

Question 20: A position tolerance is given as ⌀0.5 with datum B at MMC. If datum feature B (a pin) measures 14.8 mm and its MMC is 15.0 mm, what is the datum shift available?

0.0 mm
0.1 mm
0.2 mm (Correct answer)
0.4 mm

Correct answer: 0.2 mm

Datum shift = MMC_datum − actual_datum = 15.0 − 14.8 = 0.2 mm, which may be used to relax the positional requirement.

Question 21: A bolt circle of 8 holes equally spaced on a ⌀100 mm bolt circle has a position tolerance of ⌀0.3. What basic angular spacing is used between adjacent holes?

30°
45° (Correct answer)
40°
60°

Correct answer: 45°

360° ÷ 8 holes = 45° basic angular spacing between each adjacent hole on the bolt circle.

GD&T Position Tolerancing Calculations

A hole has a position tolerance of ⌀0.4 at MMC.
The actual hole diameter is 10.3 mm and MMC is 10.0 mm.
What is the total allowable position tolerance?

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