Study guide
9.2 Fixed and Floating Fastener 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
9.2 Fixed and Floating Fastener Formulas
Key Takeaways Explain This Topic AI
The floating fastener formula is T = H − F applied to EACH part: both parts have clearance holes and each independently receives the full H − F as its position tolerance.
The fixed fastener formula is T_total = H − F, and this total must be SPLIT between the two parts because one part locates the fastener (threaded hole or press-fit stud) and the other has the clearance hole.
H and F are evaluated at MMC for the worst case: H at the smallest clearance hole (MMC of an internal feature) and F at the largest fastener (MMC of an external feature).
Adding MMC to the position callout lets bonus tolerance grow as the actual clearance hole departs from MMC, which often lets a designer loosen the stated tolerance on the drawing.
Forgetting to split the fixed-fastener tolerance between the two parts is the most common Senior-level error; the result is a part that looks tolerant but will not assemble.
Last updated: August 2026
9.2 Fixed and Floating Fastener Formulas
Quick Answer: For a floating fastener (clearance holes in both mating parts), each part's position tolerance is T = H − F (full value to each part). For a fixed fastener (one part has the threaded/fixed hole, the other has the clearance hole), the total available tolerance is T_total = H − F , and it must be split between the two parts. Use MMC sizes for H and F so the worst case assembles.
The two assembly cases
A fastened joint falls into one of two cases depending on where the fastener is located:
Floating fastener — the fastener (bolt, screw, rivet) passes through clearance holes in both parts . The fastener is not anchored to either part; it floats through both and can shift within each clearance hole. Examples: a bolted flange joint with through-holes in both flanges; a sheet-metal bracket bolted to a frame with clearance holes in both.
Fixed fastener — the fastener is located by one part and the mating part has the clearance hole. The locating part may have a threaded hole (the bolt is threaded into it), a press-fit dowel, or a stud welded in place. Examples: a cover bolted to a cast housing with tapped holes; a dowel pin press-fit into one plate locating a mating plate.
The distinction controls how the position tolerance is distributed.
The floating fastener formula
Both parts have clearance holes of diameter H ; the fastener is diameter F . Each part is allowed to mislocate its hole pattern by some amount and still assemble, because the fastener can shift through both holes. The worst case is when both holes are at MMC (smallest clearance hole, largest fastener). The clearance left over after the fastener fills the hole is H_MMC − F_MMC , and this is the maximum the hole's axis may deviate from true position for that single part . Because each part's clearance is independent, each part gets the full T :
- T_floating (per part) = H_MMC − F_MMC
- Worked example — floating
A bolt of Ø0.25 passes through clearance holes of Ø0.28 in both flange plates. Treat sizes as MMC (no size tolerance given, or use the MMC limit).
T per part = 0.28 − 0.25 = 0.03 .
Each flange receives Ø0.03 position tolerance on its hole pattern.
The fastener can shift up to 0.03 in part A and up to 0.03 in part B; because the shifts are independent, assembly is still guaranteed — the worst case is met when both holes are at MMC, and the formula already accounts for simultaneous mislocation.
The fixed fastener formula
One part has a threaded (or fixed) hole that locates the fastener; the other has a clearance hole. The fastener's position is fixed by the threaded hole's actual location, so the clearance hole must accommodate both the fastener body and the combined mislocation of the two holes. The total clearance H − F must cover the position error of both parts together:
T_total (both parts) = H_MMC − F_MMC
This total must be allocated (split) between the two parts:
T_threaded + T_clearance = H_MMC − F_MMC
If the split is equal, each part gets (H − F)/2 . The split need not be equal — a designer may give more tolerance to the harder-to-machine part and less to the easier one — but the sum is fixed by the formula.
Worked example — fixed
The same Ø0.25 bolt threads into a tapped hole in a housing and passes through a Ø0.28 clearance hole in a cover.
T_total = 0.28 − 0.25 = 0.03 .
Equal split: each part gets Ø0.015 . The tapped hole in the housing is held to Ø0.015; the clearance hole in the cover is held to Ø0.015.
If the cover is stamped (cheap to make accurately) and the housing is cast (harder to hold), the designer might split 0.01 to the cover and 0.02 to the housing — the sum must still equal 0.03.
Why the split matters
The classic Senior trap is to apply the floating formula to a fixed joint, giving each part the full 0.03. The part will pass its individual drawing (each hole pattern is within Ø0.03) but the assembly will bind, because the threaded hole can be 0.03 off in one direction and the clearance hole 0.03 off in the opposite direction — a combined 0.06 mislocation that exceeds the 0.03 clearance. The fixed formula exists precisely to prevent this.
How MMC changes the calculation
The formulas above use H at MMC (smallest hole) and F at MMC (largest fastener) because that is the worst assembly case — least clearance. When the position callout carries an MMC modifier , the stated geometric tolerance is the value at MMC, and bonus tolerance is added as the actual clearance hole grows beyond its MMC (or as the actual fastener shrinks below its MMC):
Stated position tolerance on the clearance hole = (H_MMC − F_MMC) − bonus_already_used. More practically, designers often write the stated tolerance at the MMC limit and let bonus cover normal size variation, so the functional virtual condition stays at H_MMC − F_MMC.
A functional receiver gage sized to the virtual condition (H_MMC − T_stated for an internal feature) will accept parts that assemble at every actual size.
Worked example — fixed with MMC
Cover clearance hole Ø0.28 +0.01/−0 (MMC = 0.28); bolt Ø0.25 ±0.005 (MMC = 0.255). T_total at MMC = 0.28 − 0.255 = 0.025 , split to Ø0.0125 each. If the cover callout is Ø0.0125 at MMC , then a cover hole produced at 0.29 earns a bonus of 0.01 and may have position error up to Ø0.0225 — but the virtual condition stays at 0.28 − 0.0125 = 0.2675, which is still ≥ the fastener's MMC of 0.255, so assembly is guaranteed. The designer can write a smaller stated tolerance and rely on bonus for the typical case.
Formulas table
- Case Features Formula Distribution
- Floating fastener Clearance holes in BOTH parts; fastener passes through T = H − F Each part gets full T
Fixed fastener Threaded/fixed hole in one part; clearance hole in the other T_total = H − F Split between the two parts (T_threaded + T_clearance = H − F)
With MMC modifier Same as above, but position is at MMC Stated T at MMC; bonus = (actual − MMC) for holes Bonus added per part; virtual condition fixed
Senior-level traps
Forgetting to split the fixed-fastener tolerance. This is the single most common error. If both parts of a threaded-joint assembly are toleranced at the full H − F, the assembly will not fit at worst case.
Using LMC or nominal sizes for H and F. The formulas are worst-case and must use H at the smallest clearance hole (MMC) and F at the largest fastener (MMC). Using nominal sizes overstates the available tolerance.
Ignoring bonus when the callout is at MMC. A part that fails the stated tolerance at MMC may pass with bonus; a Senior question may give the actual size and expect you to add the bonus.
Misclassifying the joint. A stud pressed into one plate and passing through a clearance hole in another is a fixed fastener, not a floating one — the stud is located by the press-fit plate. A through-bolt with nuts on both ends, clearance holes in both parts, is floating.
Assuming equal split is mandatory. The split is a design choice; only the sum is fixed. A question may ask which allocation is valid, and any split summing to H − F is acceptable.