Tapped Hole to Clearance Hole Stackup — Rectangular Pattern

The assembly, exploded along its axis. From the top: the bolt (threaded end first), a washer, two clearance plates, and the tapped base the bolt threads into. The clearance plates have holes larger than the bolt; the base is tapped to the bolt thread.

1. The problem this solves

On the drawing, every hole is centred and everything lines up. In real parts it never does. The clearance hole is drilled a fraction of a millimetre off position. The tapped hole is cut slightly off its own position. The bolt is not perfectly straight. Each error is tiny — but the bolt has to pass through a misaligned clearance hole and thread into a misaligned tapped hole at the same time, so the errors stack. Push them far enough and the bolt binds in the clearance hole or misses the threads entirely.

This module covers holes positioned in X/Y coordinates (the rectangular method). For holes on a bolt circle, use the Tapped Circular module instead.

2. What makes a tapped stackup different

In a clearance-to-clearance joint, the bolt passes through every plate and a nut closes the other end. Every plate is the same kind of obstacle — a hole the bolt must clear — and only the tightest, most misaligned hole matters.

A tapped joint changes two things, because the bottom part anchors the bolt instead of letting it slide through:

• The gap is shared, not pooled. Instead of comparing against the clearance holes alone, the available radial gap is split equally between the clearance holes and the tapped bore.
• A new contributor appears: projection tolerance. Because the tapped hole pins one end of the bolt, any position error there tilts the bolt, and the tilt grows as the bolt projects up through the stack — a lever arm. This is the defining feature of a tapped stackup and has no equivalent in clearance-to-clearance analysis.

Assembled half-section with the key dimensions. The bolt spans the washer and clearance plates (maxProjection) and then bites into the tapped base (minEngagement). Bolt length L = maxProjection + minEngagement, the relationship the projection formula depends on.

3. The five inputs that drive the result

Five quantities feed the calculation. Once each is clear, the rest is arithmetic.

3a. Hole diameter and EBT

Every clearance hole has a nominal diameter and a tolerance. EBT (Equal Bilateral Tolerance) is the full permitted range: an EBT of 0.20 mm on a 10.50 mm hole means 10.30 to 10.70 mm. The worst case for assembly is the smallest hole — least room for the bolt — so the calculation always uses the minimum size as its base.

Radial clearance at a clearance hole. Left (worst case): every tolerance pushes the bolt to one wall, so the whole gap collects on the far side and nothing is left to spare. Right (nominal): the bolt is centred and the mean gap is half the difference between the effective hole diameter and the bolt diameter.

3b. Positional tolerance (X and Y)

A correctly sized hole in the wrong place is still a problem. The rectangular method controls how far the hole centre may drift in X and, separately, in Y. The worst shift is the diagonal — maximum X and maximum Y at once — combined with Pythagoras:

This applies to both the clearance holes and the tapped hole — each carries its own positional tolerance.

3c. Coating thickness

Paint, plating, or coating builds up on the bore wall and shrinks the usable diameter. Because it coats both sides, a 0.05 mm coating removes 0.10 mm of diameter:

The tapped hole is used as-is — tapped holes are normally not coated after machining.

3d. Bolt camber

A long bolt is never perfectly straight; it bows slightly and presses on one side of the clearance hole as it tries to straighten. The module estimates this with the same empirical formula as the clearance module:

3e. Projection tolerance — the one unique to tapped joints

This is the concept that defines a tapped stackup. When the tapped hole sits off true position, the bolt must tilt to thread into it. That small tilt at the base is magnified as the bolt rises through the stack: the thread engagement is the fulcrum, the shank is the lever, and the clearance hole is where the displacement lands.

The lever-arm effect. A small position error at the tapped hole (the fulcrum) becomes a large sideways displacement at the clearance plate. The displacement scales with the ratio of maxProjection to minEngagement — a longer stack or less thread engagement makes it worse.

4. Defining the clearance

In a tapped joint the bolt meets two kinds of bore — clearance holes in the upper plates and the tapped bore in the base — and the available radial gap is split equally between them:

The 50/50 split reflects that the bolt can shift against either bore. Using the smallest effective clearance hole for the worst-case base captures the tightest interface in the joint.

The pass/fail limit is the maximum fastener diameter, not the nominal — a bolt at its largest OD in the tightest hole is the harshest realistic combination. That is stricter than the clearance-to-clearance module, which checks against nominal.

5. Worst-case calculation, step by step

Worst-case analysis assumes every tolerance hits its most unfavourable extreme simultaneously. It is the most conservative method: if the joint passes worst-case, every possible build works.

Example values: two clearance plates (each 6 mm ±0.1 mm), M10 bolt 40 mm long, zinc coating 0.012 mm, washer 2 mm.

Step 1 — Effective hole diameter (each clearance plate)

Step 2 — EBT contribution (radial half-values throughout)

Step 3 — Position contribution (each clearance plate)

Step 4 — Tapped-hole position contribution

Step 5 — Projection tolerance

Step 6 — Bolt camber

Step 7 — Sum all contributors

Step 8 — Compare against the mean-gap base

A negative minimum gap means real, in-tolerance combinations exist where the bolt will not assemble. Bolt camber is the dominant contributor here (about 65% of the variance). The design needs work.

6. The RSS method — a realistic estimate

Worst-case assumes every tolerance lands at its extreme at once. Across thousands of assemblies that practically never happens. RSS (Root Sum of Squares) treats each contributor as an independent random variable and combines them as the square root of the sum of squares:

RSS variation (0.382 mm) is far below the worst-case figure (0.827 mm). Converting to a yield with a z-score:

So the joint is worst-case UNSAFE yet about 99.97% likely to assemble. Whether that is acceptable depends on the application: a lifting-equipment joint should be worst-case SAFE; a non-critical cover plate at 99.97% may be fine.

Worst-case range (red) versus RSS range (green), both centred on the mean gap. The RSS range is always narrower. The dashed red line is the pass/fail limit (bolt max diameter). The worst-case band crosses it; the RSS band does not — which is why yield is high even though worst-case fails.

7. Reading the contributor chart

The tool ranks each tolerance source by its share of total RSS variance — each contributor's term squared, divided by the sum of all terms squared. A longer bar means that source is eating more of the budget.

Contributor breakdown for the two-plate example above. Bolt camber dominates, with projection tolerance and tapped-hole position the smallest shares. Projection tolerance is unique to tapped joints — it never appears in a clearance-to-clearance analysis.

Camber and projection tolerance are usually the top contributors in a tapped stackup. That tells you where effort pays off: shortening the bolt, tightening the tapped-hole position, or increasing thread engagement moves the result far more than tightening clearance-hole EBTs.

8. Understanding your results

Result field	What it means
Min gap (worst-case)	Smallest possible clearance with every tolerance at its worst. Negative means some builds fail.
Max gap (worst-case)	Most clearance available. Useful for assembly planning, rarely the design driver.
Status: SAFE / UNSAFE	SAFE: even the worst combination clears the bolt. UNSAFE: at least one combination fails.
Statistical yield %	Probability a random build passes, under RSS assumptions and a normal distribution.
maxProjection	Worst-case stack the bolt spans (plates + washer). Confirm the bolt is long enough to reach the tapped hole.
minEngagement	Minimum thread engagement. Below ~1× bolt diameter, projection tolerance is inflated and the result is unreliable.

9. The GD&T connection

This module uses rectangular X/Y positional tolerances — classical coordinate dimensioning. Modern drawings often use GD&T (ASME Y14.5) instead. Here is how to bridge the two.

Converting a position callout to X/Y

GD&T controls position with a position symbol in a feature control frame, specifying a cylindrical tolerance zone — e.g. ⌀0.30 mm means the hole centre must lie within a 0.30 mm-diameter cylinder around true position. To use it here:

This is conservative: a round zone allows about 41% more area than the square zone it maps to. Using the GD&T value directly keeps you on the safe side.

Bonus tolerance at MMC

GD&T allows extra position tolerance as a hole grows past its smallest size (MMC). A larger hole has more room, so more position error is permitted. For this module, enter the position tolerance at the worst-case (MMC, smallest) hole size to stay conservative; the Datum Shift module handles full bonus budgeting.

10. Fixing a failing stackup

If the result is UNSAFE or the yield is low, use the contributor chart and start with the biggest bar — changing a small contributor barely moves the result.

Change	Effect	Impact
Shorten the bolt	Cuts camber and maxProjection, raises minEngagement — three wins at once	High
Tighten tapped-hole position	Reduces projection tolerance (scales linearly)	High
Increase thread engagement / deeper tap	Raises minEngagement, shrinking projection tolerance inversely	High
Increase clearance-hole diameter	More mean gap to spend	Medium
Tighten clearance-hole position	Less position contribution per plate	Medium
Remove the washer	Lowers maxProjection directly	Medium
Reduce plate-thickness tolerance	Lowers worst-case stack height	Low–Med
Reduce coating thickness	Larger effective hole	Low

11. Worked example — a passing design

Same bracket, but with a shorter M10 bolt (30 mm instead of 40) and larger clearance holes (12 mm nominal instead of 11).

Parameter	Plate 1	Plate 2	Tapped base
Hole nominal Ø	12.00 mm	12.00 mm	10.00 mm (tapped)
Hole EBT	0.20 mm	0.20 mm	—
Coating	0.012 mm	0.012 mm	— (none)
PosTol X	0.15 mm	0.15 mm	0.10 mm
PosTol Y	0.10 mm	0.10 mm	0.10 mm
Thickness	6.00 ±0.10	6.00 ±0.10	—

Bolt: M10, nominal 10.00 mm, max 10.058 mm, length 30 mm. Washer 2 mm.

Worst-case minimum gap is +0.114 mm — every combination clears. The extra 1 mm of clearance diameter absorbed the variation budget.

Statistical check:

Both checks pass — a robust design.

Summary

The tapped rectangular stackup in seven steps:

1. Effective hole Ø per clearance plate = nominal − 2×coating.
2. EBT term = 0.5 × EBT, per clearance plate.
3. Position term = 0.5 × √(PosTolX² + PosTolY²), per clearance plate.
4. Tapped position term = 0.5 × √(posX² + posY²).
5. Projection tolerance = (2 × tappedPos × maxProjection) / minEngagement, then halve.
6. Bolt camber = 0.006 × length + max body overage.
7. Worst-case: fails if the sum of terms exceeds (base − bolt max Ø). Statistical: use RSS of the terms for the yield.

If it fails, read the contributor chart. Shortening the bolt, tightening the tapped-hole position, or increasing thread engagement are the highest-impact moves available.

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Disclaimer: educational use only. Have any tolerance analysis reviewed by a qualified engineer before using it in safety-critical applications. These are standard methods — they do not replace a full drawing review, material analysis, or formal design verification.