9.2 Fixed and Floating Fastener Formulas

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:

1. 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.
2. 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

Senior-level traps

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.