Bolt Spacing⚠ unverified
Mechanical / Joints · Compute the recommended bolt circle spacing
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| D | D | m | 1.0 | Bolt circle diameter |
| n | n | — | 1.0 | Number of bolts (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | s | m | Arc spacing between adjacent bolts, in metres (m) |
The science & history
Understanding the Parameters
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Bolt circle diameter $D$ — the diameter of the circle through the bolt centres (not the flange outer diameter). The full bolt-circle circumference $\pi D$ is shared among the bolts.
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Number of bolts $n$ — more bolts means tighter spacing and more uniform clamping, at the cost of more holes weakening the flange and more assembly labour. Pressure flanges are almost always an even $n$ (often a multiple of 4) for balanced tightening patterns.
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Arc spacing $s$ — the along-the-circle gap. For sealed joints a common guideline keeps the bolt spacing between about $3d$ and a pressure-dependent maximum (roughly $2d$ + a term growing with pressure); too wide a spacing lets the flange bow between bolts and the gasket leak.
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Arc vs chord — $s = \pi D/n$ is the arc length; the straight-line (chord) distance is slightly smaller, $D\sin(\pi/n)$. For many bolts the two nearly coincide.
Derivation (Approaching a Proof)
Place $n$ bolts at equal angular intervals around a circle of diameter $D$ (circumference $\pi D$). Equal spacing means the angular step between neighbours is $2\pi/n$ radians. The corresponding arc length along the bolt circle is radius times angle:
$$s = R\cdot\frac{2\pi}{n} = \frac{D}{2}\cdot\frac{2\pi}{n} = \frac{\pi D}{n}.$$
Equivalently, the total circumference $\pi D$ divided equally among $n$ gaps gives $\pi D/n$ per gap. (The exact centre-to-centre straight distance is the chord $D\sin(\pi/n)$, which the arc slightly overestimates.)
Dimensional check. $s = \dfrac{\pi D}{n} = \dfrac{\text{m}}{(\text{–})} = \text{m}$ — a length, as required.
History and Development
Bolt-spacing limits are among the oldest rules in pressure-vessel and flange practice, embodied in the ASME Boiler & Pressure Vessel Code and pipe-flange standards (ASME B16.5). The minimum spacing ensures wrench clearance and avoids overlapping bolt-hole stress fields; the maximum keeps the gasket seated by preventing the flange from "bridging" between widely spaced bolts. Even, symmetric spacing also enables the cross-pattern ("star") tightening sequence that seats a gasket uniformly.
Related Concepts: Gasket Factor, Bolt Preload, Member Load External, Pressure Vessel Design, Bolt Proof Load
Notes: Arc spacing $\pi D/n$ on the bolt circle (chord $= D\sin(\pi/n)$ is slightly less). $D$ is the bolt-circle diameter, not flange OD. Sealed joints bound spacing (min ~$3d$; pressure-dependent max) to keep the gasket clamped between bolts. Even $n$ preferred for balanced tightening.