How do I calculate bolt circle hole spacing?

Divide 360° by the number of holes to get the angular pitch, then multiply the bolt circle diameter by the sine of half that pitch: C = D·sin(180°/n). For 8 holes on a 6 in circle, 45° apart with 2.296 in between adjacent holes.

What is the difference between chord and arc spacing?

The arc is the distance measured along the circle, π·D/n. The chord is the straight-line distance between adjacent hole centres, D·sin(180°/n). The chord is always shorter, and the gap is largest when there are few holes — about 10% at 4 holes on a circle.

How do I set out holes on a bolt circle?

Work from the centre: mark the radius, then step around by the angular pitch using a rotary table, a dividing head, or coordinates from the calculator. Coordinates are more accurate than stepping around, because small angular errors accumulate when you index from the previous hole rather than from the datum.

What start angle should I use?

Whatever the drawing specifies. A start angle of 0° puts the first hole on the positive X axis, which is the most common convention. Where the pattern must straddle an axis — for symmetry about a centre line — the start angle is typically half the angular pitch, so holes straddle the axis rather than sitting on it.

Bolt Circle Calculator

Compute hole coordinates, chord spacing and angular pitch for holes on a bolt circle — the layout calculation for flanges and bearing caps.

Data verified 2026-09-29 · based on n/a — standard engineering relationships, no single governing revision

Quick Answer

Holes on a bolt circle are equally spaced at 360° ÷ n. The straight-line spacing between adjacent holes is the chord, C = D·sin(180° ÷ n). For 8 holes on a 6 in circle, that is 45° apart and 2.296 in between neighbours.

Bolt Circle Layout

Bolt circle diameter (in)

Number of holes

Start angle (degrees)

Hole number to locate

The Formulas Used

Angular pitch: θ = 360° ÷ n
Chord between adjacent holes: C = D · sin(180° ÷ n)
Hole position: X = (D/2)·cos(θᵢ) Y = (D/2)·sin(θᵢ) where θᵢ = start + (i−1)·360/n

Chord Is Not Arc

The arc length and the chord length along a bolt circle are different numbers, and using the wrong one is a common layout error. The arc is π·D/n — the distance measured along the circle. The chord is D·sin(180°/n) — the straight-line distance between adjacent hole centres, which is what a caliper measures and what a bolt must span.

They converge as the number of holes rises and differ most with few holes. With 4 holes on a 6 in circle the arc is 4.712 in but the chord is only 4.243 in — a 10% difference. With 24 holes the difference is under 1%.

Frequently Asked Questions

How do I calculate bolt circle hole spacing?: Divide 360° by the number of holes to get the angular pitch, then multiply the bolt circle diameter by the sine of half that pitch: C = D·sin(180°/n). For 8 holes on a 6 in circle, 45° apart with 2.296 in between adjacent holes.
What is the difference between chord and arc spacing?: The arc is the distance measured along the circle, π·D/n. The chord is the straight-line distance between adjacent hole centres, D·sin(180°/n). The chord is always shorter, and the gap is largest when there are few holes — about 10% at 4 holes on a circle.
How do I set out holes on a bolt circle?: Work from the centre: mark the radius, then step around by the angular pitch using a rotary table, a dividing head, or coordinates from the calculator. Coordinates are more accurate than stepping around, because small angular errors accumulate when you index from the previous hole rather than from the datum.
What start angle should I use?: Whatever the drawing specifies. A start angle of 0° puts the first hole on the positive X axis, which is the most common convention. Where the pattern must straddle an axis — for symmetry about a centre line — the start angle is typically half the angular pitch, so holes straddle the axis rather than sitting on it.

Value Sources

Each data column on this page is tied to the source it came from. The numbers in square brackets correspond to the table headers above.

#	Source	Type	Revision / method
[1]	ASME B1.1 — Unified Inch Screw Threads	standard	ASME B1.1-2019 — source
[2]	ASTM A615 — Deformed steel bars for concrete reinforcement	standard	ASTM A615/A615M-20 — source
[3]	ASTM E140 — Hardness Conversion Tables	standard	ASTM E140-12b — source
[4]	Values computed in your browser	derived	Evaluated locally from the formulas shown on the page. No data leaves the device.
[5]	ISO 4287 — Surface texture: Profile method	standard	ISO 4287:1997 — source
[6]	ISO 68-1 — Basic profile	standard	ISO 68-1:2023 — source
[7]	NFPA 70 NEC Table 310.16	standard	NEC 2023 (NFPA 70-2023) — source

Data Sources

Standard	Revision	What it covers on this page
Formulas as shown on this page	n/a — standard engineering relationships, no single governing revision	every value this calculator produces

Cross-checked against:

Formulas verified against the corresponding reference chart on this site, so the calculator and the published tables agree

Derived values — the following values on this page are calculated, not taken directly from the standard:

Value	How it is derived
All outputs	Computed in the browser from the formulas above. No data leaves the device.

Outputs are computed from the formulas shown. Verify against the governing standard for design or acceptance work.

Accuracy and use. The values on this page are compiled from the published standards and cross-checked sources listed above. Where values are derived, the derivation is stated. No warranty, express or implied, is made as to the accuracy or completeness of this information, and no liability is accepted for any loss or damage arising from its use. Engineering reference data is provided for guidance in preliminary work — before a value is used for design, fabrication or acceptance testing, verify it against the current revision of the governing standard and against your own inspection. The user assumes all risk and responsibility in connection with the use of this information.

Cite This Page

Every value on this page is traceable to the sources listed above. If you use the data in a document, paper or report, cite it as:

Plain text

Engineering Reference. "Bolt Circle Calculator." https://refmanual.com/calculators/bolt-circle/ (accessed 2026-09-29). Data from Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision.

BibTeX

@misc{bolt-circle,
  title        = {Bolt Circle Calculator},
  author       = {{Engineering Reference}},
  howpublished = {\url{https://refmanual.com/calculators/bolt-circle/}},
  note         = {Accessed: 2026-09-29},
  source       = {Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision}
}

RIS (EndNote, Zotero, Mendeley)

TY  - ELEC
TI  - Bolt Circle Calculator
AU  - Engineering Reference
PB  - Engineering Reference
UR  - https://refmanual.com/calculators/bolt-circle/
PY  - 2026
DA  - 2026-09-29
N1  - Source: Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision
ER  -

Each row in the tables above also has a permanent link — hover a row and use the # link to cite a single value rather than the whole page.