Engineering Reference

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.

Page last changed 2026-10-19 · 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

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.

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