Bolt circle layout: the position of each hole, the chord between holes and a chord chart

A bolt circle -- the pitch circle diameter, PCD, of the holes -- comes down to one number per hole: its angle. From the angle come the coordinates for the drill or the CNC, and the chord between neighbouring holes, which is how the circle is stepped out with dividers when there is no protractor. This guide gives the three formulas, a worked example, a chord chart for 3 to 24 holes and the rule the flange standards follow for where the first hole goes.

The flange calculator does it for any drilling, draws the holes and fills in the ASME B16.5 and EN 1092-1 drillings with one click.

The formulas

Angle between holes

β = 360° / n n is the number of holes. Eight holes: 45°.

Position of each hole

θi = θ0 + i × β ; xi = (K / 2) × cos θi ; yi = (K / 2) × sin θi K is the bolt circle diameter and θ0 the angle of the first hole. Flange standards put θ0 at half a pitch, β / 2, so that no hole sits on a centre line.

Chord between neighbouring holes

c = K × sin(180° / n) The straight distance between two neighbouring hole centres, which is the divider setting.

Worked example: a DN 100 PN 16 flange

EN 1092-1, DN 100, PN 16: 8 holes of 18 mm on a 180 mm bolt circle. The angle between holes is 45°, and the first hole sits at 22.5°.

The chord is 180 × sin 22.5° = 68.88 mm: set the dividers to it, start at the first hole and step round the circle; the eighth step must land back on the first hole.

Bolt circle chord chart

The chord is the bolt circle diameter times a factor that depends only on the number of holes, sin(180° / n). Multiply the factor by your bolt circle, or read the 100 mm and 4 in columns.

Where the first hole goes

ASME B16.5, EN 1092-1 and the other flange standards straddle the centre lines: the first hole half a pitch off the vertical, so that the flange mates with its counterpart in any symmetric position and no bolt sits at the lowest point, where water collects. On 4 holes that is 45° from the centre line; on 8 holes, 22.5°.

Marking out by hand

1. Scribe the bolt circle from the centre punch, with a trammel or dividers set to half the bolt circle diameter.
2. Mark the first hole half a pitch from the centre line, by protractor or by its coordinates.
3. Set the dividers to the chord and step round the circle. The last step must close on the first hole; if it overshoots or falls short, correct the setting and start again.
4. Centre-punch every hole and drill a pilot before the full size.

Common mistakes

• A hole on a centre line: the flange then sits half a pitch rotated from its counterpart, and the valve or the pump goes in crooked.
• Using the radius where the formula wants the diameter: the chord is K × sin(180° / n), with K the bolt circle diameter.
• Stepping the chord on the wrong circle: the dividers go round the bolt circle, not round the outside of the flange.

Frequently asked questions

How do you calculate a bolt circle?

Divide 360° by the number of holes for the angle between them, put the first hole half a pitch off the centre line, and take each hole at x = (K / 2) × cos θ and y = (K / 2) × sin θ, with K the bolt circle diameter.

What is the distance between bolt holes on a bolt circle?

The chord, K × sin(180° / n). On a 180 mm circle with 8 holes it is 68.88 mm.

What does PCD mean?

Pitch circle diameter: the diameter of the circle through the hole centres, the same thing as the bolt circle. EN 1092-1 calls it K.