MachineCalcs

Bolt Circle (BCD) Coordinate Calculator

X-Y coordinates of every hole on a bolt-circle diameter (BCD) from the hole count, start angle and center — ready to punch into a mill or lathe — plus the angular and chord spacing. Metric and imperial. Free, no signup.

Fasteners 5 inputs 2 results

Calculator

Diameter of the circle the hole centers lie on (the radius is half this).
mm
How many holes are equally spaced around the bolt circle.
Angle of the first hole, CCW from the +X axis.
°
X coordinate of the bolt-circle center.
mm
Y coordinate of the bolt-circle center.
mm

Results

Default result
Edit inputs
Angular spacing(Δθ)
60°

360° ÷ holes

Also computed

Chord between holes(c)50mm

Method notes 6 notes
  • Hole 0: X = 50.000, Y = 0.000 (mm)
  • Hole 1: X = 25.000, Y = 43.301 (mm)
  • Hole 2: X = -25.000, Y = 43.301 (mm)
  • Hole 3: X = -50.000, Y = 0.000 (mm)
  • Hole 4: X = -25.000, Y = -43.301 (mm)
  • Hole 5: X = 25.000, Y = -43.301 (mm)

Bolt-circle hole coordinates come from the radius r = BCD/2 and an angle per hole of θ₀ + i·(360/N): each hole i sits at X = cx + r·cos(θ₀ + i·360/N), Y = cy + r·sin(θ₀ + i·360/N). Enter the bolt-circle diameter, hole count N, start angle, and centre; this calculator returns every X-Y position plus angular spacing Δθ = 360/N and the chord c = BCD·sin(180/N) between adjacent holes.

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How to use this calculator

  1. Enter the bolt circle diameter. Enter the BCD — the diameter of the circle the hole centers sit on.
  2. Enter the number of holes. Enter how many holes are equally spaced around the circle.
  3. Set the start angle and center. Set the angle of the first hole (CCW from +X) and the center coordinates, or leave the center at 0,0.
  4. Read the coordinates. Read the angular spacing, the chord between holes, and the full list of hole X-Y coordinates, then transfer them to your machine.

How it works

A bolt circle places N equally spaced holes on a circle of radius r = BCD / 2 about a center (cx, cy). Hole i (counting from i = 0) sits at the angle θi = start + i · (360 / N), measured counter-clockwise from the +X axis, so its coordinates are Xi = cx + r · cos θi and Yi = cy + r · sin θi. Adjacent holes are 360 / N degrees apart and a chord BCD · sin(180° / N) apart in a straight line.

Worked example

Verified against the live calculator

A 100 mm BCD with 6 holes starting at , centered at the origin. The radius is 50 mm, the holes are 360 / 6 = 60° apart, and the chord between neighbours is 100 · sin(30°) = 50 mm. Hole 0 lands at (50, 0), hole 1 at (25, 43.30), hole 2 at (−25, 43.30), and so on around the circle. The calculator lists all six coordinates and renders the pattern.

Frequently asked questions

How do you calculate bolt circle (BCD) coordinates?

Put each hole at angle θ = start + i·(360/N) on a circle of radius r = BCD/2, then X = cx + r·cos θ and Y = cy + r·sin θ for hole i = 0…N−1. Enter the diameter, hole count, start angle and center above and the calculator lists every X-Y position.

What is a bolt circle diameter (BCD)?

The bolt circle diameter is the diameter of the imaginary circle that passes through the centers of all the holes (bolts) in the pattern. The pattern radius is half of it, r = BCD/2.

How do I find the hole spacing on a bolt circle?

The angular spacing between equally spaced holes is 360° ÷ N, where N is the number of holes. For example, 6 holes are 60° apart and 8 holes are 45° apart.

How do I lay out a bolt pattern on a mill or lathe?

Set your work-zero at the bolt-circle center (cx, cy), then move to each X-Y coordinate the calculator lists and drill there. On a CNC, the X-Y pairs go straight into the program; on a manual machine, dial them in on the DRO from the center.

What is the chord distance between adjacent holes?

The straight-line (chord) distance between two neighbouring holes is BCD·sin(180°/N). For a 100 mm BCD with 6 holes that is 100·sin(30°) = 50 mm — useful for checking spacing with calipers.

Does this work in metric and imperial?

Yes — toggle SI/imperial in the header to enter the diameter and center in mm or inches; the coordinates and chord convert with it. The angles stay in degrees.

Method & assumptions

  • Holes are equally spaced around the bolt circle; for an unequal pattern, set each angle yourself.
  • Angles are measured counter-clockwise from the +X axis; the first hole is at the start angle.
  • Coordinates are relative to the chosen center (cx, cy) — set it to your work-zero.
  • Round the coordinates to your machine's resolution; the list is shown to 0.001 mm.
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