Bolt Circle Coordinates Calculator

Each hole is at X = R cos(θ), Y = R sin(θ), where R is half the bolt circle diameter and θ steps by 360° ÷ number of holes.

in
°
Chord distance between adjacent holes
2.25in
Angle between holes60 °
HoleAngle (°)X (in)Y (in)
102.250
2601.1251.9486
3120-1.1251.9486
4180-2.250
5240-1.125-1.9486
63001.125-1.9486

Show the math

Angle between holes = 360° ÷ 6 = 60°
Chord between neighbors = 4.5 × sin(180° ÷ 6) = 2.25 in
Each hole: X = 2.25 × cos θ, Y = 2.25 × sin θ, with θ = 0° + i × 60°

Rounded the same way as the result above.

How it works

Holes on a bolt circle sit evenly around a circle centered on your part origin. Divide 360° by the hole count for the angular step, then convert each angle to X and Y from the center using cosine and sine.

Enter the circle diameter, the number of holes, and the angle of the first hole. The table can be typed straight into a CNC program or a layout sheet.

θᵢ = start + i × 360° ÷ N Xᵢ = (D ÷ 2) × cos θᵢ Yᵢ = (D ÷ 2) × sin θᵢ Chord between neighbors = D × sin(180° ÷ N)

Worked example

Six holes on a 4.5 inch bolt circle starting at 0°:

  1. Angle between holes = 360° ÷ 6 = 60°
  2. Chord between neighbors = 4.5 × sin(180° ÷ 6) = 2.25 in
  3. Each hole: X = 2.25 × cos θ, Y = 2.25 × sin θ, with θ = 0° + i × 60°
InputValue
Bolt circle diameter4.5 in
Number of holes6
Start angle (from +X axis)0 °
ResultValue
Chord distance between adjacent holes2.25 in
Angle between holes60 °
HoleAngle (°)X (in)Y (in)
102.250
2601.1251.9486
3120-1.1251.9486
4180-2.250
5240-1.125-1.9486
63001.125-1.9486

Assumptions and limits

  • Angles are measured counter-clockwise from the positive X axis with the origin at the circle center.
  • Holes are evenly spaced. Uneven patterns need each angle entered separately.
  • Coordinates are shown to four decimal places; check the precision your machine and tolerance require.

Common questions

What is a bolt circle (PCD)?

It is the diameter of the circle passing through the centers of a set of holes, also called the pitch circle diameter.

How do I measure a bolt circle with an odd number of holes?

Measure from one hole edge to the farthest opposite hole edge and use the calculator to convert; or measure center-to-center between adjacent holes and solve for D = chord ÷ sin(180° ÷ N).

How do I rotate the pattern?

Change the start angle. A 5-hole pattern starting at 90° puts one hole at the top.

Sources

  • Plane geometry: points on a circle of radius R at equal angular spacing; chord = D sin(180° ÷ N).

Updated 2026-09-30