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Bolt Circle Calculator (Hole Coordinates)

X and Y coordinates of equally spaced holes on a bolt circle (PCD) for drilling and CNC — hole-to-hole distance, angle between holes, start angle, center offset and direction.

Bolt circle diameter (PCD)

Number of holes

Angle of the first hole

Center X

Center Y

Direction

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How it works

Angle of hole i = start ± (i − 1) × 360° ÷ n · X = Xc + (D ÷ 2) × cos(angle) · Y = Yc + (D ÷ 2) × sin(angle) · adjacent-hole distance = D × sin(180° ÷ n)

Bolt holes on flanges, wheels, motor mounts and covers are usually spaced evenly on a circle called the bolt circle or pitch circle diameter (PCD). Each hole sits at the same radius, rotated by 360° ÷ n from the previous one, so its coordinates follow from cosine and sine of its angle. Machinists use the table to drill on a mill or program a CNC; the straight-line distance between neighbouring holes (the chord) is handy for checking with calipers or laying out with dividers.

Worked example

Six holes on a 100 mm bolt circle centered at (0, 0), starting at 0° and going counterclockwise, are 60° apart and 100 × sin(30°) = 50.000 mm apart center to center. Hole 1 is at (50, 0), hole 2 at (25, 43.301), hole 3 at (−25, 43.301), hole 4 at (−50, 0), hole 5 at (−25, −43.301) and hole 6 at (25, −43.301).

Sources: Wikipedia — Bolt circle (pitch circle diameter) · Machinery’s Handbook — Bolt circle hole spacing (summarized by Engineering ToolBox)

Frequently asked questions

How do I calculate bolt hole coordinates?

For each hole, find its angle (start angle + i × 360° ÷ n), then X = center X + radius × cos(angle) and Y = center Y + radius × sin(angle). The table does this for every hole.

How do I find the distance between holes on a bolt circle?

Adjacent holes are D × sin(180° ÷ n) apart. For 4 holes on a 100 mm PCD that is 70.711 mm; for 6 holes it is exactly half the diameter.

How do I measure a bolt circle diameter?

With an even number of holes, measure center to center across opposite holes. With an odd number, measure between adjacent centers and divide by sin(180° ÷ n).

Why do flange holes straddle the centerline?

Standards such as ASME B16.5 place bolt holes symmetrically off the vertical and horizontal centerlines. Set the start angle to half the hole spacing (e.g. 45° for 4 holes, 22.5° for 8) to reproduce that layout.

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This calculator is for educational purposes. Double-check important results before acting on them.