Bolt Circle (PCD) Calculator
X/Y coordinates for any hole pattern on a pitch circle — drawn to scale so you can see it's right before you cut it, and listed as a table you can read straight onto the machine. Works backwards too: measure the gap between two adjacent holes and it gives you the PCD.
0° = 3 o'clock, measured anticlockwise.
Reverse-engineering an existing part: you can measure between two adjacent holes far more easily than you can find the true centre.
Bolt circles, PCD and hole coordinates
A bolt circle — pitch circle diameter, or PCD — is a set of holes equally spaced around a circle. The maths is straightforward trigonometry: each hole sits at angle θ = start + (360 ÷ n) × i, and its position is X = Cx + R × cos θ, Y = Cy + R × sin θ, where R is half the PCD. The reason it is worth a tool rather than a mental calculation is simply that transcribing a dozen coordinates by hand is exactly the kind of task where one digit goes astray and a part gets scrapped — which is why this one draws the pattern as well as listing it.
The reverse problem comes up more often than the forward one on the shop floor. You have a flange in front of you, you need to reproduce it, and you cannot easily find the true centre — but you can measure between two adjacent holes with a vernier. That chord length gives you the PCD directly: PCD = chord ÷ sin(180 ÷ n). For six holes it falls out particularly neatly, because the chord equals the radius exactly, so the PCD is simply twice the measured gap.
A practical note on convention: most CNC controls take 0° at 3 o'clock and measure anticlockwise, which is what this calculator does by default. Drawings are not always so consistent — plenty put the first hole at 12 o'clock. If your pattern is symmetrical it will not matter; if it is not, check the start angle carefully, because a pattern rotated by one hole spacing is a scrapped part rather than an obviously wrong one.
Worth remembering that a bolt circle with an odd number of holes has no hole directly opposite any other, which matters for clamping and for balance on rotating parts. And if the pattern must locate accurately rather than just clear a fastener, the tolerance on true position matters more than the coordinates themselves — that is the point at which it is worth talking to us about how the part will actually be fixtured and inspected.
Bolt circle calculator — FAQ
How do you calculate bolt circle coordinates?
Each hole sits at angle theta = start angle + (360 / number of holes) x hole index. Its position is X = centre X + R x cos(theta) and Y = centre Y + R x sin(theta), where R is half the pitch circle diameter.
How do you find the PCD from the distance between two holes?
PCD = chord / sin(180 / n), where chord is the centre distance between two adjacent holes and n is the number of holes. For a 6-hole pattern the chord equals the radius, so the PCD is exactly twice the measured distance between adjacent holes.
What is PCD in engineering?
PCD stands for pitch circle diameter — the diameter of the imaginary circle passing through the centres of all the holes in the pattern. It is the standard way to dimension a bolt circle on a drawing.
What angle are the holes on a 6 bolt pattern?
60 degrees apart (360 / 6). A 4-hole pattern is 90 degrees apart, 5-hole is 72 degrees, 8-hole is 45 degrees.
Does the start angle matter?
Only if the pattern is not rotationally symmetrical with the rest of the part. Most CNC controls use 0 degrees at 3 o clock measured anticlockwise, but drawings often place the first hole at 12 o clock. Check it — a pattern rotated by one hole spacing is a scrapped part.
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