Bolt circle calculator.
Enter the circle, hole count, and start angle to get X and Y for every hole, ready for a program or an inspection report.
Set the pattern
| Hole | Angle, deg | X | Y |
|---|---|---|---|
| 1 | 0.0000 | 2.0000 | 0.0000 |
| 2 | 60.0000 | 1.0000 | 1.7321 |
| 3 | 120.0000 | -1.0000 | 1.7321 |
| 4 | 180.0000 | -2.0000 | 0.0000 |
| 5 | 240.0000 | -1.0000 | -1.7321 |
| 6 | 300.0000 | 1.0000 | -1.7321 |
Chord distances for common hole counts
The chord is the straight line between the centers of two adjacent holes, and it is the fastest check on a finished pattern. Multiply the factor below by the bolt circle diameter. Six holes give a chord exactly equal to the radius, the case most people remember, and the reason six hole patterns get laid out with a compass.
| Holes | Angular step, deg | Chord factor | Chord on a 4.000 circle |
|---|---|---|---|
| 3 | 120.0000 | 0.866025 | 3.4641 |
| 4 | 90.0000 | 0.707107 | 2.8284 |
| 5 | 72.0000 | 0.587785 | 2.3511 |
| 6 | 60.0000 | 0.500000 | 2.0000 |
| 7 | 51.4286 | 0.433884 | 1.7355 |
| 8 | 45.0000 | 0.382683 | 1.5307 |
| 9 | 40.0000 | 0.342020 | 1.3681 |
| 10 | 36.0000 | 0.309017 | 1.2361 |
| 12 | 30.0000 | 0.258819 | 1.0353 |
| 16 | 22.5000 | 0.195090 | 0.7804 |
| 20 | 18.0000 | 0.156434 | 0.6257 |
| 24 | 15.0000 | 0.130526 | 0.5221 |
Questions machinists ask about bolt circles
How do you calculate bolt circle coordinates?
Divide 360 by the number of holes to get the angular step. For each hole, the angle is the start angle plus the step times the hole index. X is the circle center X plus the radius times the cosine of that angle, and Y is the center Y plus the radius times the sine. The radius is half the bolt circle diameter, which is the diameter of the circle through the hole centers, so take care not to use the hole size by mistake.
What is the distance between two adjacent holes on a bolt circle?
The straight line distance, called the chord, is twice the radius times the sine of 180 divided by the number of holes. For six holes on a four inch circle the chord is exactly two inches, the well known case where the chord equals the radius. Measuring that distance between adjacent hole centers with a caliper is a quick way to check a pattern.
Where should the first hole go?
Put the first hole where the drawing puts it, and state the start angle explicitly, because that causes the fewest arguments. Zero degrees on this page is the three o’clock position, measured counterclockwise, which matches standard mathematical convention and most CAM systems. A pattern of an even number of holes drawn with a hole at twelve o’clock needs a start angle of 90 degrees.
Can I use this for an odd number of holes?
Yes. Odd counts are where hand calculation goes wrong most often, because the pattern has no symmetry to check against. Five holes on a circle sit 72 degrees apart and seven sit 51.4286 degrees apart, and neither gives round numbers in X and Y, so the coordinates on this page carry four decimal places.
How do I check a bolt circle on a CMM or with a caliper?
On a CMM, measure each hole center and fit a circle to them. The fitted diameter is the bolt circle, and the deviation of each center from the fitted circle is what a positional tolerance is applied to. With a caliper, measure the chord between adjacent holes and compare it with the calculated value. The chord check is quick, and it catches a wrong hole count or a wrong diameter straight away.
Who made it, and what it does not do
This tool was written by Shopfloor Agency's lead engineer, who holds a bachelor’s degree in mechanical engineering and builds websites for US manufacturers. It runs entirely in your browser.
The trigonometry is exact and works in any unit: put inches in and you get inches out, and millimeters give you millimeters. What it cannot know is which angle convention your drawing uses, or whether the pattern is referenced to a datum other than the circle center. Confirm both before you drill the first hole.
If you spot an error, tell us, and we will correct the page and note the change.
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