Layout and shop math
Bolt circle calculator with coordinates
Enter the bolt circle diameter, number of holes and start angle to get X and Y for every hole.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
| Hole | Angle (°) | X (in) | Y (in) |
|---|---|---|---|
| 1 | 0 | 2.0000 | 0.0000 |
| 2 | 60 | 1.0000 | 1.7321 |
| 3 | 120 | -1.0000 | 1.7321 |
| 4 | 180 | -2.0000 | 0.0000 |
| 5 | 240 | -1.0000 | -1.7321 |
| 6 | 300 | 1.0000 | -1.7321 |
Chord between adjacent holes
in
C = D x sin(180° / N) = 4 x sin(180° / 6) = 2.0000 in
2.0000 in (50.80 mm) center to center. Angle between holes: 60°.
Hole 2, with your numbers:
X = Xc + (D / 2) x cos(A) = 0 + (4 / 2) x cos(60°) = 1.0000 in
Y = Yc + (D / 2) x sin(A) = 0 + (4 / 2) x sin(60°) = 1.7321 in
Source: Machinery's Handbook (coordinates for equally spaced holes); standard trigonometry
How it works
A = S + (n - 1) x 360 / N; X = Xc + (D / 2) x cos(A); Y = Yc + (D / 2) x sin(A); C = D x sin(180° / N)
| Symbol | Meaning | Unit |
|---|---|---|
| D | Bolt circle diameter | in or mm |
| N | Number of equally spaced holes | holes |
| n | Hole number, 1 to N | none |
| S | Start angle of hole 1, counterclockwise from +X | ° |
| A | Angle of hole n | ° |
| Xc, Yc | Bolt circle center | in or mm |
| X, Y | Hole center coordinates | in or mm |
| C | Chord: center-to-center distance between adjacent holes | in or mm |
Worked example
6 holes on a 4.000 in bolt circle, hole 1 at 0°, center at X 0, Y 0.
- Angle between holes: 360° / 6 = 60°.
- Radius: 4.000 / 2 = 2.000 in.
- Hole 2 angle: 0° + (2 - 1) x 60° = 60°.
- Hole 2 X: 0 + 2.000 x cos(60°) = 2.000 x 0.5 = 1.0000 in.
- Hole 2 Y: 0 + 2.000 x sin(60°) = 2.000 x 0.86603 = 1.7321 in.
- Repeat for holes 3 to 6 at 120°, 180°, 240° and 300°.
- Chord: 4.000 x sin(180° / 6) = 4.000 x 0.5 = 2.0000 in.
Result (in): hole 1 (2.0000, 0.0000), hole 2 (1.0000, 1.7321), hole 3 (-1.0000, 1.7321), hole 4 (-2.0000, 0.0000), hole 5 (-1.0000, -1.7321), hole 6 (1.0000, -1.7321). Holes are 2.0000 in apart.
Shop notes
- Coordinates come out as a table you can key into a DRO or a G-code program. "Copy as text" pastes it into a spreadsheet.
- Angles run counterclockwise from +X (3 o’clock), the usual math convention. Enter a negative start angle to begin below the X axis.
- Hole 1 lands on the start angle. Set the start angle to line the pattern up with a keyway or a flat.
- Check the chord with calipers across two drilled holes before drilling the rest.
FAQ
How do you find the bolt circle diameter of an existing part?
Measure center to center across two adjacent holes (the chord) and divide by sin(180° / N). Six holes 2.000 in apart center to center: D = 2.000 / sin(30°) = 2.000 / 0.5 = 4.000 in.
Which way does the calculator number the holes?
Counterclockwise from +X (3 o’clock), starting at the start angle. For clockwise order, keep hole 1 and read the rest of the table from the bottom up: 1, N, N - 1 and so on down to 2.
How do you put the first hole at 12 o’clock?
Enter a start angle of 90°. For 6 holes on a 4.000 in circle centered at 0, 0, hole 1 lands at X 0.0000 in, Y 2.0000 in.
What if the bolt circle center is not at X 0, Y 0?
Enter the center as it reads on your DRO or in your work offset. The calculator adds Xc and Yc to every hole, so the table reads straight off the DRO.
What is the distance between holes on a 6-hole, 4.000 in bolt circle?
C = D x sin(180° / N) = 4.000 x sin(30°) = 2.0000 in center to center.
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