Bolt Circle Calculator
X and Y coordinates for any number of evenly spaced holes on a bolt circle, with a start angle and a center offset, plus the distance between adjacent holes. Copy the list straight into a spreadsheet, a CNC program or a DRO.
Bolt hole pattern
Enter the number of holes (2 to 360) and the bolt circle diameter. Start angle and center default to 0.
Angles run counterclockwise from +X unless you pick clockwise. Check the drawing's zero and direction before you program.
Flanges, hubs and adapter plates to make? , or browse CNC machining shops.
The formulas
- Angle of hole i: θi = start angle + i x 360° / N (i = 0 to N - 1)
- Coordinates: X = Xc + (BCD / 2) cos θi, Y = Yc + (BCD / 2) sin θi
- Distance between adjacent holes: c = BCD x sin(180° / N)
Worked example: six holes on a 4.000" bolt circle, first hole at 0°, centered on the origin. The holes are 60° apart and 2.000" center to center.
| 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 |
Hole-to-hole distance by hole count
Multiply the bolt circle diameter by the factor to get the center distance between adjacent holes. The factor is sin(180° / N), computed here, so it works in any unit.
| Holes | Angle between holes | Chord factor | On a 4.000" circle | On a 100 mm circle |
|---|---|---|---|---|
| 3 | 120.00° | 0.86603 | 3.4641" | 86.603 mm |
| 4 | 90.00° | 0.70711 | 2.8284" | 70.711 mm |
| 5 | 72.00° | 0.58779 | 2.3511" | 58.779 mm |
| 6 | 60.00° | 0.50000 | 2.0000" | 50.000 mm |
| 8 | 45.00° | 0.38268 | 1.5307" | 38.268 mm |
| 10 | 36.00° | 0.30902 | 1.2361" | 30.902 mm |
| 12 | 30.00° | 0.25882 | 1.0353" | 25.882 mm |
| 16 | 22.50° | 0.19509 | 0.7804" | 19.509 mm |
| 20 | 18.00° | 0.15643 | 0.6257" | 15.643 mm |
| 24 | 15.00° | 0.13053 | 0.5221" | 13.053 mm |
Before you drill
- Match the drawing's zero: some prints measure the first hole from +Y (12 o'clock) rather than +X. A start angle of 90° puts hole 1 at 12 o'clock.
- Check the direction. Most prints and controls count counterclockwise; a pattern programmed the wrong way is a mirror image.
- Bolt circle position tolerances are usually called out as true position on the hole pattern. Check the feature control frame, not only the coordinates.
- Spot, then drill, then tap: see the tap and drill size chart for the drill that goes with each thread.
Frequently asked questions
- How do you calculate bolt circle coordinates?
- Space the holes evenly: hole i sits at angle start + i x 360 / N. Its coordinates are X = Xc + (BCD / 2) x cos(angle) and Y = Yc + (BCD / 2) x sin(angle), where Xc, Yc is the center of the pattern. Six holes on a 4.000" circle starting at 0 degrees land at (2, 0), (1, 1.7321), (-1, 1.7321), (-2, 0), (-1, -1.7321) and (1, -1.7321).
- How far apart are the holes on a bolt circle?
- The straight-line distance between adjacent hole centers is the chord: BCD x sin(180 / N). Six holes on a 4.000" circle are 4 x sin(30) = 2.000" apart, and eight holes on 100 mm are 38.268 mm apart. Use it to check a drilled pattern with calipers or pins.
- Which way do the holes number?
- The calculator measures angles from the +X axis and numbers holes counterclockwise as seen looking down on the XY plane from +Z, which is the view from the spindle on a vertical mill. Pick clockwise if the drawing numbers the other way, and always match the drawing's zero before you program.
- What start angle should a pipe flange use?
- Flange bolt holes are normally placed to straddle the centerlines, so no hole sits on the vertical or horizontal centerline. That puts the first hole at half the angle between holes: 45 degrees for 4 holes, 22.5 degrees for 8 and 15 degrees for 12. Confirm against the flange standard or the drawing.
