Bolt circle calculator
X/Y coordinates for holes on a bolt circle. With start angle, centre point, direction, hole spacing for checking and output as NC blocks.
| No. | Angle | X | Y |
|---|---|---|---|
| 1 | 0° | 50.000 | 0.000 |
| 2 | 60° | 25.000 | 43.301 |
| 3 | 120° | -25.000 | 43.301 |
| 4 | 180° | -50.000 | 0.000 |
| 5 | 240° | -25.000 | -43.301 |
| 6 | 300° | 25.000 | -43.301 |
0° lies on the positive X axis, positive angles run counter-clockwise, as in the top view with G17. Hole 1 is highlighted in light blue in the sketch. The NC blocks always use a decimal point, as the control expects.
Formulas at a glance
Coordinates of a hole
D is the bolt circle diameter, α the angle of the hole. Example: Ø100 with six holes starting at 0°, hole 2 lies at 60° and therefore at X 25.000 and Y 43.301.
Pitch angle and hole angle
n is the number of holes, i the hole number. Six holes give a 60° pitch, eight holes 45°.
How to calculate hole spacing
The distance between two neighbouring hole centres along the chord. Ø100 with six holes gives 50.000 mm, with eight holes 38.268 mm.
Straddling the centre lines
With this start angle the holes sit symmetrically between the axes instead of on them. 45° for four holes, 30° for six.
From the shop floor: Check the hole spacing with a caliper: measure outside edge to outside edge of two neighbouring holes and subtract the hole diameter once. If that matches, the bolt circle is right, without having to probe the centre.
Frequently asked questions
How do you calculate bolt circle coordinates?
X equals X0 plus half the bolt circle diameter times the cosine of the angle, Y equals Y0 plus half the diameter times the sine. The hole angle is the start angle plus the hole number minus one times 360 divided by the number of holes. For Ø100 with six holes, hole 2 lies at X 25.000 and Y 43.301.
What is the distance between two holes?
Bolt circle diameter times the sine of 180 degrees divided by the number of holes. For Ø100 and six holes that is exactly 50 mm, for eight holes 38.268 mm.
Where is 0 degrees on the bolt circle?
On the positive X axis, so to the right of the centre when viewed from above. Positive angles run counter-clockwise. That matches the control convention in the XY plane (G17).
When do holes straddle the centre lines?
When no hole should sit on an axis and the holes should lie symmetrically between them instead. This is common on flanges, for example. Set the start angle to half the pitch, i.e. 180 degrees divided by the number of holes.
Can the control not calculate the bolt circle itself?
Many can: Siemens with cycle HOLES2, Heidenhain with cycle 220, Haas with G70. You still need the coordinates, for example for controls without a cycle, for checking on the CMM or for the drawing.
How accurate are the coordinates?
The calculator outputs three decimal places, i.e. to the micrometre. That is finer than any position tolerance in practice. What counts is the tolerance on the drawing for the position of the holes.
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