Hong Life CalculatorsUnderstanding the bolt circle calculator — concept and principle
A bolt circle (pitch circle) is a set of holes spaced evenly around a circle, as on flanges, wheels and covers. This calculator gives the angle between holes, the straight-line spacing between neighbours and the X–Y coordinates of each hole for machining or layout.
How it is calculated
- Angle of hole k (counting from 0): θk = θ₀ + k × 360° ÷ N.
- X = Xc + (PCD ÷ 2) × cos θk; Y = Yc + (PCD ÷ 2) × sin θk.
- Chord between neighbouring holes = PCD × sin(180° ÷ N).
- Angles run counter-clockwise from the +X axis; coordinates are rounded to 0.001 mm and the first 10 holes are listed.
The principle
Equal spacing means equal angles: N holes divide the full circle into N equal sectors. Each hole lies on the circle at radius PCD ÷ 2, so its position follows from cosine and sine of its angle, the standard conversion from polar to Cartesian coordinates. The chord between neighbours is the base of an isosceles triangle with two radii as its sides, which gives the sine formula.
Worked example
Default inputs: 6 holes, PCD 100 mm, first hole at 0°, centre (0, 0).
- Angle between holes = 360 ÷ 6 = 60°.
- Chord = 100 × sin 30° = 50 mm.
- Hole 1 at 0°: (50, 0); hole 2 at 60°: (25, 43.301); hole 3 at 120°: (−25, 43.301).
- Hole 4 at 180°: (−50, 0); hole 5 at 240°: (−25, −43.301); hole 6 at 300°: (25, −43.301).
- Holes 7–10 do not exist and show —.
| Bolt circle (pitch circle) diameter (mm) | Spacing between neighbouring holes (chord, mm) |
|---|---|
| 25 | 12.5 |
| 50 | 25 |
| 75 | 37.5 |
| 100 | 50 |
| 125 | 62.5 |
| 150 | 75 |
| 200 | 100 |
How to read the result
Use the coordinates directly in CNC programs or for marking out on a drill press. If your machine measures angles clockwise or from a different axis, adjust the start angle. For six holes the chord equals the radius, a handy check.
Common mistakes
- Entering the radius instead of the pitch circle diameter.
- Starting at the wrong angle relative to the part's features.
- Mixing clockwise and counter-clockwise conventions.
- Forgetting to offset coordinates from the part's datum when the centre is not at (0, 0).
Frequently asked questions
How do you calculate bolt hole positions?
X = centre X + radius × cos θ and Y = centre Y + radius × sin θ, with θ = start angle + k × 360° ÷ N.
What is the distance between bolt holes on a circle?
The chord PCD × sin(180° ÷ N).
What is PCD?
Pitch circle diameter: the diameter of the circle through the hole centres.
Sources: Machinery's Handbook, Industrial Press (bolt circle coordinates) · ISO 7005-1, Pipe flanges — Steel flanges (bolt circle dimensions, as an application example)