Bolt Circle Calculator
Work out the X and Y position of every hole on a bolt circle (pitch circle diameter). Set the number of holes, the start angle, direction and center point, or spread the holes over a partial arc, and get a numbered drawing plus a coordinate table you can copy into a CNC program or drawing.
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Angle of hole 1, measured from the +X axis (3 o'clock)
How to use the Bolt Circle Calculator
- Enter the bolt circle diameter (or radius) and the number of holes.
- Set the start angle: 0° puts hole 1 at 3 o'clock, 90° at 12 o'clock.
- Choose the direction and, if needed, a partial arc for unevenly spread holes.
- Enter the center X and Y of the pattern on your part.
- Read the coordinates from the table, check the drawing, and download the CSV.
Bolt circle formulas
| Quantity | Formula |
|---|---|
| Angle between holes | Δθ = 360° ÷ n (full circle) or arc ÷ (n − 1) |
| Angle of hole k | θk = start ± (k − 1) × Δθ |
| X coordinate | X = cx + r × cos θ |
| Y coordinate | Y = cy + r × sin θ |
| Chord between adjacent holes | c = 2r × sin(Δθ ÷ 2) = D × sin(180° ÷ n) |
| Diameter from chord | D = c ÷ sin(180° ÷ n) |
Chord factor for equally spaced holes
Multiply the bolt circle diameter by the factor to get the center-to-center distance between neighboring holes.
| Holes | Angle | Chord factor sin(180° ÷ n) | Example on a 100 mm circle |
|---|---|---|---|
| 3 | 120° | 0.86603 | 86.603 mm |
| 4 | 90° | 0.70711 | 70.711 mm |
| 5 | 72° | 0.58779 | 58.779 mm |
| 6 | 60° | 0.50000 | 50.000 mm |
| 8 | 45° | 0.38268 | 38.268 mm |
| 10 | 36° | 0.30902 | 30.902 mm |
| 12 | 30° | 0.25882 | 25.882 mm |
| 16 | 22.5° | 0.19509 | 19.509 mm |
Tips for machining bolt circles
- Straddle the centerline: flange standards usually place holes off the vertical and horizontal centerlines. For 4 holes that means a 45° start angle; for 8 holes, 22.5°.
- Use enough decimals for the machine: 3 places in millimeters or 4 in inches is typical for CNC work.
- Check the web: keep enough material between holes; the tool flags holes that would overlap.
- Measure a pattern: for an even number of holes, measure center to center across opposite holes; that distance is the bolt circle diameter.
Frequently asked questions
How do you calculate bolt circle coordinates?
For a bolt circle of radius r centered at (cx, cy), hole k sits at angle θ = start + (k − 1) × 360° ÷ n. Its coordinates are X = cx + r × cos θ and Y = cy + r × sin θ. For 6 holes on a 100 mm circle starting at 0°, hole 2 is at 60°: X = 50 × cos 60° = 25, Y = 50 × sin 60° = 43.301.
What is the distance between two adjacent bolt holes?
The straight-line distance is the chord: 2r × sin(180° ÷ n). Six holes on a 100 mm bolt circle are 2 × 50 × sin 30° = 50 mm apart, center to center.
What is a bolt circle diameter (PCD)?
The bolt circle diameter, also called the pitch circle diameter (PCD), is the diameter of the circle that passes through the centers of all the holes. It is not the outside diameter of the flange or the distance between hole edges.
How do I measure a bolt circle with an odd number of holes?
With an odd count no hole is directly opposite another. For 5 holes, measure from the center of one hole to the outer edge of the hole farthest from it and correct for the hole size, or use the relation: bolt circle diameter = distance between adjacent holes ÷ sin(36°).
Which way is 0° and which direction are angles measured?
This calculator follows the math and CAD convention: 0° points along +X (3 o'clock) and positive angles run counterclockwise. Choose clockwise to number the holes the other way, and use a 90° start angle to put hole 1 at the top.
Can I use inches or millimeters?
Yes. The calculator works in whatever unit you type. The coordinates come out in the same unit as the diameter and center point.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.