Laying out a ring of holes by hand is error-prone trigonometry. This calculator returns the exact absolute X/Y coordinate of every hole on a bolt circle so you can key them straight into a CNC control or set them on a DRO without doing the sines and cosines yourself.
How it works
Every hole lies on a circle of radius equal to half the bolt-circle diameter,
centred on the point you specify. Hole i (counting from zero) sits at angle:
angle_i = start_angle + i × (360 / number_of_holes)
X_i = center_X + radius × cos(angle_i)
Y_i = center_Y + radius × sin(angle_i)Angles are measured counterclockwise from the positive X axis, the convention most CNC controls and DROs use. The starting-angle field rotates the entire pattern, which lets you align it with a keyway or offset it so no hole lands on a centerline.
Worked example: 6-hole pattern on a 4-inch BCD
Bolt-circle diameter: 4 in, 6 holes, center at (0, 0), starting angle 0°.
Radius = 2 in, spacing = 60° per hole.
| Hole | Angle | X | Y |
|---|---|---|---|
| 1 | 0° | 2.000 | 0.000 |
| 2 | 60° | 1.000 | 1.732 |
| 3 | 120° | -1.000 | 1.732 |
| 4 | 180° | -2.000 | 0.000 |
| 5 | 240° | -1.000 | -1.732 |
| 6 | 300° | 1.000 | -1.732 |
If you prefer no hole on the X axis, enter a 30° start angle and the entire pattern rotates so holes fall symmetrically between the centerlines.
Practical tips for CNC and DRO use
Non-origin center: Most real parts are not drilled at machine zero. Enter the actual center X and Y on your part and the tool returns coordinates relative to your work zero — ready to key in without additional offset arithmetic.
Starting angle and keyway alignment: If the pattern must not block a keyway or existing feature, adjust the starting angle until the first hole clears the feature. The equal spacing is maintained automatically.
Verifying a pattern: If you are checking an existing bolt circle against a drawing, enter the stated BCD and count, then compare the tool’s coordinates to your measured positions. A discrepancy points to a measurement error or a non-standard BCD.
Units: Enter dimensions in the unit system your control uses — typically inches or millimetres. The formula is unit-agnostic; the coordinates come out in whatever unit you put in.
Common bolt circle sizes in engineering
While any diameter and hole count is valid, certain combinations appear repeatedly in mechanical standards:
- 4 holes on a 100 mm BCD — common on small flanges and couplings
- 4 holes on a 4.75-inch BCD — SAE 5-bolt patterns on some agricultural equipment
- 5 holes on various BCDs — automotive wheel bolt patterns (e.g. 5×100 mm, 5×114.3 mm)
- 6 holes on a 150 mm BCD — bicycle chainrings (road cycling standard)
- 8 holes — larger industrial flanges and hydraulic connections
If you are matching an existing flange or wheel hub, look up the standard BCD for that application and verify with a calliper measurement before machining.