How are bolt-circle coordinates calculated?

Each hole sits on the circle at radius equal to half the bolt-circle diameter. For hole i its angle is the start angle plus i times 360 divided by the hole count. The X coordinate is center X plus radius times cosine of that angle, and Y is center Y plus radius times sine.

Where is the angle measured from?

This tool measures angles counterclockwise from the positive X axis, the standard mathematical convention used by most CNC controls. A start angle of zero places the first hole directly to the right of center; ninety degrees places it straight up.

Can I offset the first hole?

Yes. The starting-angle field rotates the whole pattern. A common choice is to offset by half the hole spacing so that no hole lands on a centerline, or to align the pattern with a feature such as a keyway.

Does it work for any number of holes?

Yes, for two or more equally spaced holes. For three holes you get a triangle, for four a square, for six a hexagon, and so on. The spacing is always 360 degrees divided by the number of holes.

What if my center is not at the origin?

Enter the actual center X and Y of the bolt circle on your part and every coordinate is returned as an absolute position relative to your part zero, so you can key them straight into the control without further offsetting.

Bolt Circle Coordinate Calculator

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.

Tips and example

For 6 holes on a 4-inch bolt circle centred at the origin with a 0 degree start, the radius is 2 inches and holes fall every 60 degrees. The first is at (2.000, 0.000), the next at (1.000, 1.732), and so on around the ring. If you would rather not have a hole on the X axis, set the start angle to 30 degrees and the whole pattern rotates so the holes straddle the centerlines instead.