Bolt circle coordinates without the trig
A bolt circle is a set of holes spaced evenly around a circle — flanges, hubs, face plates, engine covers. To drill or program them you need each holes X and Y position, not just the diameter. This calculator lays out every hole: enter the bolt circle diameter, the count, and a start angle, and it returns the coordinates plus the chord spacing between neighbors.
The math
The holes sit on a circle of radius BCD / 2. Each is one step of 360 / number-of-holes degrees from the last. A holes position is X = center X + radius x cos(angle), Y = center Y + radius x sin(angle). The straight-line spacing between adjacent holes — the chord — is BCD x sin(180 / number-of-holes).
Using the coordinates
The table gives positions relative to the center you enter, so leave the center at zero for part-origin coordinates, or set it to your fixture datum to drill straight from machine zero. Start angle rotates the whole pattern; many prints put the first hole at the top, which is a 90 degree start.
Related layout tools
For a grid or line of holes rather than a circle, use the hole pattern calculator. To convert any single radius-and-angle into X and Y, see the polar coordinate calculator.
Worked example
Six holes on a 4 in bolt circle starting at 0 degrees: they land 60 degrees apart, the first at X 2.000, Y 0.000, and the chord between neighbors is 4 x sin(30) = 2.000 in.
FAQ
Where is zero degrees?
Zero points along the positive X axis (3 oclock) and angles increase counterclockwise, the math convention. Switch direction to clockwise, or set a 90 degree start, to match your drawing.
Can I get a hole at top dead center?
Yes — set the start angle to 90 degrees and the first hole sits straight up. With an even hole count you then get one at top and one at bottom.