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A bolt circle is a ring of evenly spaced holes, like the lugs on a wheel or the holes in a flange, and to drill or machine one you need each hole's position. This gives you the X and Y coordinates of every hole from the circle's diameter, the number of holes and where you want the first one, plus the angle between holes and the straight distance from one to the next.
From a diameter to coordinates
Every hole sits on the circle at its own angle, and its coordinates are just the radius swung to that angle: X is the radius times the cosine, Y is the radius times the sine. The holes are evenly spaced, so each one is another equal step of angle around from the last, and the step is a full turn divided by the number of holes. This page does that for all of them and hands you the list, so you are not working trig at the drill press.
Where the first hole goes
The pattern is fixed once you say where the first hole sits, because the rest follow at even steps. The first-hole angle here is measured counterclockwise from the three o'clock position, so ninety degrees puts it straight up and zero puts it out to the right. Set it to match your part, a flat at the top, a keyway, a mounting tab, and every other coordinate rotates with it. Change it and watch the whole ring turn.
Coordinates from the center
The numbers come out relative to the center of the circle, with X to the right and Y upward, which is how a CNC control reads a part zeroed on that center. On the machine, set your work zero at the circle's center and the coordinates drop straight in. Marking by hand, measure each one from the center with X across and Y up and down, and punch before you drill so the bit cannot wander.
The chord is your sanity check
The hole-to-hole figure is the straight-line distance between two neighboring holes, the chord of that little arc. It is the fastest way to check a pattern: set dividers to it and walk them around the ring, and every step should land on a mark. If the last one does not close, a hole is off. It is also how you step off a pattern by hand when you trust a chord more than a protractor.
More MakerKiln tools
- equal spacingEqual Spacing CalculatorSpace holes, pins or pickets evenly across a span, or divide into equal parts.→
- metal weightMetal Weight CalculatorWeight of a bar, tube, sheet or plate from the shape, size and material.→
- tap drillTap Drill Size CalculatorMetric tap drill at the percent of thread you want, plus the clearance hole.→
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