Bolt Circle Calculator for Hole Coordinates
Use this bolt circle calculator to generate X and Y coordinates for equally spaced hole centers. Enter the pitch circle diameter, number of holes, center coordinates, and the angle of the first hole. The output uses the selected center as its coordinate origin and lists each hole’s angle and position.
The geometry is for layout and programming checks. It does not select a fastener, define an edge distance, or confirm that the surrounding part is strong enough.
Interactive calculator
Enter values and select Calculate.
Coordinates and chord spacing
For N equally spaced holes, the angular step is 360° ÷ N. The radius is half the pitch circle diameter. For each hole angle θ, measured counterclockwise from the positive X axis, coordinates are X = centerX + radius × cos(θ) and Y = centerY + radius × sin(θ).
The straight-line distance between adjacent hole centers is the chord: chord = diameter × sin(180° ÷ N). This is shorter than the arc distance along the circle. The first-hole angle changes the coordinate orientation but not the spacing.
Worked example
For a 100 mm pitch circle with four holes and a 0° first angle at the origin, the angular step is 90°. The hole centers are at (50, 0), (0, 50), (−50, 0), and (0, −50) mm. Adjacent center-to-center chord spacing is about 70.711 mm.
Check the datum and manufacturing callout
Confirm whether the drawing defines the first hole from +X, +Y, or another datum. This calculator uses counterclockwise angles from +X. A 90° first-hole angle places the first hole at +Y. Enter nonzero center coordinates when the circle center is offset from the part zero.
The calculator assumes a perfect circle and equal angular spacing. It does not account for positional tolerance, hole diameter, counterbores, bolt clearance, angular datum tolerance, or a nonuniform pattern. Verify the coordinate table against the drawing and the CNC program before cutting.
If you need to check a resulting one-dimensional size chain, use the tolerance stack-up calculator. For a reference to dimensioning and tolerancing practices, see the ASME Y14.5 standard overview.
