A bolt-circle table is a polar-to-Cartesian conversion with a few important reference choices. This guide shows the exact relationship, works a complete example, and gives you independent checks before you use the result.
What PCD means—and what it does not mean
PCD stands for pitch circle diameter. It is the diameter of the imaginary circle that passes through the center of every equally spaced hole. It is not the outside diameter of the plate, the hole diameter, or the distance between neighboring hole edges.
That distinction matters because the coordinate calculation locates hole centers. Once those centers are correct, the drawing or machining process can apply the required hole diameter and tolerance separately.
The five inputs that define a bolt-circle layout
A complete, repeatable layout needs more than the circle diameter. Record these inputs before calculating:
- PCD: the diameter through the hole centers.
- Hole count (n): the number of equally spaced positions.
- Start angle: the angular position of hole 1.
- Center X and center Y: the coordinate origin of the bolt circle.
- Direction: counterclockwise or clockwise numbering.
The free bolt-circle calculator accepts all five and returns a numbered coordinate table. Understanding the equations first makes it easier to catch a sign, angle, or reference-point mistake.
Bolt-circle coordinate formulas
Convert PCD to radius
R = PCD ÷ 2Coordinates are measured from the circle center, so the equations use radius rather than diameter.Find the angle for hole i
θᵢ = α ± (360° × i ÷ n)Use i = 0 for the first hole. Add for counterclockwise numbering and subtract for clockwise numbering.Convert polar position to X/Y
Xᵢ = cx + R cos θᵢ · Yᵢ = cy + R sin θᵢcx and cy are the bolt-circle center coordinates. Most software trigonometric functions require the angle in radians.Check adjacent center spacing
spacing = PCD × sin(π ÷ n)This chord length is a useful independent check for any two neighboring hole centers.Worked example: 120 mm PCD with eight holes
Use a 120 mm PCD, eight holes, a 0° start angle, center (0, 0), and counterclockwise numbering. The radius is 60 mm, and the angular step is 360° ÷ 8 = 45°.
For hole 2, θ = 45°. Therefore X = 60 × cos 45° ≈ 42.4264 mm and Y = 60 × sin 45° ≈ 42.4264 mm. Apply the same calculation at each 45° step.
| Hole | Angle | X (mm) | Y (mm) |
|---|---|---|---|
| 1 | 0° | 60.0000 | 0.0000 |
| 2 | 45° | 42.4264 | 42.4264 |
| 3 | 90° | 0.0000 | 60.0000 |
| 4 | 135° | −42.4264 | 42.4264 |
| 5 | 180° | −60.0000 | 0.0000 |
| 6 | 225° | −42.4264 | −42.4264 |
| 7 | 270° | 0.0000 | −60.0000 |
| 8 | 315° | 42.4264 | −42.4264 |
Start angle, direction, and center offset
Changing the start angle rotates the whole pattern without changing its size or spacing. A 90° start places hole 1 at the top in a conventional X-right, Y-up coordinate system. A 0° start places it on the positive X-axis.
Direction changes the sequence, not the physical set of points. Counterclockwise uses increasing angles; clockwise uses decreasing angles. Confirm which convention the drawing, controller, or shop process expects before numbering holes.
A center offset translates every point. With the same 120 mm PCD but center (100, 50), the first 0° hole moves from (60, 0) to (160, 50). The relative geometry remains unchanged.
Common mistakes that move every hole
- Using plate diameter or hole diameter as PCD. PCD must pass through the hole centers.
- Using PCD directly as R. Coordinate formulas need half the PCD.
- Mixing degrees and radians. Convert degrees before calling a radians-based sin or cos function.
- Ignoring the drawing’s start-angle reference. Zero degrees may be defined from a different axis in a machine or CAD setup.
- Flipping the Y-axis without noticing. Screen coordinates often increase downward; Cartesian workshop coordinates usually increase upward.
- Rounding each intermediate step. Keep full precision until the final displayed or exported coordinate.
- Forgetting the center offset. A correct pattern around (0, 0) is still wrong if the part origin is elsewhere.
A practical verification sequence
Before using the coordinate table in a drawing or setup, verify the PCD and hole count against the source drawing, check the first-hole angle and numbering direction, and confirm the coordinate origin. Then compare one adjacent pair against the chord-spacing formula.
For critical work, treat the calculated coordinates as layout data—not as a substitute for the drawing’s tolerances, datum scheme, tooling limits, or an appropriate inspection process. A second independent check is cheaper than propagating a reference error through every hole.
Calculate the full pattern without retyping formulas
Use the Bolt Circle & PCD Coordinate Calculator to generate the complete table in your browser. It supports a custom center, start angle, clockwise or counterclockwise numbering, and adjustable decimal precision.
Circle Calculator brings the same kind of focused workflow to iPhone and Android. The calculation, diagram, and coordinate table are available without requiring a Pro export; eligible Pro workflows add PDF, CSV, and DXF outputs. Current availability and purchase terms are shown by your device’s store.
Take the table with you
Continue in Circle Calculator.
Calculate bolt-circle coordinates on iPhone or Android, keep useful work on your device, and evaluate eligible Pro PDF/CSV/DXF export workflows when you need a file. Current availability and purchase terms appear in your device’s store.