Bolt Circle Calculator uses BCD, hole count, and start angle to calculate chord distance, angle step, pitch radius, and X/Y coordinates using C = BCD × sin(π/N) for circular hole layout checks in CNC.
| Hole # | Angle | X Coord (in) | Y Coord (in) |
|---|---|---|---|
| 1 | 0.000° | 2.0000 | 0.0000 |
| 2 | 72.000° | 0.6180 | 1.9021 |
| 3 | 144.000° | -1.6180 | 1.1756 |
| 4 | 216.000° | -1.6180 | -1.1756 |
| 5 | 288.000° | 0.6180 | -1.9021 |
The Number Machinists Reach For Before Touching the Mill
Laying out a bolt circle by hand — scribing radial lines, measuring chord distances, hoping the last hole lands where it should — is where flanges get scrapped. The problem isn’t the math itself; it’s that a 0.2° angular error on a 6-inch BCD compounds across five holes until your final position is off by nearly a millimeter. Polar-to-Cartesian conversion removes that accumulation entirely. Every hole gets its own independent coordinate pair calculated directly from center, so a mistake on hole 3 doesn’t drag hole 4 off with it.
That’s what this calculator produces: a full XY coordinate table for every hole in the pattern, referenced to a common center origin at (0,0). You get exact positions you can dial in at the DRO or feed directly into a CNC program, not incremental hops that stack error.
What the Calculator Is Actually Computing
Four inputs drive everything: the number of holes, the bolt circle diameter, the starting angle, and whether you’re working in inches or millimeters.
The angular step is simply 360° divided by the hole count — for 6 holes that’s 60° exactly, for 5 it’s 72°, for 3 it’s 120°. Each hole’s angle is the starting angle plus that step multiplied by its position in the sequence. Hole 1 sits at the starting angle, hole 2 at starting angle + step, hole 3 at starting angle + 2×step, and so on.
Converting those angles to coordinates uses the bolt circle’s pitch radius — which is half the BCD — and standard polar conversion:
- X = radius × cos(angle)
- Y = radius × sin(angle)
The hero figure — adjacent hole distance — is the chord length between neighboring holes. It comes from 2 × radius × sin(π ÷ N). This is a fixed distance for any two neighboring holes in a uniform bolt circle and is the dimension you’d verify with calipers before committing to the final drill pass.
The starting angle defaults to 0°, which places hole 1 directly on the positive X-axis (3 o’clock position). Rotating that to 90° puts hole 1 at the top (12 o’clock). Neither is more “correct” — it depends on how your part is oriented on the machine and what your drawing calls out.
Worked Example: Pump Flange Face Plate
A machinist rebuilding a centrifugal pump needed to drill a new mounting flange to match an existing 4-bolt ASME pattern. The original flange measured a 3.500″ BCD, four holes equally spaced. The part was fixtured with the keyway at the top, so he used a 90° starting angle to put hole 1 at 12 o’clock — matching the drawing orientation.
Inputs: 4 holes, BCD 3.500 in, starting angle 90°, US system.
Results from the coordinate table:
- Hole 1 — 90°: X 0.0000, Y 1.7500
- Hole 2 — 180°: X −1.7500, Y 0.0000
- Hole 3 — 270°: X 0.0000, Y −1.7500
- Hole 4 — 0°: X 1.7500, Y 0.0000
Adjacent hole chord distance: 2.475 in. He measured the existing flange between adjacent holes with a caliper — 2.474 in — close enough given the worn face surface. The coordinates went straight into the Bridgeport DRO as offsets from the bored center, and all four holes landed within 0.001″ of target.
The 90° starting angle was the key decision here. Had he left it at 0°, his first coordinate output would have been X 1.750, Y 0.000 — correct math, wrong orientation for how the part was sitting on the table.
Frequently Asked Questions
The minimum hole count is 2. What does a 2-hole bolt circle actually produce?
Two holes at 180° apart — diametrically opposed on the pitch circle. The angular step is 180°, the chord distance equals the full BCD, and you get two coordinates on exactly opposite sides of center. This is a legitimate use case for through-bolt patterns on small fixtures and couplings, and the calculator handles it correctly. Below 2 holes, the input is invalid and results will not populate.
Does the starting angle accept negative values?
The angle field has no minimum enforced, so you can enter negative values and the calculator will process them through the trigonometric functions without error — cos(−45°) and cos(315°) produce the same coordinate. In practice, any negative starting angle has an equivalent positive angle (add 360°), so the results are mathematically identical either way. Use whichever notation matches your drawing.
When I switch between US and metric, do my dimension inputs convert automatically?
No. The unit selector changes the label on the BCD field and the column headers in the coordinate table, but it does not convert any numbers you’ve already entered. If you typed 4.000 in US mode and then switch to metric, the calculator treats that as 4.000 mm — a very different bolt circle. Enter the correct value in the correct unit system before running the calculation.
The chord distance is the same for every adjacent pair in the table. Is that always true?
Yes, for a uniform bolt circle — which is what this tool calculates. Equal angular spacing means every adjacent pair subtends the same arc, so the chord is invariant around the pattern. If you needed an irregular bolt circle (unequal spacing), the chord would differ between pairs and this tool wouldn’t apply. For all standard flange and hub patterns, uniform spacing is the norm and the single chord value is sufficient to verify layout.
My drawing gives the BCD as a diameter but the card shows “Pitch Radius.” Which is which?
BCD is always the diameter — the full distance across the circle through center. The calculator halves it internally to get the pitch radius, which is what feeds into the coordinate math. You enter the diameter as it appears on your print. The pitch radius shown in the Angle Step card is just making that internal division visible so you can cross-check against drawings that dimension the circle by radius.
Why the Coordinate Table Matters More Than the Chord Alone
The adjacent hole chord is useful for a quick caliper check, but it has a blind spot: it can’t confirm rotational position. A pattern drilled at the right BCD but rotated 10° from its correct orientation will still have the correct chord distance between every adjacent pair. The chord won’t catch that error — the coordinate table will.
This matters most on flanges and adapters that mate to existing hardware. A 5-hole 4.5″ BCD pattern rotated 10° from nominal won’t assemble; every bolt hole misses by a predictable offset. Yet measuring chord distance between neighbors would show a perfect 2.629″ every time. Once you’re working to a specific angular reference — keyed shafts, indexed couplings, mated flanges — position the starting angle to match your drawing datum and verify from the XY table, not just the chord.
The other scenario where the table earns its keep is deep-hole work on a CNC. Programming from incremental angles introduces cumulative rounding — each position is calculated from the previous one. Absolute Cartesian coordinates (from the table) give the control system an independent position for every hole, so a repositioning move that introduces a 0.0001″ rounding error on hole 3 has zero effect on hole 4’s target.