Lay out a bolt hole circle three ways: derive the full X/Y coordinate table from a known bolt circle diameter, reverse-solve the BCD from a chord measurement between adjacent holes, or correct a caliper across-holes reading on an odd-count pattern. Supports uneven spacing, flange presets, and both millimeters and inches.
Bolt Circle Diameter
100 mm
radius 50 mm · 5 holes · step 72°
How this was computed
X = R·sin(θ), Y = R·cos(θ) — θ from 0° (12 o’clock) clockwise, step 72°
Angles run clockwise from the 12 o’clock start angle. X is right, Y is up, relative to the circle center.
| Hole | Angle | X (mm) | Y (mm) |
|---|---|---|---|
| 1 | 0° | 0 | 50 |
| 2 | 72° | 47.55 | 15.45 |
| 3 | 144° | 29.39 | -40.45 |
| 4 | 216° | -29.39 | -40.45 |
| 5 | 288° | -47.55 | 15.45 |
Six patterns that cover most of what lands on a bench or a lathe. One tap in the calculator loads the hole count and BCD; the table here is the offline version for the notebook.
| Application | Holes | BCD/PCD (mm) | Hole Ø (mm) | Step (°) |
|---|---|---|---|---|
| Bicycle chainring (road 5-arm) | 5 | 130 | 9 | 72° |
| Bicycle chainring (compact 5-arm) | 5 | 110 | 9 | 72° |
| Weld flange 2" Class 150 | 4 | 120.6 | 15.8 | 90° |
| Weld flange 4" Class 150 | 8 | 190.5 | 19 | 45° |
| Wheel / hub pattern 5×114.3 | 5 | 114.3 | — | 60° |
| JIS 10K 50A flange | 4 | 105 | 15 | 90° |
Flange rows follow ASME B16.5 Class 150 welding-flange drillings; the JIS row is JIS B2220 10K 50A. Hole diameters are standard clearance drillings — see the clearance hole chart for the full fit table.
Every bolt circle question reduces to one piece of circle geometry: holes evenly spaced on a diameter are chords of that circle, and chord length follows only from the angle between the holes. Three formulas cover every practical case.
Forward: BCD to coordinates
X = R·sin(θ) · Y = R·cos(θ) · θᵢ = start + i·(360°/n)
Reverse: adjacent chord to BCD
BCD = c / sin(180°/n)
Reverse: across-holes reading to BCD
BCD = M / cos(90°/n) for odd n · BCD = M for even n
Work one by hand to check the tool: a 4-hole pattern with 70.7 mm between adjacent hole centers gives BCD = 70.7 / sin(45°) = 100.0 mm, and each hole sits 90° apart, so with a start angle of 0° the coordinates are (0, 50), (50, 0), (0, −50), (−50, 0) mm. Run the same numbers above and the table matches to the last digit.
The step angle is the whole reason patterns are easy to generate and hard to measure: dividing 360° by any hole count is trivial, but recovering that angle from a physical part forces you through a chord, and chords contract fast as the count rises — adjacent holes on an 8-hole 100 mm circle sit only 38.3 mm apart, where a 1 mm measuring error already costs 2.6 mm of inferred diameter. High hole counts demand the widest chord you can reach, not the most convenient one.
Even counts (4, 6, 8, 10…): calipers span diametrically opposite holes, so the widest reading is the BCD. No correction — but measure hole-edge to hole-edge on the same flank of both holes, or add the hole diameter to a hole-edge reading. The classic shortcut, measuring back-edge to back-edge and subtracting one hole diameter, gives the same answer faster.
Odd counts (3, 5, 7…): there are no opposite holes, and this is where BCD estimates go wrong. The widest reachable pair sits (n−1)/2 steps apart, and its chord is shorter than the diameter by the factor cos(90°/n): 0.866 for 3 holes, 0.951 for 5, 0.975 for 7. Reading a 5-hole chainring across the widest pair and calling it the BCD understates the true circle by 4.9% — enough that a 130 mm ring measures 123.6 mm and no longer matches any catalog value. Divide by the factor (or let the calculator do it) and the catalog number reappears.
💡 The machinist’s cross-check
Before cutting, verify the derived BCD against the adjacent chord the other way: chord = BCD × sin(180°/n). If the derived diameter and the measured chord disagree by more than about 0.5% on a drilled part, suspect hole-edge burrs or a mis-counted pattern — not the trigonometry.
A 5-hole pattern: widest measurable pair = 2 steps = BCD × 0.951
The coordinate table is relative to the circle center. Either edge-find the center and set G54 (or the DRO zero) there, or add the center's machine coordinates to every X/Y pair before cutting. A mixed reference is the #1 cause of patterns drilled one radius off.
This tool starts at 12 o'clock and runs clockwise. Many DRO bolt-hole-circle functions start at 3 o'clock; Fanuc-style cycles often want the first-hole angle as a parameter in degrees from +X. Read one hole from the table, position manually, and verify before running the cycle.
Cutter radius compensation (G41/G42) changes the tool path, never the hole-center coordinates — drill centers are what the table gives. Pilot-drill, then open to final diameter; the coordinates stay identical for both passes.
If your machine expects counterclockwise angles, mirror the set: use 360° − θ for every hole. Reversing direction without mirroring produces a valid-looking table that is wrong for every hole except #1 — and it passes a single-hole spot check.
For hand layout without a DRO, the coordinate table still wins over angle-and-chord layout: marking X/Y from two datums with a height gauge repeats better than swinging a dividers through 72° steps, and any error stays a translation instead of a rotation.
Flange BCDs are standardized — 2-inch Class 150 is 120.6 mm with four ⌀15.8 holes at 90°, 4-inch is 190.5 mm with eight ⌀19 holes at 45°. Use BCD → X/Y mode to lay out a matching gasket or drill a backing ring; never reverse-solve a standard flange and expect the answer to be a round number, because standard drillings sit on raised faces with their own tolerances.
Patterns are written holes × BCD: 5×114.3, 5×120, 4×100. Even 4- and 6-lug patterns measure directly across opposite lugs; 5-lug wheels need the ÷0.951 correction on the widest pair. Measure at the lug-hole centers with the wheel off the car — measuring across studs with a wheel mounted adds cone-seat radius errors.
Road 5-arm standards are 130 mm and 110 mm BCD, measured hole-center to hole-center; MTB four-arm rings (64/104 mm) measure directly across. A worn ring with one elongated hole still yields a correct BCD if you average the widest-pair reading from two different hole pairs.
Uneven-spacing mode exists for repairs: a flange with one stripped hole re-drilled between positions, or an adapter plate bridging two different standards. Enter per-hole offsets from the even base, and the table stays a single cut sheet instead of two mismatched half-patterns.
Derived a BCD? Multiply it back through sin(180°/n) and compare to your caliper reading. Agreement within 0.5% means the pattern geometry is confirmed before any metal is cut.
Same-flank edge-to-edge equals center-to-center only across parallel hole walls. Mixed-flank or diagonal caliper reads silently add the hole diameter — up to a 20% chord error on M8 holes in a tight pattern.
The measuring and layout questions this calculator gets asked most, with the formulas behind each answer.
A bolt hole circle calculator answers the layout half of the job — hole count, angles, and X/Y positions on the bolt circle diameter. The other half is choosing the fasteners that go in those holes: the free bolt torque calculator sizes the tightening torque for the grade and lubrication you assemble with, and the rest of the bolt calculators cover shear, length, weight, and anchor embedment — all built on the same published standards, so a pattern laid out here matches a spec written there.
The circle is laid out — size, tighten, and account for the hardware with the companion tools.
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