Enter how many holes, the bolt circle diameter (PCD) and where hole 1 sits: you get each hole's X / Y, the pitch between neighbours and the plastic left between them, drawn to scale. Then make the part — the same pattern opens in the flange generator, ready to print or to send as a STEP.
| Hole | Angle | X | Y |
|---|---|---|---|
| 1 | 0° | 50 | 0 |
| 2 | 60° | 25 | 43.301 |
| 3 | 120° | -25 | 43.301 |
| 4 | 180° | -50 | 0 |
| 5 | 240° | -25 | -43.301 |
| 6 | 300° | 25 | -43.301 |
Millimetres from the centre you entered, 3 decimals. The copied table is tab-separated: it pastes into a spreadsheet or a CAD sketch table.
The flange generator builds a round plate with exactly this pattern — outside Ø 120 mm suggested (hole centres 1.5 holes from the rim), your centre bore, holes at the clearance size you chose. Download STL to print or STEP for CAD.
Every hole sits on a circle of radius r = PCD / 2 around the centre. Hole 1 is at the start angle; the others follow counter-clockwise, 360° / N apart. The X and Y of each hole are plain trigonometry, worked out exactly — there is nothing to approximate.
The pitch between two neighbouring holes is the chord of that circle. The rule is old: Machinery's 1914 reference on locating holes says to divide 360 by twice the number of holes, find the sine of that angle and multiply by the circle's diameter.
θi = start + (i − 1) · 360° / N (i = 1 … N) xi = cx + (PCD / 2) · cos θi yi = cy + (PCD / 2) · sin θi pitch (neighbours) = PCD · sin(180° / N) holes k apart = PCD · sin(k · 180° / N) PCD from a pitch = pitch / sin(180° / N)
Check: Machinery's own example puts 11 holes on an 8-inch circle — 8 × sin(16.36°) = 2.252 in between neighbours. The calculator gives 2.2539 in with the unrounded angle (180° / 11 = 16.3636°).
A DN50 PN16 flange has 4 holes of Ø18 for M16 bolts on a 125 mm bolt circle, 165 mm outside (EN 1092-1 tables). Pipe flanges place the holes so that they straddle the centre lines — for 4 holes the first one is at 45°. With PCD 125, N 4 and a start of 45°, r = 62.5 and every coordinate is 62.5 × cos 45° = 44.194 mm:
| Hole | Angle (°) | X (mm) | Y (mm) |
|---|---|---|---|
| 1 | 45 | 44.194 | 44.194 |
| 2 | 135 | −44.194 | 44.194 |
| 3 | 225 | −44.194 | −44.194 |
| 4 | 315 | 44.194 | −44.194 |
Neighbouring holes are 125 × sin 45° = 88.388 mm apart and opposite holes 125 mm. With Ø18 holes that leaves 70.4 mm of material between neighbours and (165 − 125) / 2 − 9 = 11 mm from each hole to the rim. Open it: the DN50 row in the table below fills in all of this, and its second link makes the flange.
On pipe flanges the holes are not on the centre lines: ASME B16.5 §6.5 says “pairs of bolt holes shall straddle fitting centerlines”. For 4 holes that puts hole 1 at 45°, for 8 holes at 22.5°, for 12 at 15° — half the angle between holes. Motor flanges are drawn the same way.
This calculator, like most CAD, measures angles counter-clockwise from the +X axis (3 o'clock). If your drawing counts from 12 o'clock, add 90°; if it counts clockwise, use 360° minus its angle.
Pipe flanges (EN 1092-1, PN10 and PN16 drill alike up to DN150) and IEC B14 motor face flanges, where the flange code is the bolt circle. Each row opens in the calculator, or straight into the flange generator.
| Flange | D outside | K bolt circle | Holes | Calculator | Part |
|---|---|---|---|---|---|
| EN 1092-1 PN16 DN15 | 95 | 65 | 4 × 14 | Open | Make it |
| EN 1092-1 PN16 DN25 | 115 | 85 | 4 × 14 | Open | Make it |
| EN 1092-1 PN16 DN50 | 165 | 125 | 4 × 18 | Open | Make it |
| EN 1092-1 PN16 DN80 | 200 | 160 | 8 × 18 | Open | Make it |
| IEC B14 FT65 | 80 | 65 | 4 × M5 | Open | Make it |
| IEC B14 FT85 | 105 | 85 | 4 × M6 | Open | Make it |
| IEC B14 FT100 | 120 | 100 | 4 × M6 | Open | Make it |
| IEC B14 FT130 | 160 | 130 | 4 × M8 | Open | Make it |
The flange generator is the same pattern as parametric CAD: bolt circle, number of holes and start angle as here, a screw size that sets an ISO 273 clearance hole (plus a print allowance), an outside diameter, a centre bore, an optional hub for a pipe or shaft, and counterbores for socket head screws. It exports STEP with exact cylinders for every hole, so a machinist or a CAD program reads the pattern directly.
It refuses what would not hold together, and says what to change: less than half a hole of plastic to the rim, the bore or the next hole, or neighbours closer than 2.2 holes centre to centre (Eurocode 3's minimum for steel). An outside diameter that is too small simply grows to fit.
The circle through the centres of a ring of bolt holes, given by its diameter — the bolt circle diameter, BCD, or pitch circle diameter, PCD. With the number of holes and where the first one sits, it fixes every hole: that is all this calculator needs.
With an even number of holes, measure from the centre of one hole to the centre of the opposite one: that is the PCD. With an odd number, measure between neighbouring centres (outer edge to outer edge minus one hole diameter works with calipers) and divide by sin(180° / N) — for 5 holes, by 0.5878.
Four holes on a square of side a lie on a circle of diameter a × √2, starting at 45°. A 31 mm square is a 43.841 mm bolt circle with holes at 45°, 135°, 225° and 315°.
For printed plastic plates, put the hole centre at least 1.5 hole diameters from the edge — ACRYLITE's rule for plastic sheet, and AISC's minimum for steel; the outside diameter this page suggests follows it. The flange generator's hard limit is half a hole of plastic to the rim, which is about what steel pipe flanges keep (EN 1092-1 DN15: 8 mm beside a 14 mm hole).
The coordinates do — enter the PCD in inches and read X / Y in inches. The screw sizes and the flange generator are metric: for a part, enter millimetres.
ISO 273 gives three series per screw (fine, medium, coarse — M6: 6.4 / 6.6 / 7.0). The clearance hole chart beside this page lists them all, plus how much a printed hole needs on top.
Every number on this page comes from these documents (the version or the date we read them is given).
