Bolt Circle Calculator
X and Y coordinates for evenly spaced holes on a bolt circle or partial arc, with start angle, centre offset, direction, hole spacing and CSV download.
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About this toolWhat is the Bolt Circle Calculator?
A bolt circle (or pitch circle diameter, PCD) is a ring of holes spaced evenly around a centre: flanges, wheel hubs, motor mounts, encoder discs. To drill one on a mill or mark it out on a plate you need each hole's X and Y coordinate. This bolt circle calculator works them out from the diameter and number of holes, with any start angle, centre offset, direction and either 3 o'clock or 12 o'clock as zero.
It also handles partial patterns (holes spread over an arc rather than a full circle), gives the straight-line spacing between neighbouring holes for checking with calipers, and draws a preview with hole 1 highlighted. Copy the table, download it as CSV for a DRO, CAM or spreadsheet, or use the reverse panel to find the PCD from a measured distance between two holes.
- Full circles and partial arcs, 2 to 360 holes
- Start angle, centre offset, 0° at 3 or 12 o'clock, CW or CCW
- Chord and arc spacing between holes
- Preview drawing with hole numbers
- Copy or download the coordinate table as CSV
- PCD from a measured distance between holes
How to use the Bolt Circle Calculator
- Enter the bolt circle diameter and the number of holes.
- Set the first hole angle and choose whether 0° is at 3 o'clock or 12 o'clock and whether holes run clockwise or counter-clockwise.
- For a partial pattern, enter the angle from the first hole to the last; leave 0 for a full circle.
- Enter the centre coordinates if the circle is not at the origin, and choose mm or inches and the decimal places.
- Read the coordinate table and hole spacing, check the preview, then copy or download the CSV.
Worked examples
Six holes on a 100 mm flange
Input
PCD 100, 6 holes, first at 0°, CCW from 3 o'clock
Output
(50, 0), (25, 43.301), (−25, 43.301), (−50, 0), (−25, −43.301), (25, −43.301); chord 50.000
Sixty degrees between holes, and the chord equals the radius for six holes.
Four holes rotated 45°
Input
PCD 100, 4 holes, first at 45°
Output
(±35.355, ±35.355), chord 70.711
Starting at 45° puts the holes at the corners of a square rather than on the axes.
Wheel pattern 5 × 4.5 in from 12 o'clock
Input
PCD 4.5 in, 5 holes, 0° at 12 o'clock, clockwise
Output
Hole 1 (0, 2.25), hole 2 (2.1399, 0.6953); spacing 2.6450 in
Clockwise from the top, the second stud is to the right and slightly above centre.
Eight holes off-centre
Input
PCD 200, 8 holes from 22.5°, centre (50, −30)
Output
Hole 1 (142.388, 8.268), hole 2 (88.268, 62.388)
The offset is added to every hole, so the table is ready for a part whose datum is not the circle centre.
PCD from a caliper reading
Input
5 holes, neighbouring studs 67.18 mm apart
Output
PCD 114.30 mm
67.18 ÷ sin 36° = 114.3. On a 5-lug wheel this identifies the common 5 × 114.3 pattern.
Background and insight
Each hole sits at radius r = PCD ÷ 2 from the centre. With angles measured counter-clockwise from the +X axis, as in mathematics and most CAD packages, a hole at angle θ is at x = cx + r·cos θ and y = cy + r·sin θ. For N holes on a full circle the angle between holes is 360° ÷ N; for a partial arc it is the included angle ÷ (N − 1), so the first and last holes land on the ends of the arc. Drawings often measure from 12 o'clock and number holes clockwise instead; the calculator converts either convention.
The straight-line distance between two neighbouring holes is the chord, c = PCD × sin(180° ÷ N). For six holes on 100 mm that is exactly 50 mm, the same as the radius, which is why a hexagon fits a circle so neatly. Holes k positions apart are PCD × sin(k × 180° ÷ N) apart, so for an even number of holes the distance across opposite holes is the PCD itself. Turned around, the same formula finds an unknown PCD from a caliper reading.
Wheel bolt patterns are a common case: 5 × 114.3 means five studs on a 114.3 mm (4.5 in) circle, with neighbouring studs 67.18 mm apart. Five-lug patterns have no opposite stud, which is why a direct measurement across is awkward; measuring neighbouring studs and dividing by sin 36° gives the PCD. Many CNC controls also have a built-in bolt hole circle cycle, but a coordinate table works on any machine, including a manual mill with a DRO, and lets you check the program.
Common use cases
Manual milling with a DRO
Move to each coordinate in turn and drill, without a rotary table or dividing head.
CNC programming
Paste coordinates into a drilling program or check a canned cycle's output.
Flange and adapter design
Lay out pipe flanges, motor adapters, spacers and hub adapters in CAD or on paper.
Identifying wheel patterns
Measure two studs and find the PCD to check whether wheels or adapters will fit.
Tips and limitations
- Check one known chord with calipers after drilling the first two holes; it catches a wrong PCD or angle early.
- Some machines have Y pointing toward the operator. If your table appears mirrored, flip the sign of Y or change direction.
- For hand layout, step off the chord with dividers from a centre-punched circle instead of using coordinates.
- Keep enough decimals: four places in inches or three in mm is usual for drilling.
- For holes that must line up with a mating part, drill both parts together or use a drill jig.
Frequently asked questions
How do you calculate bolt circle hole coordinates?
Each hole is at x = r·cos θ and y = r·sin θ from the centre, where r is half the bolt circle diameter and θ is the hole's angle. For N holes on a full circle the angles step by 360° ÷ N.
What is the distance between holes on a bolt circle?
The straight-line distance between neighbouring holes is PCD × sin(180° ÷ N). Six holes on 100 mm are 50 mm apart; five on 114.3 mm are 67.18 mm apart.
How do I measure a 5-lug bolt pattern?
Measure centre to centre between two neighbouring studs and divide by sin 36° (0.5878). 67.2 mm gives about 114.3 mm, the 5 × 114.3 (5 × 4.5 in) pattern.
What does PCD mean?
Pitch circle diameter: the diameter of the circle through the centres of the holes. It is the same thing as bolt circle diameter.
How is a partial bolt circle spaced?
With an included angle A from the first to the last hole, the spacing is A ÷ (N − 1). Three holes over 90° sit at 0°, 45° and 90°.
Which way do the holes run?
Choose either. Counter-clockwise from 3 o'clock is the mathematical and most CAD convention; many drawings and wheel specs start at 12 o'clock and go clockwise.
Is there an in-depth guide to the Bolt Circle Calculator?
Yes. “Bolt Circle Coordinates: Drilling Holes on a Pitch Circle” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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