What this calculator does
Holes evenly spaced on a circle are separated by a chord, not by the arc. For six holes on a 150 mm bolt circle, the chord is exactly 75 mm, which happens to equal the radius.
That six-hole coincidence is worth knowing: a hexagon inscribed in a circle has sides equal to the radius, which makes six-hole patterns easy to check and easy to lay out. For any other count the chord is twice the radius times the sine of half the angle between holes.
The formula
The chord between adjacent holes is twice the radius multiplied by the sine of pi over the number of holes. The angle between holes is 360 degrees divided by the count, and the arc length is that angle in radians times the radius. The chord is what you measure with calipers; the arc is the distance around the circle.
| Term | Meaning |
|---|---|
| Bolt circle | The circle through the centres of the holes, also called the pitch circle diameter or PCD. |
| Chord | The straight-line distance between adjacent hole centres, which is what you measure. |
| Arc | The distance around the circle between holes, always slightly longer than the chord. |
| PCD | Pitch circle diameter, the usual term in automotive and machine work. |
The inputs explained
| Field | What to enter |
|---|---|
| Bolt circle diameter (mm) | Bolt circle diameter in millimetres, measured through the hole centres. |
| Number of holes | Number of holes, evenly spaced around the circle. |
When to use it
Laying out a flange
Marking hole positions from the chord is more accurate than stepping around with a protractor.
Checking a wheel PCD
Measuring the chord between adjacent studs identifies the bolt pattern.
Setting out on a rotary table
The angle between holes is what the table is indexed by.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What is the spacing for each hole count?
The same circle with a range of hole counts.
| Number of holes | Spacing between adjacent holes (chord) | Angle between adjacent holes | Arc length between adjacent holes |
|---|---|---|---|
| 3 holes | 129.90 mm | 120.00° | 157.08 mm |
| 4 holes | 106.07 mm | 90.00° | 117.81 mm |
| 6 holes | 75.00 mm | 60.00° | 78.54 mm |
| 8 holes | 57.40 mm | 45.00° | 58.90 mm |
| 12 holes | 38.82 mm | 30.00° | 39.27 mm |
Questions
Why is the chord different from the arc?
Because the chord cuts straight across while the arc follows the curve. The difference is negligible for many closely spaced holes and substantial for a few widely spaced ones. Measure the chord with calipers; the arc is only useful for wrapping a tape around the circle.
How do I measure a bolt circle with an odd number of holes?
You cannot measure straight across, since no hole sits opposite another. Measure the chord between two adjacent holes and work backwards, or measure from one hole centre to the far edge of the circle. Five-stud wheel patterns are the common case.
Why is the six-hole chord equal to the radius?
Because six points evenly spaced on a circle form a regular hexagon, and a regular hexagon inscribed in a circle has sides exactly equal to the radius. It is a useful check: if your six-hole chord does not match the radius, something is out.
What does PCD mean?
Pitch circle diameter, the same thing as bolt circle diameter. Wheel fitments are quoted as a count and a PCD, such as 5×114.3, meaning five studs on a 114.3 mm circle. The terms are interchangeable.
For arc geometry generally, see the arch radius calculator. For thread specifications, see the metric thread calculator.