Bolt Circle Calculator (Hole Coordinates and Spacing)

A bolt circle is a ring of equally spaced holes: flanges, wheel hubs, chuck backplates, lamp bases, turned platters with feet. Enter the diameter of the circle through the hole centres, the number of holes and where the first hole sits, and this calculator gives the X and Y coordinates of every hole, the straight-line spacing between neighbouring holes and the angle between them. The coordinates can be measured from the centre of the circle or from any zero point you choose, which is what you need on a mill with a digital readout or on a CNC.

Bolt circle calculator

How it works

With n holes the angle between them is 360 ÷ n degrees. Each hole sits at radius R = D ÷ 2 from the centre, so for the hole at angle a:

X = centre X + R × cos(a)
Y = centre Y + R × sin(a)
hole-to-hole spacing (a chord of the circle) = D × sin(180° ÷ n)

Angles are measured counterclockwise from the 3 o’clock position, the usual mathematical convention. Setting the first hole at 90 degrees puts it at 12 o’clock. The spacing is handy for checking a layout with dividers or calipers: set them to the chord length and walk them round the circle; the last step should land exactly on the first hole.

Worked example

Six holes on a 4 in bolt circle, with the first hole at 12 o’clock and coordinates from the centre:

Units: Inches
Bolt circle diameter: 4 in
Number of holes: 6
Angle of the first hole: 90 degrees
Centre X: 0 in
Centre Y: 0 in

The calculator gives:

Hole-to-hole spacing (centre to centre): 2 in
Angle between holes: 60 degrees
Radius: 2 in
Hole 1 at 90 degrees: X 0.0000, Y 2.0000
Hole 2 at 150 degrees: X -1.7321, Y 1.0000
Hole 3 at 210 degrees: X -1.7321, Y -1.0000
Hole 4 at 270 degrees: X 0.0000, Y -2.0000
Hole 5 at 330 degrees: X 1.7321, Y -1.0000
Hole 6 at 30 degrees: X 1.7321, Y 1.0000

For six holes the spacing equals the radius, 2 in, which is why a compass set to the radius steps a circle into six. The holes are 60 degrees apart. To drill them on a mill, zero the readout on the centre of the part and move to each X and Y in turn. With a rotary table you only need the angles: 90, 150, 210, 270, 330 and 30 degrees.

Bolt circle constants: hole spacing per unit of diameter

Holes	Angle between holes	Spacing ÷ bolt circle diameter	Spacing on a 4 in circle	Spacing on a 100 mm circle
3	120°	0.86603	3.4641 in	86.6 mm
4	90°	0.70711	2.8284 in	70.71 mm
5	72°	0.58779	2.3511 in	58.78 mm
6	60°	0.5	2 in	50 mm
8	45°	0.38268	1.5307 in	38.27 mm
10	36°	0.30902	1.2361 in	30.9 mm
12	30°	0.25882	1.0353 in	25.88 mm
16	22.5°	0.19509	0.7804 in	19.51 mm
20	18°	0.15643	0.6257 in	15.64 mm
24	15°	0.13053	0.5221 in	13.05 mm

Spacing = diameter × sin(180° ÷ n). Multiply your bolt circle diameter by the constant to get the centre-to-centre distance between neighbouring holes.

Notes and limits

Check which way your machine counts angles. Some readouts and CAM programs measure clockwise or from 12 o’clock; if so, enter the first hole angle to match and read the list in the other direction.
Wheel bolt patterns such as 5 × 4.5 in are bolt circles: five lugs on a 4.5 in circle are 2.645 in apart centre to centre, 72 degrees apart.
For the hole sizes themselves, see the clearance hole calculator for bolts passing through, and the tap drill calculator for threaded holes.
Centre punch each position and start with a small pilot drill; a centre drill or spot drill keeps a larger bit from wandering off the mark.
Up to 36 holes are listed one by one. For finer divisions use the angle between holes from the first one, or an indexing head.

Frequently asked questions

How do you calculate a bolt circle?

Divide 360 by the number of holes for the angle between them. Each hole is at X = R × cos(angle) and Y = R × sin(angle) from the centre, where R is half the bolt circle diameter. The spacing between neighbouring holes is the diameter × sin(180° ÷ number of holes).

What is the spacing of 4 holes on a 5 inch bolt circle?

3.5355 in centre to centre (5 × sin 45°). With the first hole at 45 degrees the holes sit at X and Y = ±1.7678 in from the centre.

How do I measure a bolt circle with an even number of holes?

Measure from the centre of one hole straight across to the centre of the opposite hole; that is the bolt circle diameter. With an odd number of holes no hole is opposite another, so measure the spacing between two neighbours and divide by sin(180° ÷ n).

What is the difference between bolt circle and pitch circle diameter?

None for practical purposes: both mean the diameter of the circle through the hole centres. PCD (pitch circle diameter) is the usual term in metric drawings.

Sources

Last reviewed: 25 October 2026. The calculation is covered by automated tests with known answers taken from the sources above. Found an error? Please let us know.