Bolt Circle Calculator (PCD)
Find the X and Y position of every hole on a bolt circle or pitch circle diameter (PCD), plus the angle and distance between neighbouring holes.
New: please check your results.
For guidance only. This is not a substitute for a qualified engineer, and important designs should be checked by one.
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- Distance between neighbouring holes
- 50 mm
- Angle between holes
- 60°
- Pitch circle radius
- 50 mm
Hole positions (from your datum)
| Hole | Angle (°) | X (mm) | Y (mm) |
|---|---|---|---|
| 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 |
What it does
Works out where to drill holes equally spaced around a circle: the bolt circle, or pitch circle diameter (PCD), of a flange, wheel hub, mounting plate or chuck. Enter the PCD and number of holes to get the X and Y position of every hole from your datum, ready for marking out, a drill with a digital readout or a CNC program. You also get the angle between holes and the straight-line distance from one hole to the next.
How to use it
- Pitch circle diameter (PCD)
The diameter of the circle through the centres of the holes, not their edges. A wheel marked 5×112 has a 112 mm PCD.
- Number of holes
How many holes, equally spaced around the circle.
- First hole angle
Where the first hole sits, measured from 3 o'clock (the +X direction). Use 90 to put it at 12 o'clock, or half the angle between holes to have two holes level across the top.
- Numbering direction
Which way round the holes are numbered. Most drawings and CNC machines count angles anticlockwise.
- Centre X
Where the circle's centre is, measured from your datum (0, 0) along X. Leave at 0 to get positions from the centre itself.
- Centre Y
The same for Y. Positive is up (or away from you on a drill table), as on a drawing.
Common uses
- Drilling pipe flanges, mounting plates and covers.
- Checking a wheel's stud pattern, such as 5×112 or 4×100.
- Setting hole positions on a DRO or in a CNC program.
- Choosing the drill size for tapped holes. Try the Tap Drill Size Calculator
- Tightening the bolts to the right torque. Try the Bolt Torque Calculator
The formula
Angle between holes = 360° ÷ number of holesAngle of hole n = first hole angle + (n − 1) × angle between holesX = centre X + (PCD ÷ 2) × cos(angle)Y = centre Y + (PCD ÷ 2) × sin(angle)Distance between holes = PCD × sin(180° ÷ number of holes)Where:
- PCD
- pitch circle diameter, through the hole centres
Angles are measured anticlockwise from 3 o'clock (the +X direction), as on most drawings and CNC machines. Choosing clockwise counts the holes the other way.
Worked example
For 6 holes on a 100 mm pitch circle, with the first at 0°:
- Angle between holes: 360° ÷ 6 = 60°
- Pitch circle radius: 100 mm ÷ 2 = 50 mm
- Hole 2 is at 60°, so X = 50 × cos(60°) = 25 mm and Y = 50 × sin(60°) = 43.301 mm
- Distance between neighbouring holes: 100 mm × sin(30°) = 50 mm
Every hole's position is in the table.
Questions people ask
What is PCD?
Pitch circle diameter: the diameter of the imaginary circle that passes through the centres of all the holes. It's measured centre to centre, not from the edges of the holes.
How do I measure the PCD of a 5-stud wheel?
With an odd number of studs you can't measure straight across. Measure from the centre of one stud to the centre of the next one, then divide by sin(180° ÷ 5), which is 0.5878. For example, 65.83 mm between studs gives a PCD of 112 mm.
Can I mark out the holes without a CNC machine?
Yes. Either measure each X and Y from a corner or centre line and centre-punch the point, or set a pair of dividers to the distance between neighbouring holes and step it round the pitch circle from the first hole.
Last checked 28 October 2026 · Last rev. 31 October 2026 · c743