Bolt Circle Calculator

Marking a bolt circle by hand means dividing 360 by the number of holes and then either swinging a protractor and hoping, or walking dividers round the rim and finding the last gap is not like the others. The number that makes it accurate is the chord — the straight line between neighbouring holes — which is not the same as the distance round the rim.

Pitch circle diameter in millimetres

The circle the hole centres sit on.

How many holes

Between 2 and 200, equally spaced.

First hole, degrees from twelve o'clock

Clockwise. 0 puts a hole straight up.

Hole diameter in millimetres

Used to check there is metal left between them.

Set dividers to 58.78mm

Step that round the 100mm circle 5 times and the last step lands on the first hole. Round the rim it would be 62.83mm, which is why walking a tape measure round overshoots. There is 46.78mm of metal between neighbouring holes.

Hole	Angle	Across	Up
1	0°	0mm	50mm
2	72°	47.553mm	15.451mm
3	144°	29.389mm	-40.451mm
4	216°	-29.389mm	-40.451mm
5	288°	-47.553mm	15.451mm

Across and up are measured from the centre, positive to the right and upwards.

✓ Every hole is the same distance from the centre — 5 holes, all 50mm out, measured from the coordinates rather than assumed
✓ Every gap is the same, including the last one back to the first — all 5 chords are 58.779mm — set dividers to that and the last step lands on the first hole
✓ The chord is shorter than the arc — 58.779mm straight across against 62.832mm round the rim — measuring round the rim overshoots
✓ The angles divide the circle exactly — 72 degrees apart, 5 times, is exactly a full turn
✓ There is metal left between the holes — 46.779mm between neighbouring holes for a 12mm hole

What this generator does

Works out the straight-line distance between neighbouring holes, the angle of each, and where each sits across and up from the centre.

How to use this tool

Type the pitch circle diameter and how many holes.
Set where the first hole sits, if it matters.
Set dividers to the chord and step round.
Or mark each hole from the centre using the across and up figures.

Understanding the controls

Pitch circle diameter: The circle the hole centres sit on, in millimetres — not the outside of the part, and not the circle the holes' edges touch.
How many holes: Equally spaced round the whole circle. Two to two hundred, though a protractor stops being useful long before the top end.
First hole, degrees from twelve o'clock: Clockwise, so zero puts a hole straight up. It turns the whole pattern without changing any of the spacing.
Hole diameter: Not used for the spacing, only to check there is enough metal left between neighbouring holes.

Common use cases

Drilling a flange, a wheel or a face plate
Marking out a clock face or a compass rose
Spacing fence posts round a circular bed
Laying out holes for a lamp shade or a lantern
Checking a pattern before committing a drill to it

How this generator works

The chord between neighbouring holes is twice the radius times the sine of pi over the number of holes — the formula nobody remembers, and the reason walking a tape measure round the rim overshoots. Every hole's position is then computed in Cartesian coordinates, and the checker measures those rather than trusting the trigonometry: every hole must be the same distance from the centre, and every neighbouring pair the same distance apart, including the last pair back to the first, which is exactly where stepping round with dividers accumulates its error.

Randomness and fairness

Nothing is random. The same circle always marks out the same way.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

This is the geometry; drill wander, workholding and the accuracy of your centre punch decide what you actually get.
The metal-left check is a rough guide, not a strength calculation.
Coordinates assume the centre is where you say it is, which is often the hardest part of the job.
Odd numbers of holes have no line of symmetry, so there is no shortcut for marking half of them.

Privacy and your data

The geometry is worked out in your browser. No measurements are transmitted or stored.