Machining and Fastener Charts

Bolt circle hole coordinates.

Enter the bolt circle (pitch circle) diameter and the number of equally spaced holes. You get each hole angle with its X and Y coordinates, the spacing between holes and the centre offset if the pattern is not at zero. Runs in your browser; nothing is sent or stored.

Inputs

Result

Fill the form and press Calculate.

Answer first. Hole i on a bolt circle of radius R = PCD / 2 is at x = R cos(angle), y = R sin(angle), with the angle stepping 360 / N degrees from the first hole.

Worked example

Five holes on a 100 mm bolt circle: R = 50 mm and the step is 72 degrees. The first hole is at (50, 0). The second is at 50 cos 72 = 15.451 and 50 sin 72 = 47.553, so (15.451, 47.553). The chord between neighbouring holes is 100 x sin(36 degrees) = 58.78 mm.

How it works

Centre offset. If the pattern is centred at (Xc, Yc) rather than the origin, add Xc to every X and Yc to every Y. Set the centre fields to do this.

Start angle. The first hole defaults to the +X axis. Enter another angle to rotate the whole pattern, for example 90 to put the first hole at the top.

Spacing. The straight-line distance between neighbouring holes is PCD x sin(180 / N). It is handy for checking a layout with calipers.

Note. Coordinates are rounded to six decimals. Different CAM systems and forum posts use different zero directions and rotation conventions; confirm yours before cutting metal.

Sources

Bolt Circle Calculator - Omni Calculator (coordinate formulas) (opened 2026-10-16)
Bolt Circle Hole Pattern Calculator - ToolGrit (machining use) (opened 2026-10-16)

The coordinate formulas x = Xc + R cos(angle) and y = Yc + R sin(angle) are from the first page. A five-hole, 100 mm example from that formula is checked in this tool's tests.

FAQ

What is a bolt circle?

A bolt circle, or pitch circle diameter (PCD), is the circle that passes through the centres of a pattern of holes, such as the studs of a wheel or the bolts of a flange.

How do I find the coordinates of holes on a bolt circle?

Use x = R cos(angle) and y = R sin(angle), where R is half the PCD and the angle steps by 360 divided by the number of holes.

How do I find the PCD from a measurement?

With an even number of holes, measure centre to centre across opposite holes. Otherwise measure the centre-to-centre distance between neighbouring holes and use PCD = chord / sin(180 / N).

Can I enter inches?

Yes. The tool is unit-free: the coordinates come back in whatever unit you used for the diameter.

What is the angle between holes?

360 divided by the number of holes. Five holes sit 72 degrees apart; six sit 60 degrees apart.