Bolt Circle Calculator

Bolt-circle formulas

A bolt circle is the imaginary circle passing through the centers of equally spaced holes, studs or lugs. Its diameter is commonly called PCD (pitch circle diameter) or BCD (bolt circle diameter).

For a known diameter D and N holes:

• Radius: R = D / 2
• Angular pitch: Δ = 360° / N
• Adjacent center-to-center chord: S = D × sin(π / N)

If a center-to-center chord C spans k equal hole intervals, the diameter is:

D = C / sin(kπ / N)

Adjacent holes use k = 1. Two positions apart use k = 2. Opposite holes on an even pattern use k = N / 2. The chord is a straight line between centers, not the distance along the circle.

Coordinate convention

With the usual mathematical and machining convention, 0° is on the positive X-axis and angles increase counterclockwise. For hole index i = 0, 1, …, N − 1:

θᵢ = start angle + i × 360° / N

Xᵢ = center X + R × cos(θᵢ)

Yᵢ = center Y + R × sin(θᵢ)

Selecting clockwise numbering reverses the sign of the angular step. Choosing a different zero-angle axis rotates the whole pattern before the start angle is applied.

Worked example: four holes on a 100 mm PCD

For D = 100 mm, N = 4, center (0, 0), start angle 0° and counterclockwise order:

The adjacent center spacing is 100 × sin(45°) = 70.7107 mm.

Before machining

• Confirm whether the drawing gives a diameter or radius.
• Measure chords center-to-center; edge measurements require a separate correction for hole or stud diameter.
• Keep millimetres and inches consistent throughout the setup.
• Check the sign and orientation of the machine axes instead of assuming the screen preview matches the machine.
• Treat the results as ideal geometry. They do not define positional tolerances, hole clearance, fastener strength, wheel fitment, flange capacity or safe CNC moves.

The CSV contains coordinate points, not an executable machining program. Controller-specific G-code also needs a verified work offset, tool, safe height, drilling cycle, feed, spindle and machine limits.