Bolt Circle (PCD) Hole Coordinates Calculator

What is a bolt circle?

On flanges, covers and hubs the bolt holes sit equally spaced on a circle. Its diameter is the bolt circle diameter or pitch circle diameter, usually written PCD on drawings. What you need at the drill press, on the mill or when marking out is the X and Y coordinate of every hole.

How are the coordinates calculated?

The angle between holes is 360 / N degrees. If the first hole is at θ₀, hole number i is at θ = θ₀ + i × 360 / N. The coordinates follow from the radius: x = x₀ + (PCD / 2) × cos θ and y = y₀ + (PCD / 2) × sin θ.

The straight distance between the centres of two adjacent holes is the chord: c = PCD × sin(180 / N). This is the dimension to set on dividers or to check with calipers.

Example

Four holes on a 100 mm circle with a 45 degree start angle each sit 50 / √2 = 35.355 mm from the axes: (35.355, 35.355), (−35.355, 35.355), (−35.355, −35.355), (35.355, −35.355). Adjacent holes are 70.711 mm apart.

Why the start angle matters

On pipe flanges the holes normally straddle the main centre lines instead of sitting on them. For a four hole flange that means a 45 degree start angle, for eight holes 22.5 degrees. The rule is given in the relevant flange standard and on the manufacturing drawing, and the drawing always governs.

Limits

The tool only gives the geometry of an equally spaced pattern. Bolt count, bolt size, hole diameter and flange thickness come from the flange standard or a strength calculation. If your machine axes point differently, flip the coordinate signs to match.