Hole spacing on a bolt circle

What does this quantity describe?

For N holes evenly spaced on a circle of diameter PCD, the straight-line distance between two adjacent hole centers is the chord length s = PCD · sin(π/N). This formula follows directly from the geometry of a regular N-gon whose vertices lie on the bolt circle.

A flange with four holes on a 100 mm bolt circle has holes 90° apart; the straight-line distance between two adjacent holes isn't simply a quarter of the circumference, but the chord length of that circle segment — about 70.7 mm in this example, noticeably less than the naive 'circumference divided by hole count' approach would give.

Formula and variables

s = PCD · sin(π/N)

• s = PCD · sin(π/N)
• PCD = s / sin(π/N)
• N = π / arcsin(s/PCD)

Choose the inputs correctly

Enter two of the three quantities. Hole spacing requires bolt circle diameter and hole count, bolt circle diameter requires spacing and hole count, hole count requires spacing and bolt circle diameter. Since N must be a whole number, round the result to the nearest sensible integer when solving for it.

How to use the calculator

Select the target quantity and enter the two known values with units. When solving for hole count, check whether the calculated value is already an integer or whether an adjacent whole number of holes with a slightly different spacing is the more practical solution.

Worked example

Given PCD = 100 mm and N = 4 holes, substitution gives s = 100 · sin(45°) ≈ 70.71 mm.

Understand the result and units

A hole spacing of 70.71 mm is the direct distance between two adjacent hole centers — the value you'd actually measure with calipers or dividers when laying out the pattern, not the arc distance along the circle's circumference.

Hole spacing and bolt circle diameter are given in the same length unit, usually millimetres. Hole count N is a dimensionless integer.

Typical applications

Hole spacing is used when laying out flanges, wheel hub and coupling bolt circles, CNC programming, and checking existing components without a technical drawing.

Assumptions, limits and common mistakes

The formula assumes exactly evenly spaced holes on a true circle. For irregular hole patterns or oval bolt circles it gives no valid value; manufacturing tolerances of real hole positions are not included either.

Common mistake: Do not confuse hole spacing with arc spacing (circumference divided by hole count) — the straight-line chord is always shorter than the corresponding arc at the same angle. Also, when calculating hole count from a measured spacing, round the result to a sensible integer, since non-integer hole counts don't physically exist.