Flange Bolt Circle: PCD Hole Positions and Chord Spacing

For a full circle of diameter $D$ with $n$ equally spaced holes, $R=D/2$ and $\Delta\theta=360^\circ/n$. Let $s=+1$ for counterclockwise numbering and $s=-1$ for clockwise numbering. For a reference direction $\beta$, the on-line preset uses $\alpha=\beta$ and the half-pitch preset uses $\alpha=\beta+s\Delta\theta/2$. Custom placement uses the entered first-hole angle.

For hole $k=1,\ldots,n$, wrap $\theta_k=\alpha+s(k-1)\Delta\theta$ into $[0^\circ,360^\circ)$. Resolve the radius into $X_k=X_c+R\cos\theta_k$ and $Y_k=Y_c+R\sin\theta_k$. The implementation uses degree-aware sine and cosine.

Bisecting the isosceles triangle formed by two adjacent radii gives $c=2R\sin(\Delta\theta/2)=D\sin(180^\circ/n)$. This straight centre-to-centre chord is the divider setting. The arc pitch $a=2\pi R/n$ is shown separately in the calculation steps.

These equations are derived here from circle geometry. HEIDENHAIN’s Position Display Units for Milling Machines (6/99), pp. 21–23, documents centre/radius/start-angle input conventions. Independent numerical comparisons use the NORAMARK six-hole worked example and chord factors, and Planichapa’s eight-hole worked example. Pythagorean radius and adjacent-distance checks include the closing pair.

• All hole centres lie in one plane on one exact circle and are uniformly spaced around a complete turn.
• +X is right and +Y is up when looking from +Z toward the XY plane. A custom angle remains counterclockwise from +X for either numbering direction.
• Centre offsets translate the coordinate table. The schematic is centred on the bolt pattern, and its outline, bore and hole diameters are illustrative.
• Half-pitch placement straddles the chosen reference direction. With a hole count divisible by four, it also straddles the perpendicular direction. Straddling the actual X/Y axes additionally depends on the reference angle (0° or 90° are straightforward choices). It is not automatic compliance with any flange standard.
• Values are nominal geometry. Displayed decimals do not specify manufacturing accuracy.

Use positive PCD and a whole hole count from 2 to 72. The hole to inspect must be within the pattern. Linear inputs and coordinates support metric/US display conversion; all formulas use the declared units internally.

This is a layout calculation, not a standard flange dimension lookup, stress check, pressure-rating selection or machine program. It excludes nonuniform patterns, partial arcs, drill sizes, bore/edge clearance, bolt fit, thermal distortion and tolerances. Input PCD and hole count from the applicable drawing. ASME B16.5 and EN 1092-1 are named for context only; no edition is implemented or reproduced. Check against the standard in force when specifying a standard flange. Confirm datum, handedness and positional tolerance before using the coordinates. Divider closure is a practical check, not a tolerance assessment.