Centre to centre spacing is frequently used in cable calculations.  This is particularly obvious in the calculation of inductance. Where the spacing varies between cores (for example, in flat configurations), an average spacing is used; the geometric mean distance.

Geometric Mean Distance

Given  known spacing between conductors, the geometric mean distance is given by:

$d=\sqrt[3]{d_{L1L2}{d}_{L1L3}{d}_{L2L3}}$

and 

$d_{LN}=\sqrt[3]{d_{L1LN}{d}_{L2LN}{d}_{L3LN}}$

where:
d             - geometric mean distance between phases, m
d_n            - geometric mean distance between phase and neutral, m
L_XL_X        - spacing (centre to centre) between phases, m
                        L₁L₂        - between L1 and L2
                        L₁L₃        - between L1 and L3
                        L₂L₃        - between L2 and L3
                        L₁L_N        - between L1 and N
                        L₂L_N        - between L2 and N
                        L₃L_N        - between L3 and N

Cable Configurations - Distance Between Conductors

The spacing between cores depends on the cable arrangement and configuration.  The starting point is a set of standard cable/core configurations:

	cables or cores arranged in trefoil $$\begin{gathered} L_1{L}_2=d \\ {L}_1{L}_3 =d \\ {L}_2{L}_3 =d \\ {L}_1{L}_N =d \\ {L}_2{L}_N =\sqrt{3}d \\ {L}_3{L}_N =2d \end{gathered}$$
	cables or cores in flat formation (touching) $$\begin{gathered} L_1{L}_2=d \\ {L}_1{L}_3 =2d \\ {L}_2{L}_3 =d \\ {L}_1{L}_N =3d \\ {L}_2{L}_N =2d \\ {L}_3{L}_N =d \end{gathered}$$
	cables or cores in flat formation (spaced) $$\begin{gathered} L_1{L}_2=d \\ {L}_1{L}_3 =2d \\ {L}_2{L}_3 =d \\ {L}_1{L}_N =3d \\ {L}_2{L}_N =2d \\ {L}_3{L}_N =d \end{gathered}$$
	cable or cores in 4-core arrangement $$\begin{gathered} L_1{L}_2=d \\ {L}_1{L}_3 =d \\ {L}_2{L}_3 =\sqrt{2}d \\ {L}_1{L}_N =\sqrt{2}d \\ {L}_2{L}_N =d \\ {L}_3{L}_N =d \end{gathered}$$
	cable or cores in 5-core arrangement $$\begin{gathered} L_1{L}_2=d \\ {L}_1{L}_3 =\frac{h}{\cos \left({\displaystyle \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}\right)} \\ {L}_2{L}_3 =d \\ {L}_1{L}_N =\frac{h}{\cos \left({\displaystyle \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}\right)} \\ {L}_2{L}_N =\frac{h}{\cos \left({\displaystyle \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}\right)} \\ {L}_3{L}_N =d \end{gathered}$$ where: $r=\frac{d}{2*\sin \left({\displaystyle \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}\right)}$ and $h=r \left[1+\cos \left(\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$5$}\right.\right)\right]$ * angles are in radians

For single core cables, d is the overall diameter of the cable.  For cores of a low voltage multicore cable, d is the diameter of the core over the insulation. For medium voltage cables, d is the diameter over the insulation and including any insulation semi-conducting layer and metallic screen.

The distances given in the table are accurate for circular conductors.  For sector-shaped conductors, using the values above will result in insignificant minor variations against actual geometric mean distances.