Geometric Mean Distance for Cable Spacing Calculations

Definition and formulae for geometric mean distance in cable spacing, inductance, reactance and impedance calculations.

Updated May 27, 2026

Centre-to-centre spacing is frequently used in cable calculations, particularly when calculating inductance. Where 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:

$d = \sqrt[3]{d_{L 1 L 2} d_{L 1 L 3} d_{L 2 L 3}}$

and

$d_{L N} = \sqrt[3]{d_{L 1 L N} d_{L 2 L N} d_{L 3 L N}}$

Symbols

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	spacing between L1 and L2
L₁L₃	spacing between L1 and L3
L₂L₃	spacing between L2 and L3
L₁L_N	spacing between L1 and N
L₂L_N	spacing between L2 and N
L₃L_N	spacing between L3 and N

Cable Configurations: Distance Between Conductors

The spacing between cores depends on the cable arrangement and configuration. The standard cable/core configurations are shown below.

Cables or cores arranged in trefoil

L₁L₂	d
L₁L₃	d
L₂L₃	d
L₁L_N	d
L₂L_N	$\sqrt{3} d$
L₃L_N	2d

Cables or cores in flat formation (touching)

L₁L₂	d
L₁L₃	2d
L₂L₃	d
L₁L_N	3d
L₂L_N	2d
L₃L_N	d

Cables or cores in flat formation (spaced)

L₁L₂	d
L₁L₃	2d
L₂L₃	d
L₁L_N	3d
L₂L_N	2d
L₃L_N	d

Cable or cores in 4-core arrangement

L₁L₂	d
L₁L₃	d
L₂L₃	$\sqrt{2} d$
L₁L_N	$\sqrt{2} d$
L₂L_N	d
L₃L_N	d

Cable or cores in 5-core arrangement

L₁L₂	d
L₁L₃	$\frac{h}{\cos (\frac{π}{10})}$
L₂L₃	d
L₁L_N	$\frac{h}{\cos (\frac{π}{10})}$
L₂L_N	$\frac{h}{\cos (\frac{π}{10})}$
L₃L_N	d

Where:

$r = \frac{d}{2 * \sin (\frac{π}{5})}$

and

$h = r [1 + \cos (\frac{π}{5})]$

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, including any insulation semi-conducting layer and metallic screen.

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

Related cable spacing calculations

Geometric mean distance is mainly used where conductor spacing affects impedance, inductance and reactance. For the wider calculation context, see cable impedance, cable inductance and cable reactance.

For practical installation arrangements that influence spacing, see cable installation supports, ducts and draw pits.