This is the geometric mean distance $a$ between phases according to IEC 60287.
The formulae for $GMD$ were taken from the book Electric Power Generation, Transmission, and Distribution by Leonard L. Grigsby (2006), chapter 14.1.2.7.
In case of three single-core cables in flat formation, equal distance, with regular transposition, $GMD$ becomes the equation $2 \sqrt[3]{2}\cdot s_{c}$ as it is used in IEC 60287-1-1, chapter 2.3.2.
| $\left(a_{12} a_{23} a_{31}\right)^{\frac{1}{3}} \frac{1}{1000}$ | conductor to conductor, three cables, individual |
| $S_m$ | conductor to conductor, three cables, trefoil |
| $2^{\frac{1}{3}} S_m$ | conductor to conductor, three cables, flat |
| $2^{\frac{1}{6}} S_m$ | conductor to conductor, three cables, rectangular |
| $S_m$ | conductor to conductor, two cables |
| $D_E$ | conductor, one cable |
| $GMR_{cc}$ | conductor to conductor, multi-core cable |
| $\left({a_m}^{n_{sw}}-\left(\frac{d_s}{2}\right)^{n_{sw}}\right)^{\frac{1}{n_{sw}}} \frac{1}{1000}$ | screen of single-core cable to conductor of other cable |
| $\left({a_m}^2-\left(\frac{d_s}{2}\right)^2\right)^{\frac{1}{2}} \frac{1}{1000}$ | sheath of single-core cable to conductor of other cable |
| $\left({a_m}^{n_{ar}}-\left(\frac{d_{ar}}{2}\right)^{n_{ar}}\right)^{\frac{1}{n_{ar}}} \frac{1}{1000}$ | armour of single-core cable to conductor of other cable |
