## Wikipedia - Raggio d'inerzia (it) radius of gyration, $$s$$

https://doi.org/10.1351/goldbook.R05121
A parameter characterizing the size of a particle of any shape. For a rigid particle consisting of mass elements of mass $$m_{i}$$, each located at a distance $$r_{i}$$ from the centre of mass, the radius of gyration, $$s$$, is defined as the square root of the mass-average of $$r_{i}^{2}$$ for all the mass elements, i.e. $s = \sqrt{\frac{\sum _{i}m_{i}\ r_{i}^{2}}{\sum _{i}m_{i}}}$ For a non-rigid particle, an average over all conformations is considered, i.e. $\sqrt{ < s^{2} > } = \frac{\sqrt{< \sum _{\begin{array}{c} i \end{array}}m_{i}\ r_{i}^{2} > }}{\sqrt{\sum _{\begin{array}{c} i \end{array}}m_{i}}}$ The subscript zero is used to indicate unperturbed dimensions, as in $$\text{<}s^{2}\text{>}_{0}^{1/2}$$.
Source:
Purple Book, 1st ed., p. 48 [Terms] [Book]