radius of gyration, s

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 = ∑ i m i r i 2 ∑ i m i
For a non-rigid particle, an average over all conformations is considered, i.e.
< s 2 > = < ∑ i m i r i 2 > ∑ i m i
The subscript zero is used to indicate unperturbed dimensions, as in < s 2 > 0 1 / 2.
Purple Book, p. 48