A parameter characterizing the size of a particle of any shape. For a rigid particle consisting of mass elements of mass
, each located at a distance
from the centre of mass, the radius of gyration,
, is defined as the square root of the mass-average of
for all the mass elements, i.e.
For a non-rigid particle, an average over all conformations is considered, i.e.
The subscript zero is used to indicate unperturbed dimensions, as in
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook