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 mi, each located at a distance ri from the centre of mass, the radius of gyration, s, is defined as the square root of the mass-average of ri2 for all the mass elements, i.e. s=∑imi ri2∑imi For a non-rigid particle, an average over all conformations is considered, i.e. <s2>=<∑imi ri2>∑imi The subscript zero is used to indicate unperturbed dimensions, as in <s2>01/2.
Source:
Purple Book, 1st ed., p. 48 [Terms] [Book]
Citation: 'radius of gyration' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.R05121 RIS BibTex EndNote
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Last revised: February 24, 2014