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The Radius of Gyration

A measure of the average distance of a protein from its center of mass, reflecting its overall shape and compactness.
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The statement of the theorem

Let ri\mathbf{r}_i be the position vector of the ii-th atom (where i=1,2,…,Ni=1, 2, \dots, N) in the protein structure. The center of mass RCM\mathbf{R}_{CM} is defined as the weighted average of atomic positions: \n\nRCM=1N∑i=1Nri\mathbf{R}_{CM} = \frac{1}{N} \sum_{i=1}^{N} \mathbf{r}_i \n\nThe Radius of Gyration, RgR_g, is then defined as the root mean square distance of all atoms from the center of mass: \n\nRg=1N∑i=1N∣∣ri−RCM∣∣2R_g = \sqrt{\frac{1}{N} \sum_{i=1}^{N} ||\mathbf{r}_i - \mathbf{R}_{CM}||^2}
Source: Wikipedia