Radius of Gyration

Radius of Gyration Formula
\( k \;=\; \sqrt{ \dfrac{ I }{ A_c } }\) \( I \;=\; k^2 \cdot A_c \) \( A_c \;=\; \dfrac{ I }{ k^2 } \)
Symbol	English	Metric
\( K \) = Radius of Gyration	\(in\)	\(mm\)
\( I \) = Moment of Inertia	\(in^4\)	\(mm^4\)
\( A_c \) = Area Cross-section	\(in^2\)	\(mm^2\)

The radius of gyration is a measure used in engineering and physics to describe how the area, mass, or particles of an object are distributed relative to an axis. It represents the distance from the axis at which the entire area or mass of the object could be concentrated without changing its moment of inertia. In structural engineering, it is commonly applied to columns and beams to assess their resistance to buckling. Mathematically, the radius of gyration is calculated as the square root of the ratio of the moment of inertia to the area cross-section (for area distribution) or mass (for mass distribution). A larger radius of gyration generally indicates that the object’s material is distributed farther from the axis, which increases its ability to resist bending or buckling.

Radius of Gyration Formula
\( k \;=\; \sqrt{ \dfrac{ I }{ m } }\) \( I \;=\; k^2 \cdot m \) \( m \;=\; \dfrac{ I }{ k^2 } \)
Symbol	English	Metric
\( K \) = Radius of Gyration	\(in\)	\(mm\)
\( I \) = Moment of Inertia	\(in^4\)	\(mm^4\)
\( m \) = Total Mass of Body	\(lbm\)	\(kg\)