Sources and scope for this page: Industry convention — no single governing standard (conventional usage, definitions vary between sources), covering the definition of radius of gyration. No independent source check is recorded for this page: the content rests on the sources listed and on the working shown on the page. How sources, methods and updates are recorded.
Definition
Radius of gyration r = √(I ÷ A) converts a section's shape into a single length, and that length is what appears in column buckling formulas as the slenderness ratio K·L/r.
A section with a larger r resists buckling better for the same area, which is why hollow sections beat solid ones in compression: moving material away from the centroid raises I much faster than it raises A.
Common misuse
Comparing sections by area alone for a compression member. The radius of gyration, not the area, governs buckling.