Radius of Gyration and Column Slenderness

The radius of gyration of a cross-sectional area about a selected centroidal axis is:

$$i=\sqrt{\frac{I}{A}}.$$

The column slenderness ratio is:

$$\lambda=\frac{l_{eff}}{i}=\frac{\mu L}{i}.$$

For buckling assessment, use the minimum radius of gyration:

$$i_{min}=\sqrt{\frac{I_{min}}{A}},\qquad \lambda_{max}=\frac{\mu L}{i_{min}}.$$

• $i$ — radius of gyration;
• $I$ — centroidal second moment of area;
• $A$ — cross-sectional area;
• $\lambda$ — slenderness ratio;
• $l_{eff}=\mu L$ — effective length;
• $i_{min}$, $I_{min}$ — minimum radius of gyration and minimum centroidal second moment of area.

The larger $\lambda$ is, the more slender the member and the more likely its load capacity is to be governed by buckling rather than material strength alone.

The calculator below evaluates radius of gyration, second moment of area, or cross-sectional area. Slenderness $\lambda$ is not included because the calculator registry has no separate dimensionless quantity for this parameter.