Radius of Gyration
Definition  Transfer of Axis  Area Moment of Inertia 


The Radius of Gyration k_{x} of an Area (A) about an axis (x) is defined as:  
equ. (1)  
k_{x}  equ. (2)  
Where I_{x} is the Moment of Inertia about the axis (x), and A is the area. If no axis is specified the centroidal axis is assumed.  
Using the Perpendicular Axis Theorem and equ. (1) from above it can be shown that:  
equ. (3) 


The Radius of Gyration k_{xx} of a Mass (m) about an axis (x) is defined as: 

equ. (4)  
k  equ. (5)  
Where I is the Moment of Inertia about the axis (x), and m is the mass.  
If no axis is specified the centroidal axis is assumed.  
Radius of Gyration Definition and Concept 
Definition  Transfer of Axis  Area Moment of Inertia 