Radius Of Gyration Formula

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Area Radius of Gyration

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)

Mass Radius of Gyration

The Radius of Gyration k_xx of a Mass (m) about an axis (x) is defined as:

equ. (4)

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.

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