Radius of Gyration Calculator

Formula

The formula to calculate the radius of gyration is:

\[ k_x = \sqrt{\frac{I_x}{m}} \]

Where:

\( k_x \) is the Radius of Gyration (m)
\( I_x \) is the Moment of Inertia (kg·m²)
\( m \) is the Total Mass (kg)

What is Radius of Gyration?

The radius of gyration is the distance to a point that would have a moment of inertia as a distributed mass. It is a useful concept in structural engineering and mechanics.

Example Calculation

Let's assume the following values:

Moment of Inertia (Ix): 200 kg·m²
Total Mass (m): 50 kg

Using the formula to calculate the radius of gyration:

\[ k_x = \sqrt{\frac{200}{50}} = 2 \text{ m} \]

The radius of gyration is 2 meters.