Calculate radius of gyration k for beam cross-sections and common rotating bodies from dimensions like width, diameter, radius and length.

Choose the stated axis. Mass presets assume uniform density; shell, rod and plate presets use thin-body models.

Radius of Gyration Formula

The radius of gyration is measured from a specified axis. Use mass moment of inertia for a body or area second moment for a cross-section.

Mass: kx = sqrt(Ix / m); Area: kx = sqrt(Ix / A)
  • Where kx is the radius of gyration about the chosen x-axis
  • Ix is the body mass moment of inertia, or the cross-section area second moment, about that same axis
  • m is total mass for a mass radius; A is cross-sectional area for an area radius

For a uniform rectangular cross-section, kx = h/√12 about the centroidal axis parallel to its width. A 120 mm height gives kx ≈ 34.641 mm. For a uniform thin hoop about its central normal axis, k = R.

Radius of Gyration Definition

Radius of gyration is the distance from an axis at which the total mass, or cross-sectional area, could be concentrated while preserving its moment about that axis.

Radius of Gyration Example

How to calculate radius of gyration?

  1. First, choose the shape and axis.

    Select an area cross-section or a mass body and its stated axis. Mass presets assume uniform density; thin-body presets neglect thickness.

  2. Next, enter the dimensions.

    Enter the requested positive dimensions and choose their units. For a hollow circle, the inner diameter may be zero but must be less than the outer diameter.

  3. Finally, calculate the radius of gyration.

    Select Calculate to obtain the radius for the chosen axis. Expand Calculation details for the shape formula, substitutions and unit conversions.

FAQ

What is a radius of gyration?

Radius of gyration describes how mass or cross-sectional area is distributed relative to a specified axis: k = √(I/m) for mass and k = √(I/A) for area. Changing the axis can change the radius.