Moment of Inertia Calculator
Calculate second moment of area for various cross-sections
How to use Moment of Inertia Calculator
- 1Select the cross-section shape from the list or choose custom input.
- 2Enter the required dimensions such as width, height, diameter, or radius.
- 3Review the area moment of inertia and radius of gyration for bending and deflection calculations.
Area moment of inertia in beams
Rectangle: I = b × h^3 / 12; Circle: I = π × d^4 / 64The area moment of inertia measures how a cross-section resists bending; larger values mean less deflection under the same load.
It depends on the shape and orientation of the cross-section, not on the material itself.
The radius of gyration relates the moment of inertia to the cross-sectional area and is useful for buckling analysis.
Frequently asked questions
Is this the same as mass moment of inertia?
No; area moment of inertia relates to bending stiffness, while mass moment of inertia relates to rotational inertia.
Why does orientation matter for a rectangle?
A beam laid flat has a much lower I about the bending axis than the same beam standing upright.
Can I use this for composite shapes?
Yes, by splitting the section into simple shapes and applying the parallel axis theorem.
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