Moment of Inertia Calculator

Calculate area moment of inertia, weak-axis inertia, section modulus, radius of gyration, cross-sectional area, bending stress, and simplified moment capacity. Use this moment of inertia calculator for rectangular beams, round bars, pipes, tubes, HSS shapes, I-section approximations, wood beams, steel members, joists, and preliminary structural planning.

Calculate Moment of Inertia

Area moment of inertia measures how a cross-section resists bending. Section modulus S = I ÷ c. Radius of gyration r = √(I ÷ A).
Your result will appear here.

How the moment of inertia calculator works

Shape properties:
The calculator estimates area, strong-axis inertia, weak-axis inertia, section modulus, and radius of gyration from the selected cross-section.

Strong and weak axes:
For rectangular and tube shapes, the calculator estimates both Iₓ and Iᵧ so you can compare bending directions.

Bending stress:
The calculator converts moment to inch-pounds and divides by section modulus to estimate bending stress.

Capacity check:
The calculator multiplies section modulus by allowable bending stress to estimate simplified moment capacity.

Why use a moment of inertia calculator?

A moment of inertia calculator helps compare cross-section stiffness before choosing a beam, joist, tube, shaft, pipe, or structural member.

It can help compare strong-axis inertia, weak-axis inertia, section modulus, radius of gyration, bending stress, required section modulus, and simplified moment capacity.

What your result means

Your result shows estimated cross-sectional area, strong-axis moment of inertia, weak-axis moment of inertia, controlling inertia, extreme fiber distance, section modulus, radius of gyration, bending stress, allowable bending stress, moment capacity, and simplified utilization. These are preliminary planning estimates only.

Moment of inertia formulas

Frequently asked questions

What is moment of inertia in structural calculations?

Area moment of inertia is a cross-section property that helps describe how resistant a shape is to bending and deflection. Larger values usually mean a stiffer member for the same material and span.

Is moment of inertia the same as section modulus?

No. Moment of inertia is used heavily for stiffness and deflection, while section modulus is used for bending stress. Section modulus equals moment of inertia divided by the extreme fiber distance.

Why does depth increase beam stiffness so much?

For a rectangular section, strong-axis moment of inertia equals b × d³ ÷ 12, so increasing depth has a cubed effect on inertia.

Can this calculator replace beam design?

No. This calculator estimates section properties and simplified bending stress only. Final design should also check shear, deflection, bearing, lateral bracing, load combinations, connections, material grade, and local code requirements.