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