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Moment of Inertia Calculator

Calculate second moment of area for rectangle, circle, and sections.

I_xx (strong axis)
66.6667 ×10⁶ mm⁴
I_yy (weak axis)
16.6667 ×10⁶ mm⁴
Area
20000.00 mm²
r_x (radius of gyration)
57.735 mm
Section: b=100mm, d=200mm
I_xx = 66666666.67 mm⁴ · I_yy = 16666666.67 mm⁴

Second moment of area for structural sections

Calculate Ixx and Iyy for standard cross-sections including rectangle, circle, hollow sections, I-beam, and T-section. Results include area and radius of gyration.

Frequently asked questions

What is moment of inertia in structural engineering?
The second moment of area (I) measures a cross-section's resistance to bending. A higher I means less deflection under the same load. The formula for a rectangle is I = bd³/12.
What is the radius of gyration?
Radius of gyration r = √(I/A). It represents the distance from the centroidal axis at which the entire area could be concentrated to produce the same moment of inertia. Used in column buckling analysis.
Why do I-sections have high moment of inertia?
I-sections concentrate material in flanges away from the neutral axis. Since I = ∫y²dA, material far from the neutral axis contributes more to I. This makes I-sections efficient for bending resistance with less material.

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