Calculate area, centroid, moment of inertia, and section modulus for I-beams, rectangles, channels, and custom sections.
Select the section shape (I-beam, Rectangular, Circular, or Tube). Enter the required dimensions like flange width, web thickness, and height.
The calculator determines the Area Moment of Inertia (Ix and Iy). This value represents the shape's resistance to bending based on its geometry.
For I-beams, the majority of the bending resistance comes from the distance of the flanges from the neutral axis. This is why tall, thin beams are efficient.
Moment of inertia Ix governs deflection and stiffness; section modulus Sx = Ix/c governs bending stress (σ = M/Sx); and radius of gyration rx = √(Ix/A) governs buckling. A 50×200 mm rectangle, for example, has Ix = 3.33×10⁷ mm⁴, Sx = 333,000 mm³, and rx ≈ 57.7 mm — three different numbers describing three different failure modes.
Inertia scales with the cube of the depth in the bending direction. Standing a 50×200 mm section on its narrow edge gives 16 times the moment of inertia of laying it flat (3.33×10⁷ vs 2.08×10⁶ mm⁴). This is why floor joists are installed tall and thin rather than wide and shallow.
Hollowing out material near the neutral axis removes weight where it contributes little. A 100 mm round tube with an 80 mm bore retains about 59% of the solid bar's moment of inertia while using only 36% of its cross-sectional area — a large stiffness-to-weight gain, which is why tubes dominate masts and frames.
Sx assumes the section stays elastic; Zx assumes the whole section has yielded and is used in limit-state (LRFD) design. Their ratio is the shape factor — 1.5 for a rectangle, around 1.12–1.18 for a typical I-beam — representing the reserve strength between first yield and a full plastic hinge.