Area, centroid, Ix, Iy, section modulus and radius of gyration for rectangle, circle, hollow sections, I-beam, T-beam, channel and angle — with a to-scale diagram and a step-by-step parallel axis breakdown.
Drawn to scale · blue cross marks the centroid
Ix
8,871 cm⁴
Iy
676.18 cm⁴
Area
58.08 cm²
Mass
45.6 kg/m
Ix
88,709,184
mm⁴
Iy
6,761,776
mm⁴
Centroid ȳ
150
mm
Centroid x̄
0
mm
Sx, top
591,395
mm³
Sx, bottom
591,395
mm³
rx
123.59
mm
ry
34.12
mm
Parallel axis theorem: each part's own moment of inertia, plus its area times the square of its distance from the composite centroid.
| Part | Area (mm²) | I₀ (mm⁴) | d (mm) | A·d² (mm⁴) | Total (mm⁴) |
|---|---|---|---|---|---|
| Bottom flange | 1,800 | 21,600 | -144 | 37,324,800 | 37,346,400 |
| Web | 2,208 | 14,016,384 | 0 | 0 | 14,016,384 |
| Top flange | 1,800 | 21,600 | 144 | 37,324,800 | 37,346,400 |
| Ix total | 88,709,184 |
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Ready to take the next step?
Two sections with identical area can have wildly different moments of inertia depending on how that area is arranged. Pushing material away from the centroid — like an I-beam's flanges, or a hollow section's walls — increases I far more than it increases weight, which is why structural steel sections are shaped the way they are rather than being solid bars.
This calculator handles that shape-dependence for you: pick a shape, enter its dimensions, and it works out exactly how the area is distributed and what that means for bending resistance.