Estimate centroidal Ix and Iy values for common beam shapes used in construction. The calculator also reports area, radii of gyration, section modulus values, centroid location, and a quick major-axis interpretation for early design screening.
Enter section dimensions
Example data table
| Shape | Example dimensions | Area | Ix | Iy |
|---|---|---|---|---|
| Solid rectangle | b = 300 mm, h = 500 mm | 150,000 mm² | 3,125,000,000 mm⁴ | 1,125,000,000 mm⁴ |
| Hollow rectangle | B = 400 mm, H = 600 mm, bi = 320 mm, hi = 520 mm | 73,600 mm² | 3,450,453,333.3333 mm⁴ | 1,780,053,333.3333 mm⁴ |
| I-section | bf = 250 mm, h = 450 mm, tf = 25 mm, tw = 16 mm | 18,900 mm² | 650,437,500 mm⁴ | 65,240,700 mm⁴ |
Formula used
Core definitions
Second moment of area measures how far section area sits from the bending axis.
- Rectangle: Ix = b × h³ / 12, Iy = h × b³ / 12
- Circle: Ix = Iy = π × d⁴ / 64
- Hollow circle: Ix = Iy = π × (D⁴ − d⁴) / 64
- Hollow rectangle: subtract the inner rectangle from the outer one
Composite sections
I, T, channel, and angle sections use the parallel-axis theorem.
- Find each rectangle area and centroid.
- Locate the overall centroid from the area-weighted average.
- Shift each local inertia by A × d².
- Add positive parts and subtract voids or overlaps.
How to use this calculator
- Choose the beam shape that best matches your section profile.
- Select one unit system and keep every dimension in that same unit.
- Enter the shape dimensions, then choose the output precision.
- Press Calculate inertia to show the result block above the form.
- Review Ix, Iy, centroid location, radii of gyration, and section modulus values.
- Use the export buttons to save the result for reports, checking sheets, or estimate files.
Frequently asked questions
1) What does beam moment of inertia describe?
It describes how section area is distributed around an axis. A larger value means the section resists bending more effectively about that axis.
2) Why are Ix and Iy different?
They are measured about different centroidal axes. Most beam sections are stiffer in one direction, so the strong and weak axes rarely match.
3) Can I mix millimeters and inches?
No. Use one unit for every dimension in the same calculation. The output unit becomes that chosen length unit raised to the fourth power.
4) Is this the same as mass moment of inertia?
No. This tool calculates area moment of inertia for bending checks. Mass moment of inertia is used in dynamics and depends on mass distribution.
5) Why does a deeper beam usually have much larger Ix?
Depth has a cubic effect in many beam formulas. Small increases in depth can greatly increase bending stiffness and reduce deflection.
6) What is the section modulus shown here?
Section modulus divides inertia by the distance to the extreme fiber. It is helpful for linking bending moment demand to stress capacity.
7) Does the calculator handle unsymmetrical sections?
Yes. Channel and angle sections can produce different left and right section modulus values because their centroids are offset from the envelope center.
8) Can I use these results for final structural design?
Use them for preliminary sizing and checking. Final design should still follow project drawings, material standards, and the governing structural code.