I Beam Section Property Inputs
Formula Used
The calculator splits the I beam into three rectangles. These are the bottom flange, web, and top flange.
Area: A = bbtb + twhw + bttt
Centroid from bottom: ȳ = Σ(Aiyi) / ΣAi
Strong axis inertia: Ix = Σ[(bh³ / 12) + A(yi - ȳ)²]
Weak axis inertia: Iy = Σ(hb³ / 12)
Section modulus: S = I / c
Radius of gyration: r = √(I / A)
The model assumes a centered web and rectangular parts. It ignores fillets, radii, holes, taper, and weld buildup.
How to Use This Calculator
- Enter the top flange width and thickness.
- Enter the web thickness and clear web height.
- Enter the bottom flange width and thickness.
- Select the dimension unit used for all geometry fields.
- Set the material density if mass per meter is needed.
- Choose decimal places for the displayed result.
- Press calculate and review the result above the form.
- Use the CSV or PDF button to save the calculation.
Example Data Table
| Example |
Top Flange |
Web |
Bottom Flange |
Total Depth |
Ix mm⁴ |
Iy mm⁴ |
| Light symmetric beam |
100 × 10 mm |
6 × 180 mm |
100 × 10 mm |
200 mm |
20,982,666.67 |
1,669,906.67 |
| Medium symmetric beam |
150 × 12 mm |
8 × 276 mm |
150 × 12 mm |
300 mm |
88,709,184.00 |
6,761,776.00 |
| Heavy symmetric beam |
200 × 16 mm |
10 × 368 mm |
200 × 16 mm |
400 mm |
277,596,160.00 |
21,364,000.00 |
| Unequal flange beam |
180 × 14 mm |
8 × 322 mm |
160 × 12 mm |
348 mm |
145,489,153.54 |
10,913,738.67 |
Moment of Inertia I Beam Guide
What This Calculator Does
This I beam calculator estimates the main section properties of a built up or rolled style beam. It works with equal flanges, unequal flanges, and a centered web. The tool converts every input to a common base unit before it calculates area, centroid position, strong axis inertia, weak axis inertia, section modulus, radius of gyration, and mass per length. These values help describe how a shape resists bending, buckling, and deflection.
Why Moment of Inertia Matters
Moment of inertia is not mass inertia here. It is the second moment of area. A larger value means the section spreads more material away from the neutral axis. That usually improves bending stiffness. For an I beam, most strong axis stiffness comes from the flanges. The web adds area and shear depth, but its weak axis contribution is smaller. This is why deep beams often perform well for vertical bending.
Centroid and Section Modulus
The centroid is the balance point of the cross section. A symmetric I beam has a centroid at mid depth. An unequal beam does not. The calculator locates that neutral axis by adding each rectangle area times its centroid distance. Section modulus then divides inertia by the farthest distance to the top or bottom edge. This value is useful for quick bending stress checks.
Practical Design Notes
Use actual measured dimensions when possible. Rolled shapes may have fillets, tapers, and rounded corners. This calculator treats the beam as three clean rectangles. That makes it fast and clear, but it is an approximation for real catalog shapes. For final structural design, compare results with verified section tables and local design standards.
Export and Review
After calculation, review the result block before the form. The CSV export is useful for spreadsheets and logs. The PDF export is useful for design notes, shop records, or quick project files. Keep units consistent across entries. If you switch units, recheck every dimension before submitting. The density input adds an estimated mass per length. Steel often uses 7850 kg per cubic meter. Always round results only after the final calculation. Early rounding can change section modulus, especially for shallow beams or very thin webs during high load checks and audits too.
FAQs
What is moment of inertia for an I beam?
It is the second moment of area of the I shaped section. It shows how strongly the section resists bending about an axis.
Does this calculator handle unequal flanges?
Yes. You can enter different top and bottom flange widths and thicknesses. The centroid will shift automatically when the beam is not symmetric.
What is the strong axis?
The strong axis is usually the horizontal centroidal axis of an I beam. It gives the larger inertia value for vertical bending.
What is the weak axis?
The weak axis is usually the vertical centroidal axis. It often gives a much smaller inertia value because flange width controls that direction.
Are fillets included in the calculation?
No. The calculator uses three rectangular parts. Real rolled sections may include fillets, slopes, and rounded edges that slightly change properties.
Which units can I use?
You can use millimeters, centimeters, meters, inches, or feet. Keep every entered dimension in the same selected unit.
What does section modulus mean?
Section modulus equals inertia divided by distance to the extreme fiber. It is commonly used for elastic bending stress checks.
Can I use the PDF as a final design report?
Use it as a calculation note or quick record. For final design, verify section data, loads, codes, and safety factors separately.