Analyze T sections with fast property calculations. See centroid shifts, inertias, and derived values clearly. Download clean reports, inspect formulas, and validate example data.
| Flange Width | Flange Thickness | Web Thickness | Web Height | Centroid from Top | Ix | Iy |
|---|---|---|---|---|---|---|
| 120.00 mm | 20.00 mm | 30.00 mm | 100.00 mm | 43.3333 mm | 7,380,000.0000 mm4 | 3,105,000.0000 mm4 |
| 150.00 mm | 25.00 mm | 40.00 mm | 140.00 mm | 61.9118 mm | 24,628,743.8725 mm4 | 7,777,916.6667 mm4 |
| 200.00 mm | 30.00 mm | 50.00 mm | 180.00 mm | 78.0000 mm | 64,440,000.0000 mm4 | 21,875,000.0000 mm4 |
Flange area: A1 = B × tf
Web area: A2 = tw × hw
Total area: A = A1 + A2
Overall height: H = tf + hw
Centroid from top: ȳ = (A1y1 + A2y2) / A
Where: y1 = tf / 2 and y2 = tf + hw / 2
Centroidal x axis inertia: Ix = (Btf3 / 12) + A1d12 + (twhw3 / 12) + A2d22
Centroidal y axis inertia: Iy = (tfB3 / 12) + (hwtw3 / 12)
Polar area moment: J = Ix + Iy
Section modulus: S = I / c
Radius of gyration: r = √(I / A)
These relations assume a centered web and a symmetric T section about the vertical axis.
Enter the flange width first. Add the flange thickness next. Then enter the web thickness and the web height below the flange.
Choose a unit label like mm, cm, or in. Select the number of decimal places you want in the final report.
Press the calculate button. The result appears above this form and below the header section. Review the centroid, area, inertia values, and section modulus values.
Use the CSV button for spreadsheet review. Use the PDF button when you need a quick printable report.
The T shape moment of inertia measures how a section resists bending. It is also called the second moment of area. Designers use it when they study stiffness, stress distribution, and deflection. A larger value usually means better resistance to bending about that axis.
A T section combines a wide flange with a narrower web. This shape places more material away from the neutral axis. That can improve bending performance while keeping material use efficient. The web also carries shear and connects the flange to the rest of the member.
The centroid of a T section is not located at mid depth in most cases. The flange area pulls the centroid upward. Because of that shift, the parallel axis theorem becomes important. Each rectangle has its own local inertia, and each part must be moved to the shared centroidal axis.
This calculator finds total area, overall height, centroid from the top, centroid from the bottom, Ix, and Iy. It also shows the polar area moment, top section modulus, bottom section modulus, and radii of gyration. These outputs help with quick checks for beams, frames, brackets, and machine elements.
Use Ix when bending happens about the horizontal centroidal axis. Use Iy when bending happens about the vertical centroidal axis. The correct axis depends on loading direction and support conditions. Always match the section property to the real structural problem.
Keep all dimensions in one consistent unit. Confirm that the web is centered below the flange. Review whether you need area properties or torsion constants, because those are not the same thing. For engineering design, pair these values with material strength, loading, and code requirements.
It is the second moment of area for a T section. It shows how strongly the section resists bending about a selected centroidal axis.
The model treats the T section as two rectangles. Using the web height below the flange avoids double counting the overlap region.
Ix is the inertia about the horizontal centroidal axis. Iy is the inertia about the vertical centroidal axis. Each value answers a different bending case.
Yes. It calculates the centroid from the top and from the bottom. Those distances are needed for section modulus and parallel axis calculations.
No. Here J means Ix + Iy, which is the polar area moment. It is not the same as the torsional constant used in detailed torsion design.
Yes. Enter any consistent unit label you want. Keep all dimensions in the same unit so the output remains correct.
The centroid is usually not centered vertically in a T section. That makes the top and bottom distances to extreme fibers different, so the section modulus changes.
It is useful for geometry based section properties and quick checks. Final design should also consider loads, material behavior, buckling, safety factors, and design code rules.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.