Section Properties Calculator
Area, second moment of area, section modulus and radius of gyration for rectangle, circle, pipe, I/H, channel and angle sections, with a dimension drawing; send the result to the beam and shaft calculators
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Calculates the area, centroid, second moment of area, section modulus and radius of gyration of rectangular, tubular, circular, pipe, I/H, channel and angle sections, with a dimension drawing, for use before a beam deflection or stress check.
How to use
- Choose a shape under "Section" and the "Unit" (mm, cm or inch).
- Enter the dimensions named in the drawing, such as "Width b", "Height h" and "Thickness t"; "Load example" fills in common sizes.
- A, Ix, Iy, Zx, Zy, rx and ry appear at once. An angle also shows Ixy and the principal values; a circle or pipe shows the polar moment J.
- Press the send button for the beam deflection or shaft strength calculator to carry I and Z, or the diameter, into that tool.
How it works
- Rectangle b×h: Ix = bh³ ÷ 12, Zx = bh² ÷ 6. Circle d: I = πd⁴ ÷ 64, Z = πd³ ÷ 32, J = πd⁴ ÷ 32.
- I, channel and angle sections are split into rectangles and summed with the parallel-axis theorem I = Σ(Iᵢ + Aᵢdᵢ²); Z divides by the distance to the farthest edge, and the smaller value governs the stress.
- Corner fillets and flange taper are not included, so values differ by a few percent from rolled-section tables; use the manufacturer's table for a standard section.
Questions and answers
- What is the difference between the second moment of area and the section modulus?
- I (mm⁴) measures resistance to bending and is used for deflection; Z = I ÷ y (mm³) gives the bending stress σ = M ÷ Z.
- How do I calculate the moment of inertia of an I-beam?
- Ix = (bh³ − (b − tw)(h − 2tf)³) ÷ 12. An H200×100×5.5×8 gives about 17.6 million mm⁴, a little below the table value of 18.4 million, which includes the fillets.
- Why does an angle section show principal axes?
- An angle is unsymmetrical, so Ixy is not zero and its weakest direction is a principal axis near 45°. Buckling checks use the minimum principal moment I2.
- What is the radius of gyration used for?
- r = √(I ÷ A) gives the slenderness ratio L ÷ r of a column; the smaller it is, the more easily the column buckles in that direction.