Free Moment of Area Calculator
Calculate the second moment of area (moment of inertia) for a rectangular cross-section about its centroidal axis.
Ixx (about horizontal axis)
66,666,667 mm^4
Ixx (about horizontal axis) vs Width (b)
Second Moment of Area for a Rectangle
The second moment of area (often called moment of inertia of the cross-section) governs how a beam resists bending.
Formula
Ixx = b h^3 / 12
Iyy = h b^3 / 12
where b is the width and h is the height of the rectangle. The axis with the larger I value provides greater bending resistance. That is why beams are oriented with the taller dimension vertical.
Example Calculation
A rectangular timber section 100 mm wide and 200 mm tall.
- 01Ixx = 100 x 200^3 / 12 = 100 x 8,000,000 / 12 = 66,666,667 mm^4
- 02Iyy = 200 x 100^3 / 12 = 200 x 1,000,000 / 12 = 16,666,667 mm^4
- 03Ixx in cm^4 = 66,666,667 / 10,000 = 6,666.67 cm^4
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