Free Moment of Area Calculator

Calculate the second moment of area (moment of inertia) for a rectangular cross-section about its centroidal axis.

mm
mm

Ixx (about horizontal axis)

66,666,667 mm^4

Iyy (about vertical axis)16,666,667 mm^4
Ixx in cm^46,666.67 cm^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.

  1. 01Ixx = 100 x 200^3 / 12 = 100 x 8,000,000 / 12 = 66,666,667 mm^4
  2. 02Iyy = 200 x 100^3 / 12 = 200 x 1,000,000 / 12 = 16,666,667 mm^4
  3. 03Ixx in cm^4 = 66,666,667 / 10,000 = 6,666.67 cm^4

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