Moment of Inertia and Centroid of a Square Angle

Section properties of a Square Angle: area, centroid location and second moment of area (moment of inertia) about the centroidal axes and about the base and left edge. These values are used to size beams and columns, compute bending stresses (σ = M·y/I) and deflections.

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Square Angle cross section with its dimensions and centroid
  • aa = side
  • tt = thickness
PropertySymbolFormula
AreaAAa2−(a−t)2a^2 - (a-t)^2
PerimeterPP4a4a
Centroid from the left edgexˉ\bar{x}a2+at−t22(2a−t)\frac{a^2 + at - t^2}{2(2a - t)}
Centroid from the bottom edgeyˉ\bar{y}a2+at−t22(2a−t)\frac{a^2 + at - t^2}{2(2a - t)}
Moment of inertia about the centroidal x-axisIˉx\bar{I}_xIx−yˉ2AI_x - \bar{y}^2 A
Moment of inertia about the centroidal y-axisIˉy\bar{I}_yIy−xˉ2AI_y - \bar{x}^2 A
Moment of inertia about the baseIxI_xt(a3+at2−t3)3\frac{t(a^3 +at^2 -t^3)}{3}
Moment of inertia about the left edgeIyI_yt(a3+at2−t3)3\frac{t(a^3 +at^2 -t^3)}{3}

The origin is the bottom-left corner of the bounding box. The moments of inertia about the base and the left edge follow from the parallel axis theorem: Ix=Iˉx+Ayˉ2I_x = \bar{I}_x + A\bar{y}^2.

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Enter the dimensions and get the area, centroid and moments of inertia instantly, with the section drawn to scale. Metric and imperial units.

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