Moment of Inertia and Centroid of a Thin-Walled Rectangle

Section properties of a Thin-Walled Rectangle: 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.

Calculate with your values
Thin-Walled Rectangle cross section with its dimensions and centroid
  • bb = base
  • hh = height
  • tt = wall thickness
PropertySymbolFormula
AreaAAbh−bihib h - b_i h_i
Outer perimeterPoutP_{out}2(b+h)2(b + h)
Inner perimeterPinP_{in}2(bi+hi)2(b_i + h_i)
Centroid from the left edgexˉ\bar{x}b2\frac{b}{2}
Centroid from the bottom edgeyˉ\bar{y}h2\frac{h}{2}
Moment of inertia about the centroidal x-axisIˉx\bar{I}_xbh312−bihi312\frac{b h^3}{12} - \frac{b_i h_i^3}{12}
Moment of inertia about the centroidal y-axisIˉy\bar{I}_yb3h12−bi3hi12\frac{b^3 h}{12} - \frac{b_i^3 h_i}{12}
Moment of inertia about the baseIxI_xbh33−bihi312−bihih24\frac{b h^3}{3} - \frac{b_i h_i^3}{12} -\frac{b_i h_i h^2}{4}
Moment of inertia about the left edgeIyI_yb3h3−bi3hi12−bihib24\frac{b^3 h}{3} - \frac{b_i^3 h_i}{12} -\frac{b_i h_i b^2}{4}
Inner widthbib_ib−2tb-2t
Inner heighthih_ih−2th-2t

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.

Calculate it with your dimensions

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

Calculate with your values

Other sections