Moment of Inertia and Centroid of a Quarter Circle

Section properties of a Quarter Circle: 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
Quarter Circle cross section with its dimensions and centroid
  • rr = radius
PropertySymbolFormula
AreaAAπr24\frac{\pi r^2}{4}
PerimeterPPπr2+2r\frac{\pi r}{2} + 2r
Centroid from the left edgexˉ\bar{x}4r3π\frac{4r}{3\pi}
Centroid from the bottom edgeyˉ\bar{y}4r3π\frac{4r}{3\pi}
Moment of inertia about the centroidal x-axisIˉx\bar{I}_x(π16−49π)r4\left(\frac{\pi}{16} - \frac{4}{9\pi}\right) r^4
Moment of inertia about the centroidal y-axisIˉy\bar{I}_y(π16−49π)r4\left(\frac{\pi}{16} - \frac{4}{9\pi}\right) r^4
Moment of inertia about the baseIxI_xπr416\frac{\pi r^4}{16}
Moment of inertia about the left edgeIyI_yπr416\frac{\pi r^4}{16}

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