Moment of inertia of a rectangular section
Enter the width and the height to get the moments of inertia, the area, the section moduli and the radii of gyration of a rectangular section.
Formulas
About this calculator
The rectangle is the base case for beams and columns. Its moment of inertia about the horizontal axis grows with the cube of the height, which is why a joist is set on edge: for the same area it becomes far stiffer in bending.
Moment of inertia of a rectangle: deriving Ix = bh³/12Frequently asked questions
About the centroidal horizontal axis Ix = b·h³/12 and about the vertical axis Iy = h·b³/12, where b is the width and h the height.
Wx = Ix / (h/2) = b·h²/6. It tells you what bending moment the section carries at a given allowable stress.