Moment of inertia of a rectangular section with a hole
Outer contour minus inner: the properties of a hollow rectangular section follow by subtraction.
Formulas
About this calculator
A box section keeps almost the stiffness of a solid one at a much smaller area: material near the axis contributes little to bending, so it is removed. The formulas follow by subtracting the hole from the outer rectangle, which is valid as long as both share the same centroid.
Moment of inertia of a rectangle: deriving Ix = bh³/12Frequently asked questions
For a symmetric hole the properties simply subtract: Ix = (b₁h₁³ − b₂h₂³)/12. An off-centre hole needs the parallel-axis transfer, which the interactive calculator does for you.
Less than the area suggests: material near the neutral axis barely resists bending. That is what makes box sections so efficient by weight.