Parallel Axis Theorem

1 min read Updated Fri Apr 24 2026 03:46:02 GMT+0000 (Coordinated Universal Time)

I_x = I_{x_1} + A\bar{y}^2

I_y = I_{y_1} + A\bar{x}^2

I_{xy} = I_{x_1 y_1} + A\bar{x}\bar{y}

Here

On LHS, the moments of area are about some $x$ , $y$ axes.
On RHS, the moments of area are about centroidal axes $x_1$ , $y_1$ parallel to x, y.
$\bar{x}$ is the distance between $x$ and $x_2$ axes.
$\bar{y}$ is the distance between $y$ and $y_1$ axes.