Engineering formula

Parallel-Axis Theorem for Second Moments of Area

$$I = Ic + Aa²$$

The second moment of area about an axis parallel to a centroidal axis is found from the parallel-axis theorem:

$$I_x=I_{x_c}+Aa^2,$$

where Ixc is the second moment about the parallel centroidal axis, A is the area, and a is the distance between the axes.

Similarly:

$$I_y=I_{y_c}+Ab^2.$$

For a composite section, the transferred contributions of all parts are summed algebraically; holes are treated with negative area.

Related theory