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The moment of inertia relative to the axis {{math|''z′''}}, which is a perpendicular distance {{math|''d''}} along the ''x''-axis from the centre of mass, is
:<math>I = \int \left[(x +
Expanding the brackets yields
:<math>I = \int (x^2 + y^2) \, dm +
The first term is {{math|''I''<sub>cm</sub>}} and the second term becomes {{math|''md''<sup>2</sup>}}. The integral in the final term is a multiple of the x-coordinate of the [[center of mass]]{{snd}}which is zero since the center of mass lies at the origin. So, the equation becomes:
:<math> I = I_\mathrm{cm} +
=== Tensor generalization ===
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