The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function σ(x, y) is M = integral integral σ(x, y) d A, and the coordinates of the centroid (also called the center of gravity) are x^_ | = | ( integral integral x σ(x, y) d A)/M y^_ | = | ( integral integral y σ(x, y) d A)/M. The centroid of a lamina is the point on which it would balance when placed on a needle. The centroid of a solid is the point on which the solid would "balance."
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