The first moment of area is a geometric property that measures the distribution of an area about a particular axis. It is often used in engineering and structural analysis to help determine the centroid of a shape or area. The first moment of area (denoted as \( Q \)) is defined for a specific axis and is calculated as the integral (or sum) of the area times the distance from that axis.
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For a planar region of finite positive area , its first moments of area about the coordinate axes are the displayed double integrals, provided they exist. Its centroid is . This follows by applying the definition to each component. The subscript indicates the axis about which the moment is taken: the first moment about the -axis weights by , not .