First moment of area, abbreviated as \(Q\), also called first moment of inertia, is the measurement of a shape's area cross-section relative to an axis, located in space. In practical terms and of relavance to this site, the shape is generally a beam or piece of pipe. It is the resistance of an object to bend around a certain axis. It can be used to determine the location of the centroid, which is the point where the sum of all moments of inertia are equal.
First Moment of Area Formula |
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\( Q \;=\; A \cdot \bar y \) ( First Moment Area) \( A \;=\; \dfrac{ Q }{ \bar y } \) \( \bar y \;=\; \dfrac{ Q }{ A } \) |
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| Symbol | English | Metric |
| \( Q \) = First Moment of Area | \(lbm \;/\; in^2 - sec\) | \(kg \;/\; mm^2\) |
| \( A \) = Area Cross-section | \(in^2\) | \(mm^2\) |
| \( \bar y \) = Distance from Centroid of the Area to the Reference Axis | \(in\) | \(mm\) |
