The first moment of area, sometimes misnamed as the first moment of inertia, is based in the mathematical construct moments in metric spaces, stating that the moment of area equals the summation of area times distance to an axis [Σ(a x d)]. It is a measure of the distribution of the area of a shape in relationship to an axis.

First moment of area is commonly used in engineering applications to determine the centroid of an object or the statical moment of area.

Given an area, A, of any shape, and division of that area into n number of very small, elemental areas (dA_i). Let x_i and y_i be the distances (coordinates) to each elemental area measured from a given x-y axis. Now, the first moment of area in the x and y directions are respectively given by:

and

.

The SI unit for first moment of area is a cubic metre (m³). In the American Engineering and Gravitational systems the unit is a cubic foot (ft³) or more commonly inch³.

The static or statical moment of area, usually denoted by the symbol Q, is a property of a shape that is used to predict its resistance to shear stress. By definition:

In mathematics, a moment is, loosely speaking, a quantitative measure of the shape of a set of points. The "second moment", for example, is widely used and measures the "width" (in a particular sense) of a set of points in one dimension or in higher dimensions measures the shape of a cloud of points as it could be fit by an ellipsoid. Other moments describe other aspects of a distribution such as how the distribution is skewed from its mean, or peaked. The mathematical concept is closely related to the concept of moment in physics, although moment in physics is often represented somewhat differently. Any distribution can be characterized by a number of features (such as the mean, the variance, the skewness, etc.), and the moments of a function describe the nature of its distribution.

The 1st moment is denoted by μ₁. The first moment of the distribution of the random variable X is the expectation operator, i.e., the population mean (if the first moment exists).

In higher orders, the central moments (moments about the mean) are more interesting than the moments about zero. The first central moment is 0. The zero-th central moment, μ₀ is one. The second central moment is the variance.