We investigate the random variable defined by the volume of the zero set of a smooth Gaussian field, on a general Riemannian manifold possibly with boundary. We prove a new explicit formula for its Wiener-Itô chaos decomposition that is notably simpler than existing alternatives and which holds in greater generality, without requiring the field to be compatible with the geometry of the manifold. A key advantage of our formulation is a significant reduction of the complexity of the computations of the variance of the nodal volume. Unlike the standard Hermite expansion, which requires evaluating the expectation of products of 2+2n Hermite polynomials, our approach reduces this task—in any dimension n—to computing the expectation of a product of just four Hermite polynomials. As a consequence, we establish a new exact formula for the variance. This is a joint work with Michele Stecconi.