  The multipolar expansion of the electromagnetic field plays a key role in the
study of light-matter interactions. All the information about the radiation and
coupling between the incident wavefield and the object is embodied in the
electric and magnetic scattering coefficients $\{a_{\ell m}, b_{\ell m} \}$ of
the expansion. However, the experimental determination of $\{a_{\ell m},
b_{\ell m} \}$ requires measuring the components of the scattered field in all
directions, something that is exceptionally challenging. Here, we demonstrate
that a single measurement of the Stokes vector unlocks access to the
quadrivector $ \mathbf{D}_{\ell m} = \left[|a_{\ell m}|^2, |b_{\ell m}|^2, \Re
\{ a_{\ell m} b^*_{\ell m} \}, \Im \{ a_{\ell m} b^*_{\ell m} \} \right]$.
Thus, our Stokes polarimetry method allows us to capture $|a_{\ell m}|^2$ and
$|b_{\ell m}|^2$ separately, a distinction that can not be achieved by
measuring the total energy of the scattered field via an integrating sphere.
Importantly, we demonstrate the robustness of our Stokes polarimetry method,
showing its fidelity with just two measurements of the Stokes vector at
different scattering angles. Our findings, supported by analytical theory and
exact numerical simulations, can find applications in Nanophotonics and greatly
facilitate routine light-scattering measurements in optical laboratories.
