Brillouin spectroscopy has emerged as a novel analytical tool for biophotonic research and applications. It operates on a microscopic scale and in the GHz spectral range, providing a new spatial and frequency window for the analysis of the materials elasticity. Here we investigate spectral moments calculation as a means of analysing Brillouin and Raman spectra, providing rapid access to peak intensity and frequency shift, with robust application to fast scanning measurements. This work demonstrates the potential of the method, especially in the case of micro-structured samples, typical of bio-medical applications.