Nowadays, narrow linewidth lasers are unavoidable tools for fundamental and applied physics. One promising approach to generate coherent laser emission is based on stimulated Brillouin scattering (SBS) optical nonlinearity. Implementing SBS in an optical cavity gives rise to coherent emission with impressive performances in terms of noise and linewidth. Cascading the SBS process can even, under given conditions, improves the coherent emission specifications. To achieve such performances it is crucial to determine the Brillouin gain coefficient. Usual pump-probe methods are carried out in single pass waveguides. The probe intensity is proportional to e gBP in L eff / A eff where P in is the incident pump power, A eff the effective mode area and L eff the usual effective interaction length. To observe significant probe amplification one needs either long waveguides or strong pump power to reach the SBS threshold. We propose a method, based on the cavity ringdown spectroscopy, to directly characterize the Brillouin gain coefficient inside a resonator. This configuration allows to extract Brillouin parameters from the light recirculation with both a reduced waveguide length and input pump power when compared to usual methods.