We propose and investigate an accurate method for the experimental measurement of the stimulated Brillouin scattering gain coefficient in optical fiber. The gain is extracted from measuring the transmitted pump power at the threshold of stimulated Brillouin scattering (SBS) laser oscillation in a Fabry-Perot cavity formed by Fresnel reflection at the fiber ends. The method is free from a range of uncertainties and difficulties of commonly used approaches and is easy to implement. Experimental evidence of the variation of the SBS gain coefficient with numerical aperture of the fiber, first predicted in [Phys. Rev. Lett. 85, 1879 (2000)], is proven.