The sensitivity of a recently reported optical-fiber ring interferometer as a gyroscope has been analyzed. Photomixing SNRs were derived for the detection schemes. Noise sources due to the Rayleigh, Brillouin, Mie, and core-cladding interface light scattering processes are assessed quantitatively. Optimum gyroscope sensitivities are discussed via numerical examples for optical wavelengths of 0.633 and 1.1 micron and both spontaneous and stimulated noises. Results show that (a) to reduce trapped scattered light by a factor of 100, mode stripping is essential, (b) the 1.1-micron wavelength is a more promising wavelength to use, and (c) high optical power operation, where the only noise is due to stimulated Brillouin scattering, gives better sensitivity than the low-power case. Examples show that at 0.633-micron wavelength, the achievable sensitivities are 0.0078 deg/h at 2 mW and 0.0009 deg/h at 81 mW; and at 1.1-micron wavelength, they are 0.0025 deg/h at 2 mW and 0.0007 deg/h at 14.4 mW. These calculated sensitivities are better than those of current laser ring gyroscopes.