In this article the Campbell's theorem is used to evaluate the equilibrium emittance and energy spread in a Compton ring. This method allows us to have an efficient analytical approach separating the contributions of the Compton cross section from the luminosity factor. The consequent advantage is given by the possibility to have an easy extrapolation for the "nonclassical" cases like the polarized Compton backscattering or the evaluation of the equilibrium given by different radiation mechanisms. The effects accounting for the polarized Compton backscattering in the article are evaluated numerically. The analytical results in the nonpolarized case and in the negligible recoil effect approximation are in excellent agreement with the values obtained by matching the Compton damping rate with the quantum fluctuations, and they show that the equilibrium energy spread and emittance are independent from the luminosity.