An analytic method for error estimate is applied to reactor theory. The method is based on the functional analysis technique and gives upper bounds to the errors. There are two main advantages to the method. First, error estimates can be obtained in cases for which no other known method succeeds. Second, any upper bound to the error obtained by this method is reliable. This method finds an upper bound to the errors in the eigenvalues of homogeneous equations and in the relative RMS solutions of the inhomogeneous equations. When the method is applied to the inhomogeneous integral transport equations, upper bounds to the relative RMS of the fluxes result. Application of the method is further extended to homogeneous equations such as the integral transport equations and even to unbounded equations such as diffusion equations. For these cases the errors in reactivity and time decay constants are studied.