The local demagnetization factor for the ring-core flux gate is derived analytically, based on a tangential magnetization model. The results are in good agreement with experimental data for a wide range of ring shape parameters. Approximate expressions in the limit of a narrow, thin ring are obtained, and indicate that the local demagnetization factor scales with the ratio of the cross-sectional area to the total area of the ring. Analytical modeling of the demagnetization factors for a uniform magnetization state results in an underestimate of the local cross-section averaged demagnetization factors by 50% or more.