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A circular loop antenna is often numerically modeled using a regular polygon. This approach is simple and robust, yet it alters the circumference of the loop and may thus shift the resonance frequency in the numerical model. This letter introduces a simple analytical formula for predicting and relating the accuracy of resonance frequency determination to the number of segments used. The result of testing on commercial software WIPL-D showed an excellent match between the prediction and numerically derived results. It is expected that the approach can be extended onto other structures with curvatures.