Recently, we developed a crossing frequency method using the cutoff probe, which is believed as applicable for measuring electron density regardless of chamber pressures. Although computational and experimental studies demonstrated its operation, the analytic formula for the crossing frequency (fcross) has yet to be investigated. In this paper, we derive the analytic formula based on a circuit model for the cutoff probe. As a result, the analytic formula explains the behavior of the fcross. Based on this formula, the meaning of the fcross is analyzed and it is proved that the fcross is independent of the chamber pressure.