This paper proposes a quasi-static conformal mapping analysis to analytically evaluate the input resistance of Archimedean spiral antenna at its radiation region. The deviation from the original constructs of band theory for two-wire spiral antennas leads to the concept of common slot-line mode radiation. The per-unit-length capacitance and the characteristic impedance of the quasi-TEM fundamental propagating mode in periodic coplanar waveguide (PCPW) structure are obtained in terms of spiral parameters including substrate properties. This formula enables little computational effort on the computation of input resistance at the radiation mode of balanced-excited two-arm Archimedean spiral antennas. The numerical simulation demonstrates the accuracy of derived formulas both in free space and when a dielectric layer is presented.