New analytical expressions and numerical results for the quality factor and directivity as well as computationally convenient expressions for the input admittance of a symmetrical biconical antenna of arbitrary length $L$ and cone angle $\theta_0$ are presented. The quality factor for a wide-angle biconical antenna is shown to very closely approach the Chu’s limit of $Q = (kL)^{-1}\{1+(kL)^{-2}\}$. Numerical calculations based on the analytical formula for antenna admittance confirm the conjecture that Foster’s reactance theorem remains invalid even for perfectly conducting antennas. Furthermore, the variation of directivity of a wide-angle biconical antenna is a slowly varying function of its electrical length and is shown to depart significantly from that of a thin cylindrical dipole.