The acoustic radiation impedance of an annular ring in a rigid infinite planar baffle has been the subject of several recent papers [A. S. Merriweather, J. Sound Vibration 10, 369–379 (1971); W. Thompson, Jr., J. Sound Vibration 17, 221–233 (1961); and C. J. Boukwamp, J. Sound Vibration 17, 499–508 (1971)]. In contrast to the earlier papers, a time domain approach is presented in this paper to evaluate the radiation impedance. Rather than directly evaluate the well-known Kirchoff double surface integral, the impulse response or inverse Fourier transform of the impedance is first evaluated from the integral. A closed-form expression for the impulse response which is valid for all ring sizes is presented, and several interesting characteristics of the solution are noted and discussed. Since the impulse response and radiation impedance of a ring are a Fourier transform pair, the Fourier transform of the impulse response must be evaluated to obtain the impedance. Although the Fourier transform can not be readily evaluated analytically, an approximate expression for the radiation impedance of the ring can be obtained and is presented. Numerical results for the radiation impedance of different sized rings are also presented as a function of normalized frequency.