An apparatus is described that determines an estimated rotational speed of a rotating component of a machine in the absence of a reliable tachometer signal to indicate an actual rotational speed. The apparatus includes a processor that produces a spectral plot of the vibrational data, locates peaks in the spectral plot, and scans the spectral plot in predetermined rotational speed increments to provide candidate rotational speeds. For each candidate rotational speed, associated harmonics are identified, closest peaks in the spectral plot to the candidate rotational speed and its harmonics are located, gaps between the closest peaks and the candidate rotational speed and its harmonics are measured, and a sum of the gaps is recorded. The estimated rotational speed is the candidate rotational speed associated with a minimum sum of the gaps.