The waveform fitting technique has been a prevailing method for accurate extraction of a range of objects from an observed signal. Exploration of range precision then became a significant research topic to evaluate the performance of the technique with the corruption of noise. In this paper, we derive an analytical solution of the maximum likelihood estimation for the Gaussian model as the probability density function (PDF) of the range estimator. The variance of the linear version of the PDF is consistent with the Cramer-Rao bound (CRB). Thus, the variance of the PDF is regarded as the theoretical range precision (TRP) compared with the CRB. The verification results show the TRP can perfectly describe the variance of the simulation data while the CRB provides a lower bound. At a higher signal-to-noise ratio (SNR), both the TRP and CRB have the ability to provide an accurate description of the range precision. At a lower SNR, the TRP still performs well while the CRB is too loose to bound the variance on the unbiased estimation.