Estimating the true signal-to-noise ratio (SNR) of magnetic resonance (MR) images with low signal is confounded by the magnitude presentation of the data. This paper suggests a simple solution to this problem. A common method of measuring SNR compares the mean signal to the standard deviation of the noise. This SNR measure was found to be satisfactory for high but not low signal-to-noise image regions because of noise bias. These inconsistencies are removed by introducing unbiased definitions of the signal and noise levels in terms of their root-mean-square values. The approaches are compared by evaluating the SNR values for MR medical images.