Delayed self-heterodyne interferometry is a commonly used technique for the measurement of laser linewidth. It typically requires the use of a very long delay fiber when measuring narrow linewidth (especially linewidths in the kHz-range) lasers. The use of long fibers can result in system losses and the introduction of 1/f noise that causes spectral line broadening. In this paper, we present a calculation method for processing the output of a delayed self-heterodyne setup using a short length of delay fiber, to determine laser linewidth. The method makes use of pairs of data points (corresponding to adjacent maxima and/or minima) in the signal generated from the self-heterodyne setup to determine the laser linewidth. Here, the power ratio or amplitude difference of the signal at these data points is of importance. One of the key benefits of this method is that it avoids 1/f noise which would otherwise be introduced into the measurement through the application of long fibers. The experimental results highlight that the method has a high calculation accuracy. Furthermore, the capacity for the method to utilize different pairs of data points in the self-heterodyne output to determine the laser linewidth, imparts a high degree of flexibility and usability to the technique when applied to real-world measurements.