Technical Abstract: Many of USDA’s existing research data on fiber processing include mean values of length-distribution parameters, but not complete length histogram data. A specific goal of this work was to derive mathematically and demonstrate experimentally in the laboratory new engineering research tools that utilize only mean values of length for the analysis of fiber breakage. These techniques allow expanded interpretations of both existing and future data by quantitatively relating fiber breakage to changes in average length rather than length histograms. These tools potentially can be applied to measure the degree and nature of breakage that occurs in a batch of cotton during passage through an individual stage of mechanical handling. This work was focused specifically on the properties of number-based averages of fiber length because fiber length by number has the special feature that simple, practical relationships exist between the mean values. That situation that is more complicated for the mass-based averages. Saved-ends analysis was used, based on the tracking of number-mean length under the assumption of a complete mass balance. Calibrated experimental breakage was applied in the laboratory to a very uniform sliver substrate by cutting it at controlled gage lengths. The mathematical tools were then demonstrated successfully with experimental data from instrument measures of fiber length before and after these processes of known breakage intensity.