On active alluvial fans, debris-flow deposits and frequent avulsions produce a rough topographic surface. As is the case in many initially rough landforms produced by catastrophic processes, the topography of alluvial fans is progressively smoothed, producing textural differences useful in establishing relative age criteria for fans. Here, we outline an approach for defining a quantitative, numerical chronology for the surfaces of alluvial fans from topographic analysis, although the method is generalizable to any arbitrary landform. Our chronology relies on predictions for the evolution of topography by purely diffusive modification. Specifically, by comparing the surface roughness of active and abandoned alluvial-fan surfaces measured from spectral transformations of topography, we can directly estimate a fan’s “morphologic age,” which is the product of the duration and efficiency of diffusive modification by surface processes. We tested the method on a suite of alluvial fans in the San Luis Valley, Colorado, USA, and evaluated the results against field observations and available geochronologic data. Estimated morphologic ages obey stratigraphic constraints and imply reasonable efficiencies of sediment transport. We highlight the fact that the oldest fan surfaces observed here, constrained to be older than 100 ka by U-series dating of pedogenic carbonates, have morphologic ages near the method’s saturation point. In addition, many fans have morphologies that are not entirely consistent with a purely diffusive modification from the initial fan morphology recorded on active fan surfaces, likely as a result of postdepositional modification by sediment transport driven by wind and overland flow. However, we remain optimistic that morphologic dating can provide useful insights into the history of alluvial-fan activity, in particular, because our method provides a means for both computing a morphologic age and assessing the validity of the assumptions required for that computation from analysis of topography alone.