MOTIVATION: Single-molecule localization microscopy resolves individual fluorophores or fluorescence-labeled biomolecules. Data are provided as a set of localizations that distribute normally around the true fluorophore position with a variance determined by the localization precision. Characterizing the spatial fluorophore distribution to differentiate between resolution-limited localization clusters, which resemble individual biomolecules, and extended structures, which represent aggregated molecular complexes, is a common challenge. RESULTS: We demonstrate the use of the convex hull and related hull properties of localization clusters for diagnostic purposes, as a parameter for cluster selection or as a tool to determine localization precision. AVAILABILITY AND IMPLEMENTATION: https://github.com/super-resolution/Ebert-et-al-2022-supplement. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.