Glacial lakes are most often located in remote places making it difficult to carry out detailed bathymetric surveys. Consequently, lake depths and volumes for unmeasured lakes are often estimated using empirical relationships developed mainly from small bathymetric datasets. In this study, we use the bathymetry dataset of the Cordillera Blanca, Peru comprising 121 detailed lake bathymetries, the most extensive dataset in the world. We assess the performance of the most commonly applied empirical relationships for lake mean depth and volume estimation, but also investigate relationships between different geometric lake variables. We find that lake volume estimation performs better when derived from lake mean depth, which in turn is estimated from lake width. The findings also reveal the extreme variability of lake geometry, which depends on glacio-geomorphological processes that empirical–statistical relationships cannot adequately represent. Such relationships involve characteristic uncertainty ranges of roughly ±50%. We also estimate potential peak discharges of outburst floods from these lakes by applying empirical relationships from the literature, which results in discharges varying by up to one-order of magnitude. Finally, the results are applied to the 860 lakes without bathymetric measurements from the inventory dataset of the Cordillera Blanca to estimate lake mean depth, volume and possible peak discharge for all unmeasured lakes. Estimations show that ca. 70% (610) of the lakes have a mean depth lower than 10 m and very few longer than 40 m. Lake volume of unmeasured lakes represent ca. 32% (5.18 × 108 m3) of the total lake volume (1.15 × 109 m3) in the Cordillera Blanca. Approximately, 50% of the lakes have potential peak discharges > 1000 m3/s in case of lake outburst floods, implying a need for additional studies for risk assessment. © 2020 John Wiley & Sons, Ltd.