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In this work we improve a previously published method to calculate in areliable way the radius of an open cluster. The method is based on thebehaviour of stars in the proper motion space as the sampling changes in theposition space. Here we describe the new version of the method and show itsperformance and robustness. Additionally, we apply it to a large number of openclusters using data from Gaia DR2 to generate a catalogue of 401 clusters withreliable radius estimations. The range of obtained apparent radii goes fromRc=1.4+-0.1 arcmin (for the cluster FSR 1651) to Rc=25.5+-3.5 arcmin (forNGC~2437). Cluster linear sizes follow very closely a lognormal distributionwith a mean characteristic radius of Rc=3.7 pc, and its high radius tail can befitted by a power law as N \propto Rc^(-3.11+-0.35). Additionally, we find thatnumber of members, cluster radius and age follow the relationship Nc \proptoRc^(1.2+-0.1) Tc^(-1.9+-0.4) where the younger and more extensive the cluster,the more members it presents. The proposed method is not sensitive to lowdensity or irregular spatial distributions of stars and, therefore, is a goodalternative or complementary procedure to calculate open cluster radii nothaving previous information on star memberships.

A catalogue of open cluster radii determined from Gaia proper motions