In this work we improve a previously published method to calculate in a reliable way the radius of an open cluster .
The method is based on the behaviour of stars in the proper motion space as the sampling changes in the position space .
Here we describe the new version of the method and show its performance and robustness .
Additionally , we apply it to a large number of open clusters using data from Gaia DR2 to generate a catalogue of 401 clusters with reliable radius estimations .
The range of obtained apparent radii goes from R _ { c } = 1.4 \pm 0.1 arcmin ( for the cluster FSR 1651 ) to R _ { c } = 25.5 \pm 3.5 arcmin ( for NGC 2437 ) .
Cluster linear sizes follow very closely a lognormal distribution with a mean characteristic radius of R _ { c } = 3.7 pc , and its high radius tail can be fitted by a power law as N \propto R _ { c } ^ { -3.11 \pm 0.35 } .
Additionally , we find that number of members , cluster radius and age follow the relationship N _ { c } \propto R _ { c } ^ { 1.2 \pm 0.1 } \cdot T _ { c } ^ { -1.9 \pm 0.4 } where the younger and more extensive the cluster , the more members it presents .
The proposed method is not sensitive to low density or irregular spatial distributions of stars and , therefore , is a good alternative or complementary procedure to calculate open cluster radii not having previous information on star memberships .