Spatial information from stellar X-ray coronae can not be assessed directly , but scaling laws from the solar corona make it possible to estimate sizes of stellar coronae from the physical parameters temperature and density . While coronal plasma temperatures have long been available , we concentrate on the newly available density measurements from line fluxes of X-ray lines measured for a large sample of stellar coronae with the Chandra and XMM-Newton gratings . We compiled a set of 64 grating spectra of 42 stellar coronae . Line counts of strong H-like and He-like ions and Fe xxi lines were measured with the CORA single-purpose line fitting tool by ( ) . Densities are estimated from He-like f/i flux ratios of O vii and Ne ix representing the cooler ( 1-6 MK ) plasma components . The densities scatter between \log n _ { e } \approx 9.5 - 11 from the O vii triplet and between \log n _ { e } \approx 10.5 - 12 from the Ne ix triplet , but we caution that the latter triplet may be biased by contamination from Fe xix and Fe xxi lines . We find that low-activity stars ( as parameterized by the characteristic temperature derived from H- and He-like line flux ratios ) tend to show densities derived from O vii of no more than a few times 10 ^ { 10 } cm ^ { -3 } , whereas no definitive trend is found for the more active stars . Investigating the densities of the hotter plasma with various Fe xxi line ratios , we found that none of the spectra consistently indicates the presence of very high densities . We argue that our measurements are compatible with the low-density limit for the respective ratios ( \approx 5 \times 10 ^ { 12 } cm ^ { -3 } ) . These upper limits are in line with constant pressure in the emitting active regions . We focus on the commonly used ( ) scaling law to derive loop lengths from temperatures and densities assuming loop-like structures as identical building blocks . We derive the emitting volumes from direct measurements of ion-specific emission measures and densities . Available volumes are calculated from the loop-lengths and stellar radii , and are compared with the emitting volumes to infer filling factors . For all stages of activity we find similar filling factors up to 0.1 .