  Carbon nanotubes tend to collapse when their diameters exceed a certain
threshold, or when a sufficiently large external pressure is applied on their
walls. Their radial stability of tubes has been studied in each of these cases,
however a general theory able to predict collapse is still lacking. Here, we
propose a simple model predicting stability limits as a function of the tube
diameter, the number of walls and the pressure. The model is supported by
atomistic simulations, experiments, and is used to plot collapse phase
diagrams. We have identified the most stable carbon nanotube, which can support
a maximum pressure of 18 GPa before collapsing. The latter was identified as a
multiwall tube with an internal tube diameter of 12nm and 30 walls. This
maximum pressure is lowered depending on the internal tube diameter and the
number of walls. We then identify a tube diameter domain in which the radial
mechanical stability can be treated as equivalent to macroscopic tubes, known
to be described by the canonical L\'evy-Carrier law. This multiscale behavior
is shown to be in good agreement with experiments based on O-ring gaskets
collapse, proposed as a simple macroscopic parallel to nanotubes in this
domain.
