We investigate the gravitational fragmentation in expanding shells by applying an instability ’thermometer’ similar to the Toomre parameter for instabilities in self-gravitating disks. For Sedov–like evolving systems the onset of instability is mainly depending on the density of the ambient medium and the sound speed of the shell matter, whereas the energy injection rate is less important. Shells evolve towards gravitational instability, if the density gradient of the ambient medium is shallower than an isothermal profile, otherwise they become more stable. For density gradients flatter than ∝ r−1, the fragmentation becomes non-linear on the same time scale as the gravitational instability needs to start. In a homogeneous ambient medium the typical size of gravitationally unstable shells is 1 kpc for a gas density of n = 1 cm−3 and decreases to 10 pc for n = 104 cm−3.