  Highly twisted magnetic flux ropes, with finite length, are subject to kink
instabilities, and could lead to a number of eruptive phenomena in the solar
atmosphere, including flares, coronal mass ejections (CMEs) and coronal jets.
The kink instability threshold, which is the maximum twist a kink-stable
magnetic flux rope could contain, has been widely studied in analytical models
and numerical simulations, but still needs to be examined by observations. In
this article, we will study twists released by 30 off-limb rotational solar
coronal jets, and compare the observational findings with theoretical kink
instability thresholds. We have found that: 1) the number of events with more
twist release becomes less; 2) each of the studied jets has released a twist
number of at least 1.3 turns (a twist angle of 2.6$\pi$); and 3) the size of a
jet is highly related to its twist pitch instead of twist number. Our results
suggest that the kink instability threshold in the solar atmosphere should not
be a constant. The found lower limit of twist number of 1.3 turns should be
merely a necessary but not a sufficient condition for a finite solar magnetic
flux rope to become kink unstable.
