  We study the number of elements $x$ and $y$ of a finite group $G$ such that
$x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$
of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and
has connection with the exterior degree, introduced few years ago in [P.
Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra
39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor
degree allows us to find interesting structural restrictions for the whole
group.
