  We give an explicit formula for the $L^2$ analytic torsion of the finite
metric cone over an oriented compact connected Riemannian manifold. We provide
an interpretation of the different factors appearing in this formula. We prove
that the analytic torsion of the cone is the finite part of the limit obtained
collapsing one of the boundaries, of the ratio of the analytic torsion of the
frustum to a regularising factor. We show that the regularising factor comes
from the set of the non square integrable eigenfunctions of the Laplace
Beltrami operator on the cone.
