  The reach of a set $M \subset \mathbb R^d$, also known as condition number
when $M$ is a manifold, was introduced by Federer in 1959. The reach is a
central concept in geometric measure theory, set estimation, manifold learning,
among others areas.
  We introduce a universally consistent estimate of the reach, just assuming
that the reach is positive. Under an additional assumption we provide rates of
convergence. We also show that it is not possible to determine, based on a
finite sample, if the reach of the support of a density is zero or not. We
provide a small simulation study and a bias correction method for the case when
$M$ is a manifold.
