  In this paper we will give a computation of the \'{e}tale fundamental group
of an integral arithmetic scheme. For such a scheme, we will prove that the
\'{e}tale fundamental group is naturally isomorphic to the Galois group of the
maximal formally unramified extension over the function field. It consists of
the main theorem of the paper. Here, formally unramified will be proved to be
arithmetically unramified which is defined in an evident manner and coincides
with that in algebraic number theory. Hence, formally unramified has an
arithmetic sense. At the same time, such a computation coincides with the known
result for a normal noetherian scheme.
