Let \(k\) be a global field and \(G\) a semisimple algebraic group defined over \(k\). Let S be a finite set of places of \(k\) containing the archimedean ones. For \(G\) simply connected and absolutely quasi-simple a formula is given for the volume of \(G(k_S)/\Lambda\), where \(\Lambda\) is an \(S\)-arithmetic subgroup of \(G(k)\). The derivation of this formula is possible thanks to the theory of reductive groups over local fields of Bruhat and Tits. The same computations give a bound for class numbers.