For a totally complex number field \(k\), let \(d_ k\) denote the absolute value of the discriminant of \(k\). Let \({\mathcal O}_ k\) denote the ring of algebraic integers of \(k\), \(E_ k\) the group of units of \({\mathcal O}_ k\), \(\text{Cl}(k)\) the class group of \({\mathcal O}_ K\). Let \(I\) be an ideal of \({\mathcal O}_ k\) and \(k_ I\) the ray class field of \(k\) with conductor \(I\). Let \({\mathcal O}_ k\to {\mathcal O}_ k/I\) denote the natural projection. \(E_ k\) will be mapped into \(\text{Im}(E_ k)\). Then the relative degree \(k_ I=[k_ I:k]\) is equal to \[ h_ I=\#\bigl(({\mathcal O}_ k/I)^ \times /\text{Im}(E_ k)\bigr)\cdot \#\text{cl}(k). \] The authors use this well-known formula to find number fields with relatively small discriminants.