  The Ptolemy coordinates for boundary-unipotent SL(n,C)-representations of a
3-manifold group were introduced in Garoufalidis-Thurston-Zickert inspired by
the A-coordinates on higher Teichm\"{u}ller space due to Fock and Goncharov. In
this paper, we define the Ptolemy field of a (generic) PSL(2,\C)-representation
and prove that it coincides with the trace field of the representation. This
gives an efficient algorithm to compute the trace field of a cusped hyperbolic
manifold.
