It is well known that, given a ring R, if M is an R-module such that pdR (M)<∞, then GidR (M)= idR (M)(Holm, 2004). This shows in particular that if R is a Noetherian ring such that Gid (R)<∞, then R is Gorenstein. Dually, if M is an R-module such that idR (M)<∞, then GpdR (M)= pdR (M)(Holm, 2004). Regarding the Gorenstein flat dimension, there have been no appropriate analogs of these two theorems. The unique result, in this vein, states, under the strong hypothesis of R being a left and right coherent ring with finite right finitistic projective dimension, that GfdR (M)= fdR (M) for any R-module M such that idR (M)<∞(Holm, 2004). We give the appropriate analogs of the above two formulas for the Gorenstein flat dimension. Actually, in the general setting, we prove that if M is an R-module admitting a short flat resolution 0→ K→ Fn− 1→ Fn− 2→···→ F0→ M→ 0 such that K is Gorenstein flat and fdR (M+)<∞, then K is flat and GfdR (M)= fdR (M), where A+ stands for the Pontryagin dual HomZ (A, Q/Z) of a module A. This implies, in particular, that if R is a left GF-closed ring, then GfdR (M)= fdR (M) for any R-module M such that fdR (M+)<∞. Dually, we prove that if R is left GF-closed, then GfdR (N+)= fdR (N+) for any R-module N such that fdR (N)<∞.