The pK(a)'s of substituted thiols are important for understanding their properties and reactivities in applications in chemistry, biochemistry, and material chemistry. For a collection of 175 different density functionals and the SMD implicit solvation model, the average errors in the calculated pK(a)'s of methanethiol and ethanethiol are almost 10 pK(a) units higher than for imidazole. A test set of 45 substituted thiols with pK(a)'s ranging from 4 to 12 has been used to assess the performance of 8 functionals with 3 different basis sets. As a expected, the basis set needs to include polarization functions on the hydrogens and diffuse functions on the heavy atoms. Solvent cavity scaling was ineffective in correcting the errors in the calculated pK(a)'s. Inclusion of an explicit water molecule that is hydrogen bonded with the H of the thiol group (in neutral) or S- (in thiolates) lowers error by an average of 3.5 pK(a) units. With one explicit water and the SMD solvation model, pK(a)'s calculated with the M06-2X, PBEPBE, BP86, and LC-BLYP functionals are found to deviate from the experimental values by about 1.5-2.0 pK(a) units whereas pK(a)'s with the B3LYP, omega B97XD and PBEVWN5 functionals are still in error by more than 3 pK(a) units. The inclusion of three explicit water molecules lowers the calculated pK(a) further by about 4.5 pK(a) units. With the B3LYP and omega B97XD functionals, the calculated pK(a)'s are within one unit of the experimental values whereas most other functionals used in this study underestimate the RTC's. This study shows that the omega B97XD functional with the 6-31+G(d,p) and 6-311++G(d,p) basis sets, and the SMD solvation model with three explicit water molecules hydrogen bonded to the sulfur produces the best result for the test set (average error 0.11 +/- 0.50 and +0.15 +/- 0.58, respectively). The B3LYP functional also performs well (average error -1.11 +/- 0.82 and -0.78 +/- 0.79, respectively).