We report the measurement of cumulants (C-n,n = 1, ..., 4) of the net-charge distributions measured within pseudorapidity (vertical bar eta vertical bar < 0.35) in Au + Au collisions at root s(NN) = 7.7-200 GeV with the PHENIX experiment at the Relativistic Heavy Ion Collider. The ratios of cumulants (e.g., C-1/C-2, C-3/C-1) of the net-charge distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of C-1/C-2 and C-3/C-1 can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy. The extracted baryon chemical potentials are in excellent agreement with a thermal-statistical analysis model.