We present and validate a new network of atmospheric thermo-chemical and photo-chemical sulfur reactions. We use a 1-D chemical kinetics model to investigate these reactions as part of a broader HCNO chemical network in a series of hot and warm Jupiters. We find that temperatures approaching $1400K$ are favourable for the production of H2S and HS around $10-3\mathrm{bar}$, the atmospheric level where detection by transit spectroscopy may be possible, leading to mixing ratios of around $10-6$. At lower temperatures, down to $1000K$, the abundance of S2 can be up to a mixing ratio of $10-5$ at the same pressure, at the expense of H2S and HS, which are depleted down to a mixing ratio of $10-6$. We also investigate how the inclusion of sulfur can manifest in an atmosphere indirectly, by its effect on the abundance of non-sulfur-bearing species. We find that in a model of the atmosphere of HD 209458 b, the inclusion of sulfur can lower the abundance of NH3, CH4 and HCN by up to two orders of magnitude around $10-3\mathrm{bar}$. In the atmosphere of the warm Jupiter 51 Eri b, we additionally find the inclusion of sulphur depletes the peak abundance of CO2 by a factor of five, qualitatively consistent with prior models. We note that many of the reactions used in the network have poorly determined rates, especially at higher temperatures. To obtain a truly accurate idea of the impact of sulfur chemistry in hot and warm Jupiter atmospheres, new measurements of these reaction rates must take place.