The interstitial chemical impurities hydrogen, oxygen, nitrogen, and carbon are important for niobium metal production and particularly for the optimization of niobium SRF technology. These atoms are present in refined sheets and can be absorbed into niobium during processing treatments, resulting in changes to the residual resistance and the performance of SRF cavities. A first-principles approach is taken to study the properties of carbon in niobium, and the results are compared and contrasted with the properties of the other interstitial impurities. The results indicate that C will likely form precipitates or atmospheres around defects rather than strongly bound complexes with other impurities. On the basis of the analysis of carbon and hydrogen near niobium lattice vacancies and small vacancy chains and clusters, the formation of extended carbon chains and hydrocarbons is not likely to occur. Association of carbon with hydrogen atoms can, however, occur through the strain fields created by interstitial binding of the impurity atoms. Calculated electronic densities of states indicate that interstitial C may have a similar effect as interstitial O on the superconducting transition temperature of Nb.