A method of producing carbon fiber, yarns, and nonwoven carbon fiber cloths, includes forming suitable polymeric precursor microfibers and/or nanofibers using a centrifugal spinning process and decomposing at least a portion of the polymeric precursor fibers to form carbon fibers. The decomposition may be accomplished by treating the polymeric precursor fibers with acid vapor from an aqueous acid solution at a temperature of less than 250° C.