Disclosed are carbon fibers consisting of a plurality of single filaments, wherein the carbon fibers as a resin impregnated strand are characterized by satisfying the following relations: &sgr;≧11.1-0.75d where &sgr; is the tensile strength of said carbon fibers as a resin impregnated strand in GPa, and d is the average diameter of said single filaments in &mgr;m, and RD≧0.05 where RD is the difference in crystallinity between the inner and outer layers of each of the single filaments evaluated with RAMAN, and an acrylic fibers for producing the carbon fibers and a process for producing the acrylic fibers.