In a method of making a carbon fiber, PAN (poly(acrylonitrile-co methacrylic acid)) is dissolved into a solvent to form a PAN solution. The PAN solution is extruded through a spinneret, thereby generating at least one precursor fiber. The precursor fiber is passed through a cold gelation medium, thereby causing the precursor fiber to gel. The precursor fiber is drawn to a predetermined draw ratio. The precursor fiber is continuously stabilized to form a stabilized fiber. The stabilized fiber is continuously carbonized thereby generating the carbon fiber. The carbon fiber is wound onto a spool. A carbon fiber has a fiber tensile strength in a range of 5.5 GPa to 5.83 GPa. The carbon fiber has a fiber tensile modulus in a range of 350 GPa to 375 GPa. The carbon fiber also has an effective diameter in a range of 5.1 μm to 5.2 μm.