Like all Type XXI U-boats, U-2513 had a displacement of when at the surface and while submerged. She had a total length of , a beam length of, and a draught length of. The submarine was powered by two MAN SE supercharged six-cylinder M6V40/46KBB diesel engines each providing, two Siemens-Schuckert GU365/30 double-acting electric motors each providing, and two Siemens-Schuckert silent running GV232/28 electric motors each providing. The submarine had a maximum surface speed of and a submerged speed of. When running on silent motors the boat could operate at a speed of. When submerged, the boat could operate at for ; when surfaced, she could travel at. U-2513 was fitted with six torpedo tubes in the bow and four C/30 anti-aircraft guns. She could carry twenty-three torpedoes or seventeen torpedoes and twelve mines. The complement was five officers and fifty-two men.
A year later, August 1946, U-2513 began an extensive overhaul in Charleston, South Carolina, which was completed late in September. On 24 September, she departed Charleston and headed for Key West, Florida. The following day, she began six months of duty which included both evaluation tests of the U-boat's design and duty in conjunction with the development of submarine and antisubmarine tactics. The Greater Underwater Propulsion Power Program would be initiated because of the results of these tests. On 21 November 1946 President Harry S. Truman became the second American President to travel on a submarine when he visited U-2513. The sub went below the surface with the President on board, and a demonstration was made to him of the German schnorchel. On 15 March 1947, U-2513 headed north from Key West, Florida, bound for the New England coast, and arrived at Portsmouth, New Hampshire, on 22 March. She remained there until 8 September when she began six weeks of operations out of Portsmouth and New London, Connecticut, under the auspices of the Commander, Submarines, Atlantic Fleet. She concluded that duty on 15 October and departed New London to return to Key West. U-2513 resumed her old duties at Key West five days later and continued them until the summer of 1949. In mid-June 1949, the submarine moved from Key West, Florida, north via Norfolk, Virginia, to Portsmouth, New Hampshire, where she was placed out of service in July 1949. She remained at Portsmouth until August 1951 at which time she returned to Key West. On 2 September 1951, the Chief of Naval Operations ordered that the boat be sunk by gunfire. U-2513 was sunk west of Key West, Florida during rocket tests by the destroyer on 7 October 1951. The final resting place of U-2513 is about 23 miles northeast of the Dry Tortugas in about of water at. She is reachable only by divers experienced in decompression diving at that depth. The site is rarely dived on due to its depth and remote location.
