James F. Calvert was born and raised in Cleveland. He attended Oberlin College for two years before receiving an appointment to the United States Naval Academy. He graduated in 1942 and was assigned to attend the Naval Submarine School at the Naval Submarine Base New London. After graduating, he served for three years on the submarine USS Jack. In 1945 he was assigned to serve as executive officer of the USS Haddo (SS-255). After World War II, he was an instructor in the Torpedo Data Computer at the Submarine School. He was then assigned to serve as executive officer on the USS Charr (SS-328), the USS Harder (SS-568), and the USS Trigger (SS-564). After training by the Atomic Energy Commission, Calvert was assigned to the nuclear-powered USS Skate (SSN-578), which became the first submarine to surface at the North Pole in 1958.

Calvert rose to vice admiral and in 1968 he named as superintendent of the United States Naval Academy.

He wrote four books he wrote, including Silent Running: My Years on a World War II Attack Submarine, and Surface at the Pole: The Extraordinary Voyages of the U.S.S. Skate.