Largest naval battle in history

The title of "largest naval battle in history" is disputed between adherents of criteria which include the numbers of personnel and/or vessels involved in the battle, and the total tonnage of the vessels involved. While battles fought in modern times are comparatively well-documented, the figures from those in pre-Renaissance times are generally believed to be exaggerated by contemporary chroniclers.

The candidates

 * Salamis, September (28?) 480 BC. 371 Greek ships defeated 300-600 Persian ships in this decisive battle. Greek triremes had a crew of about 200 while their small penteconters had 50 oarsmen, which would suggest that approximately 200,000 sailors, soldiers and marines took part.
 * Red Cliffs, winter AD 208. A decisive naval engagement between forces of Cao Cao and the allied forces of Liu Bei and Sun Quan resulted in the defeat of Cao Cao and confirmed the separation between southern China and northern China along the Yangtze River Valley. Between 270,000 and 310,000 soldiers participated in the engagement.
 * Yamen, fought March 19, 1279; saw the fall of the Song empire during the conquest of China by the Yuan Dynasty of Mongolia.
 * Lepanto, 7 October 1571. 212 Holy League galleys and galleasses against 272 or more Ottoman galleys, galliots etc. (484+ total). The forces of the Holy League inflicted a crushing defeat on the Ottoman fleet. This was the last major naval battle in the Western world to be fought entirely or almost entirely between rowing vessels, and one of the earliest for which there is a reliable count of ships and personnel involved.  Around 150,000 personnel took part in the battle. The Turkish fleet lost more than 200 vessels and suffered at least 20,000 casualties.
 * Jutland, May 31–June 1, 1916. The largest battle in terms of tonnage of ships engaged and in terms of the total tonnage of ships involved in a single action. The largest surface action and the largest ship-to-ship action, in terms of the tonnage of the ships engaged.  The Imperial German Navy's High Seas Fleet commanded by Vice-Admiral Reinhard Scheer, consisting of 16 dreadnought and 5 pre-dreadnought battleships, 5 battle cruisers, 11 light cruisers, and 61 fleet torpedo boats, was engaged by the numerically superior British Grand Fleet under Admiral Sir John Jellicoe, composed of 28 battleships, 9 battle cruisers, 8 armoured cruisers, 28 light cruisers and 78 destroyers. Material losses were heavier on the British side, but the High Seas Fleet only narrowly escaped destruction and never again risked a decisive encounter with the Grand Fleet.
 * Philippine Sea, June 19–20, 1944. The largest aircraft carrier battle in history, the largest single naval battle of World War II, and arguably the largest in history, involving 15 US fleet and light carriers, nine Japanese carriers, 170 other warships and some 1,700 aircraft. The US Fifth Fleet's Task Force 58 is (in terms of tonnage) the largest single naval formation ever to give battle.
 * Leyte Gulf, October 23–26, 1944. The largest in terms of tonnage of ships in the combined orders of battle, if not necessarily in terms of tonnage of the ships engaged. Also the largest in terms of the tonnage of ships sunk, and in terms of the size of the area within which the component battles took place. The United States 3rd and 7th Fleets, including some Australian warships, comprised 8 large aircraft carriers, 8 light carriers, 18 escort carriers, 12 battleships, 24 cruisers, 141 destroyers and destroyer escorts, many other ships, and around 1,500 aircraft. They won a decisive victory over Japanese forces, which consisted of four aircraft carriers, nine battleships, 19 cruisers, 34 destroyers and several hundred aircraft. The opposing fleets carried a total of about 200,000 men. Leyte Gulf consisted of four major subsidiary battles: Battle of Sibuyan Sea, Battle of Surigao Strait, Battle off Samar and Battle of Cape Engano, along with other actions. These are counted together by virtue of their all being caused by the Japanese operation Sho-Go, which was aimed at destroying the Allied amphibious forces involved in the invasion of Leyte. However, the individual battles were separated by distances as great as two hundred miles.