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The capital ships of a navy are its most important warships; they are generally the larger ships when compared to other warships in their respective fleet. A capital ship is generally a leading or a primary ship in a naval fleet. 
There is usually no formal criterion for the classification, but it is a useful concept in naval strategy; for example, it permits comparisons between relative naval strengths in a theatre of operations without the need for considering specific details of tonnage or gun diameters.
A notable example of this is the Mahanian doctrine, which was applied in the planning of the defence of Singapore in World War II, where the Royal Navy had to decide the allocation of its battleships and battlecruisers between the Atlantic and Pacific theatres. The Mahanian doctrine was also applied by the Imperial Japanese Navy, leading to its preventive move to attack Pearl Harbor and the battleships of the U.S. Pacific Fleet.  The naval nature of the Pacific Theater of Operations, more commonly referred to as the Pacific War, necessitated the United States Navy mostly deploying its battleships and aircraft carriers in the Pacific. The war in Europe was primarily a land war; consequently, Germany's surface fleet was small, and the escort ships used in the Battle of the Atlantic were mostly destroyers and destroyer escorts to counter the U-boat threat.
Before the advent of the all-steel navy in the late 19th century, a capital ship during the Age of Sail was generally understood as a ship that conformed to the Royal Navy's rating system of a ship of the line as being of the first, second, third or fourth rates:
Frigates were ships of the fifth rate; sixth rates comprised small frigates and corvettes. Towards the end of the Napoleonic Wars and into the late 19th century, some larger and more powerful frigates were classified as fourth rates.
The term "capital ship" was first coined in 1909 and formally defined in the limitation treaties of the 1920s and 1930s in the Washington Naval Treaty, London Naval Treaty, and Second London Naval Treaty. This applied mainly to ships resulting from the dreadnought revolution; dreadnought battleships (also known first as dreadnoughts and later as battleships) and battlecruisers. 
In the 20th century, especially in World Wars I and II, typical capital ships would be battleships and battlecruisers. All of the above ships were close to 20,000 tons displacement or heavier, with large caliber guns and heavy armor protection.
Cruisers, despite being important ships, were not considered capital ships. An exception to the above in World War II was the Deutschland-classcruiser. Though this class was technically similar to a heavy cruiser, albeit slower but with considerably heavier guns, they were regarded by some as capital ships (hence the British label "Pocket battleship") since they were one of the few heavy surface units of the Kriegsmarine. The American Alaska-classcruiser, Dutch Design 1047 battlecruiser and the Japanese Design B-65 cruiser, planned specifically to counter the heavy cruisers being built by their naval rivals, have been described as "super cruisers", "large cruisers" or even "unrestricted cruisers", with some advocating that they even be considered as battlecruisers, however they were never classified as capital ships. 
During the Cold War, a Soviet Kirov-class large missile cruiser had a displacement great enough to rival World War II-era battleships and battlecruisers, perhaps defining a new capital ship for that era. In regard to technical design, however, the Kirov is simply a supersized guided-missile cruiser with nuclear propulsion.
It took until late 1942 for aircraft carriers to be universally considered capital ships. Only full-size fleet carriers (whether purpose built, or converted from battleship/battlecruiser hulls) were regarded as capital ships, while light carriers (often using cruiser hulls) and escort carriers (often using merchant ship hulls) were not. The U.S. Navy was forced    to rely primarily on its aircraft carriers after the attack on Pearl Harbor sank or damaged eight of its Pacific-fleet battleships.
In the 21st century, the aircraft carrier is the last remaining capital ship, with capability defined in decks available and aircraft per deck rather than in guns and calibers. The United States possesses supremacy in both contemporary categories of aircraft carriers, possessing 11 active duty supercarriers each capable of carrying and launching nearly 100 tactical aircraft, and nine amphibious assault ships which are equivalent in the "Sea Control Ship" configuration to the light VSTOL carriers operated by other nations. 
Ballistic missile submarines (or "boomers"), while important ships and similar in tonnage to early battleships, are usually counted as part of a nation's nuclear deterrent force and do not share the sea control mission of traditional capital ships. Nevertheless, many navies, including the Royal Navy and the United States Navy, consider these ships to be capital ships and have given some of them names previously used for battleships, e.g. Dreadnought and Vanguard.
Some navies reserve specific names for their capital ships. Names reserved for capital ships include chiefs of state (e.g. Bismarck), important places, historically important naval officers or admiralty (e.g. De Ruyter), historical events or objects (e.g. USS Constitution), and traditional names (e.g. HMS Ark Royal). However, there are some exceptions to the rule.
Beginning with USS Texas (the first U.S. battleship), U.S. capital ships were traditionally named after U.S. states. [lower-alpha 1] Cruisers are typically named after U.S. territories (e.g. Alaska-class cruisers just before and during World War II) or U.S. cities. Prior to and during World War II, the Imperial Japanese Navy also followed the practice of naming battleships after provinces (e.g. Yamato).
Despite their significance to modern fleets, the U.S. Navy has never named aircraft carriers after U.S. states. Today, U.S. aircraft carriers are usually named after politicians and other individuals notable in US naval history such as Gerald R. Ford and Chester W. Nimitz except Enterprise.
Beginning with the first class of Trident-equipped ballistic missile submarines (i.e. the Ohioclass), state names have been applied to U.S. nuclear submarines. Previous ballistic missile submarines (e.g. Poseidon missile-equipped submarines) had not been named for states. After the completion of the last Ohio-class ballistic missile submarine, state names were also applied to attack submarines (e.g. Virginiaclass). Earlier attack submarines had usually been named for marine animals or, commencing with the Los Angelesclass, cities and towns.
A battleship is a large armored warship with a main battery consisting of large caliber guns. It dominated naval warfare in the late 19th and early 20th centuries.
The battlecruiser was a type of capital ship of the first half of the 20th century. These were similar in displacement, armament and cost to battleships, but differed in form and balance of attributes. Battlecruisers typically had thinner armour and a somewhat lighter main gun battery than contemporary battleships, installed on a longer hull with much higher engine power in order to attain greater speeds. The first battlecruisers were designed in the United Kingdom, as a development of the armoured cruiser, at the same time as the dreadnought succeeded the pre-dreadnought battleship. The goal of the design was to outrun any ship with similar armament, and chase down any ship with lesser armament; they were intended to hunt down slower, older armoured cruisers and destroy them with heavy gunfire while avoiding combat with the more powerful but slower battleships. However, as more and more battlecruisers were built, they were increasingly used alongside the better-protected battleships.
A cruiser is a type of warship. Modern cruisers are generally the largest ships in a fleet after aircraft carriers and amphibious assault ships, and can usually perform several roles.
The Washington Naval Treaty, also known as the Five-Power Treaty, was a treaty signed during 1922 among the major Allies of World War I, which agreed to prevent an arms race by limiting naval construction. It was negotiated at the Washington Naval Conference, held in Washington, D.C., from November 1921 to February 1922, and it was signed by the governments of Great Britain, the United States, France, Italy, and Japan. It limited the construction of battleships, battlecruisers and aircraft carriers by the signatories. The numbers of other categories of warships, including cruisers, destroyers, and submarines, were not limited by the treaty, but those ships were limited to 10,000 tons displacement each.
A warship or combatant ship is a naval ship that is built and primarily intended for naval warfare. Usually they belong to the armed forces of a state. As well as being armed, warships are designed to withstand damage and are usually faster and more maneuverable than merchant ships. Unlike a merchant ship, which carries cargo, a warship typically carries only weapons, ammunition and supplies for its crew. Warships usually belong to a navy, though they have also been operated by individuals, cooperatives and corporations.
The Alaska class were six very large cruisers ordered before World War II for the United States Navy, of which only two were completed and saw service late in the war. The US Navy designation for the ships of this class was 'large cruiser' (CB) and the majority of leading reference works consider them as such. However, various other works have alternately described these ships as battlecruisers despite the US Navy having never classified them as such. The Alaskas were all named after territories or insular areas of the United States, signifying their intermediate status between larger battleships and smaller heavy and light cruisers.
Haruna (榛名) was a warship of the Imperial Japanese Navy during World War I and World War II. Designed by the British naval engineer George Thurston and named after Mount Haruna, she was the fourth and last battlecruiser of the Kongō class, amongst the most heavily armed ships in any navy when built. Laid down in 1912 at the Kawasaki Shipyards in Kobe, Haruna was formally commissioned in 1915 on the same day as her sister ship, Kirishima. Haruna patrolled off the Chinese coast during World War I. During gunnery drills in 1920, an explosion destroyed one of her guns, damaged the gun turret, and killed seven men.
The Soviet Navy was the naval warfare uniform service branch of the Soviet Armed Forces. Often referred to as the Red Fleet, the Soviet Navy made up a large part of the Soviet Union's strategic planning in the event of a conflict with the opposing superpower, the United States, during the Cold War (1945-1991). The Soviet Navy played a large role during the Cold War, either confronting the North Atlantic Treaty Organization in western Europe or power projection to maintain its sphere of influence in eastern Europe.
Yokosuka Naval Arsenal was one of four principal naval shipyards owned and operated by the Imperial Japanese Navy, and was located at Yokosuka, Kanagawa prefecture on Tokyo Bay, south of Yokohama.
The names of commissioned ships of the United States Navy all start with USS, for United States Ship. Non-commissioned, primarily civilian-crewed vessels of the U.S. Navy under the Military Sealift Command have names that begin with USNS, standing for United States Naval Ship. A letter-based hull classification symbol is used to designate a vessel's type. The names of ships are selected by the Secretary of the Navy. The names are those of states, cities, towns, important persons, important locations, famous battles, fish, and ideals. Usually, different types of ships have names originated from different types of sources.
United States ship naming conventions for the U.S. Navy were established by congressional action at least as early as 1862. Title 13, section 1531, of the U.S. Code, enacted in that year, reads, in part,
The vessels of the Navy shall be named by the Secretary of the Navy under direction of the President according to the following rule: Sailing-vessels of the first class shall be named after the States of the Union, those of the second class after the rivers, those of the third class after the principal cities and towns and those of the fourth class as the President may direct.
World War II saw the end of the battleship as the dominant force in the world's navies. At the outbreak of the war, large fleets of battleships—many inherited from the dreadnought era decades before—were one of the decisive forces in naval thinking. By the end of the war, battleship construction was all but halted, and almost every remaining battleship was retired or scrapped within a few years of its end.
The Amagi class was a series of four battlecruisers planned for the Imperial Japanese Navy (IJN) as part of the Eight-eight fleet in the early 1920s. The ships were to be named Amagi, Akagi, Atago, and Takao. The Amagi design was essentially a lengthened version of the Tosa-class battleship, but with a thinner armored belt and deck, a more powerful propulsion system, and a modified secondary armament arrangement. They were to have carried the same main battery of ten 41 cm (16.1 in) guns and been capable of a top speed of 30 knots.
The Lexington-class battlecruisers were officially the only class of battlecruiser to ever be ordered by the United States Navy. While these six vessels were requested in 1911 as a reaction to the building by Japan of the Kongō class, the potential use for them in the U.S. Navy came from a series of studies by the Naval War College which stretched over several years and predated the existence of the first battlecruiser, HMS Invincible. The fact they were not approved by Congress at the time of their initial request was due to political, not military considerations.