The United States Navy during the War of 1812 was just starting out, a relatively young Naval force made up of frigates consisting only of 22 commissioned vessels. By contrast the British Royal Navy had nearly 85 vessels in American Waters in the months before actual war broke out. The Standard British Warship had 38 mounted guns and other large guns including huge 18-pound cannon.
While the American Warships were out manned in numbers, they made up for it in Firepower. The American warships of the era, the USS United States, the USS President, and the USS Constitution were ships that carried 44 guns apiece, and their main guns were larger than the British typical Frigate firepower, with 24-pound cannon.
In early fighting, the three American Warships, along with the other 19 vessels in the American Fleet were surprisingly successful in their early matchups with British Warships. Their successful use caused Great Britain to immediately commission five new warships; each with 40 guns and each of the guns were the newer, heavier 24-pound cannon similar to the American Cannon. Britain was attempting to protect its ships to and from Halifax and Canada, and to try and disrupt the Americans with an Atlantic blockade. While the Atlantic blockade was for the most part successful, the American efforts spurred the British to pour more ships and men into the action. Despite superior numbers, the American Navy ships were successful because of their greater physical size and for the most part heavier cannon and guns.
This War was the first testing of the new American Nation, and while it was never a clear victory on either side, the willingness of the American Navy to fight to the last man, where necessary, convinced an increasingly war weary Britain to sue for peace. The American Coastline had been largely blockaded, but was still breached at regular intervals by an increasingly successful U.S. Navy effort. The war became a milestone around the necks of British Citizens, causing a slowdown of their economy and a huge expense to keep the blockade going. Finally in December 1814, on Christmas Eve representatives met in Ghent, Belgium (was then United Kingdom of the Netherlands) and signed the Treaty of Ghent. The American Congress later ratified it on February 16th, 1815. Only because of the willingness of American Forces, both Army and U.S. Navy had led to the willingness of the United Kingdom to settle for Peace.