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1813 (MDCCCXIII) was a common year starting on Friday of the Gregorian calendar and a common year starting on Wednesday of the Julian calendar, the 1813th year of the Common Era (CE) and Anno Domini (AD) designations, the 813th year of the 2nd millennium, the 13th year of the 19th century, and the 4th year of the 1810s decade. As of the start of 1813, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.
- April 8 – War of 1812: Colonel James Ball arrives at Fort Meigs, with 200 dragoons.
- April 27 – War of 1812 – Battle of York: United States troops raid, destroy, but do not hold the capital of Upper Canada, York (present day Toronto).
- May 1–May 9 – War of 1812: Fort Meigs is first besieged, by British allied forces under General Henry Proctor and Chief Tecumseh.
- May 2 – Napoleonic Wars – Battle of Lützen: Napoleon wins against the German alliance.
- May 11 –Gregory Blaxland, William Lawson and William Wentworth leave on an expedition, to cross the Blue Mountains (New South Wales) of Australia.
- May 20–May 21 – Napoleonic Wars: Battle of Bautzen: Napoleon again defeats his combined enemies.
- May 27 –War of 1812: In Canada, American forces capture Fort George.
- June 6
- June 21 – Peninsular War – Battle of Vitoria: A British, Spanish, and Portuguese force of 78,000, with 96 guns under Wellington defeats a French force of 58,000, with 153 guns under Joseph Bonaparte.
- October 2 – The Philomathean Society of the University of Pennsylvania is founded (the oldest continuously existing literary society in the United States).
- October 5 – War of 1812 –Battle of the Thames in Upper Canada: William Henry Harrison defeats the British, and native leader Tecumseh is killed in battle.
- October 14 – After a ceremony in Caracas, Venezuela, the municipality gives Simón Bolívar the title of El Libertador.
- October 16–19 – Napoleonic Wars – Battle of Leipzig: Napoleon is defeated by the forces of the Sixth Coalition. More than 600,000 troops are in the field, with well over 10% killed, wounded or missing. Many of the German states forming the Confederation of the Rhine defect from Napoleon to the Coalition, as a result of the battle.
- October 24–November 5 – Persia and Russia sign the Treaty of Gulistan at the end of the Russo-Persian War, by which Persia loses modern-day Georgia, Dagestan and most of Azerbaijan to Russia.
- October 26 – War of 1812 – Battle of the Chateauguay: Charles de Salaberry defeats an American invasion.
- November 11 –War of 1812 – Battle of Crysler's Farm: An outnumbered British–Canadian force repels an American attack, forcing the Americans to give up their attempt to capture Montreal.
- November 21 – An independent government is restored in the Netherlands.
- December 8 – Ludwig van Beethoven's Symphony No. 7, together with his Wellington's Victory, are premiered in Vienna under the composer's baton, in a benefit concert for Austrian and Bavarian soldiers wounded at the Battle of Hanau.
- December 18–19 – War of 1812: British soldiers and native allies invade the United States, and are successful in the Capture of Fort Niagara, and attack Lewiston, New York.
- December 29 – War of 1812: British soldiers burn Buffalo, New York.
- January 19 –Sir Henry Bessemer, English inventor (d. 1898)
- January 21 – John C. Frémont, American soldier, explorer (d. 1890)
- January 26 – Juan Pablo Duarte, founder of the Dominican Republic (d. 1876)
- February 11 – Otto Ludwig, German writer (d. 1865)
- February 12 – James Dwight Dana, American geologist, mineralogist (d. 1895)
- February 15 – Frederick Holbrook, Vermont governor (d. 1909)
- March 14 –Joseph P. Bradley, Associate Justice of the Supreme Court of the United States (d. 1892)
- March 15 –John Snow, English doctor, pioneer of Epidemiology (d. 1858)
- March 16 – Gaëtan de Rochebouët, Prime Minister of France (d. 1899)
- March 18 – Christian Friedrich Hebbel, German poet, playwright (d. 1863)
- March 19 – David Livingstone, Scottish missionary, explorer (d. 1873)
- March 21 – James Strang, Mormon splinter group leader (d. 1856)
- March 27 – Nathaniel Currier, American illustrator (d. 1888)
- April 1 – Karl Friedrich August Rammelsberg, German mineralogist (d. 1899)
- April 19 – David Settle Reid, American politician (d. 1891)
- April 23 – Stephen A. Douglas, American Senator from Illinois, Presidential candidate (d. 1861)
- May 5 – Søren Kierkegaard, Danish philosopher (d. 1855)
- May 15 – Stephen Heller, Hungarian composer (d. 1888)
- May 21 – Robert Murray M'Cheyne, Scottish clergyman (d. 1843)
- May 22 – Richard Wagner, German composer (d. 1883)
- June 2 – Daniel Pollen, 9th Prime Minister of New Zealand (d. 1896)
- June 8 – David Dixon Porter, American admiral (d. 1891)
- June 24 – Henry Ward Beecher, American clergyman, reformer (d. 1887)
- July 15 – George Peter Alexander Healy, American portrait painter (d. 1894)
- July 19 – Samuel M. Kier, American industrialist (d. 1874)
- August 21 – Jean Stas, Belgian chemist (d. 1891)
- August 29 – Henry Bergh, American founder of the American Society for the Prevention of Cruelty to Animals (d. 1888)
- September 17 – John Sedgwick, Union Army General, American Civil War (d. 1864)
- September 24 – Gerardo Barrios, President of El Salvador (d. 1865)
- October 10 – Giuseppe Verdi, Italian composer (d. 1901)
- October 17 – Georg Büchner, German playwright (d. 1837)
- November 13
- November 19 – Augusta Schrumpf, Norwegian actor (d. 1900)
- November 30 – Charles-Valentin Alkan, French composer (d. 1888)
- December 19 – Thomas Andrews, Irish chemist (d.1885)
- January 6 –Louis Baraguey d'Hilliers, French general (b. 1764)
- January 15 –Anton Bernolák, Slovak linguist (b. 1762)
- January 20 –Christoph Martin Wieland, German writer (b. 1733)
- January 24 –George Clymer, American signer of the Declaration of Independence (b. 1739)
- February 13 –Samuel Ashe, Governor of North Carolina (b. 1725)
- February 26 –Robert Livingston, American signer of the Declaration of Independence (b. 1746)
- April 10 –Joseph-Louis Lagrange, Italian mathematician (b. 1736)
- April 19 – Benjamin Rush, Founding Father of the United States (b. 1746)
- April 27 –Zebulon Pike, American general (b. 1779)
- April 28 –Mikhail Kutuzov, Russian field marshal (b. 1745)
- April 29 –John Andrews, American clergyman, Provost of the University of Pennsylvania, considered America's first scholar (b. 1746)
- May 1 –Jean-Baptiste Bessières, French marshal (killed in combat) (b. 1768)
- May 23 –Géraud Duroc, French general (mortally wounded in battle) (b. 1772)
- June –Wossen Seged, Meridazmach of Shewa (murdered) (b. 1808)
- June 6
- June 17 –Charles Middleton, 1st Baron Barham, English sailor, politician (b. 1726)
- July 17 – Fredrica Löf, Swedish actress (b. 1760)
- June 28 –Gerhard von Scharnhorst, Prussian general (b. 1755)
- July 29 –Jean-Andoche Junot, French general (suicide) (b. 1771)
- August 11 –Henry James Pye, English poet (b. 1745)
- August 15 –Abigail Amelia, First born daughter of John and Abigail Adams (b. 1765)
- August 23 –Alexander Wilson, Scottish-born ornithologist (b. 1766)
- August 26 – Theodor Körner, German author, soldier (b. 1791)
- September 2 – Jean Victor Marie Moreau, French general (mortally wounded in battle) (b. 1763)
- September 13 – Hezqeyas, deposed Emperor of Ethiopia
- September 15 – Antoine Étienne de Tousard, French general, military engineer (b. 1752)
- September 22 – Rose Bertin, French fashion designer (b. 1747)
- October 5 – Tecumseh, Native American (Shawnee) leader (b. 1768)
- October 19 – Józef Poniatowski, Polish prince, Marshal of France (friendly fire) (b. 1763)
- November 12 – Jean de Crèvecœur, French-American writer (b. 1735)
- November –William Franklin, son of Benjamin Franklin (b. ca. 1730)
- December 24 – Empress Go-Sakuramachi of Japan (b. 1740)
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