|Covid-19|January 24 – The Philharmonic Society founded in London (later the Royal Philharmonic Society).
January 28 – Jane Austen's Pride and Prejudice is published anonymously in London.
January 31 – The Assembly of the Year XIII is inaugurated in Buenos Aires.
February – General Harrison sends out an expedition to burn the British vessels at Fort Malden by going across Lake Erie via the Bass Islands in sleighs, but the ice is not hard enough and the expedition returns.
February 3 – Argentine War of Independence: José de San Martín and his Regiment of Mounted Grenadiers gain a largely symbolic victory against a Spanish royalist army in the Battle of San Lorenzo.
February 7 – Napoleonic Wars: Action of 7 February 1813 between the French frigate Aréthuse (1812) and HMS Amelia (1796) in British service in the Îles de Los on the Guinea Coast; both ships retire unbeaten.
February 9 – Prussia abolishes the canton system
February 11 – War of 1812: Construction of Fort Meigs in Ohio under the command of General William Henry Harrison begins. Major Amos Stoddard assumes command of its artillery.
Cyril VI of Constantinople is elected Ecumenical Patriarch.
James Madison is sworn in for a second term as President of the United States.
March 17 – Napoleonic Wars: Prussia declares war on France.
March 29 – Mexican War of Independence –Battle of Rosillo Creek: The Republican Army of the North defeats the Spanish Royalist Army in present-day Bexar County, Texas.
April 8 – 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 – First siege of Fort Meigs by British allied forces under General Henry Proctor and Chief Tecumseh.
May 2 –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 –Battle of Bautzen: Napoleon again defeats his combined enemies.
May 27 –War of 1812: In Canada, American forces capture Fort George.
War of 1812 –Battle of Stoney Creek: A British force of 700 under John Vincent defeat an American force three times its size under William Winder and John Chandler.
Gregory Blaxland, William Lawson and William Wentworth succeed in crossing the Blue Mountains and return home.
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.
July –War of 1812 –Second siege of Fort Meigs by British allied forces fails.
July 5 –War of 1812: Three weeks of British raids on Fort Schlosser, Black Rock and Plattsburgh, New York begin.
The Carabinieri, the national military police of Italy, are founded by Victor Emmanuel I as the police force of the Kingdom of Sardinia.
Missionaries Adoniram Judson and his wife Ann Hasseltine Judson arrive in Burma.
August 12 – Austria declares war on France.
August 19 –Gervasio Antonio de Posadas joins Argentina's second triumvirate.
August 23 –Battle of Großbeeren: Napoleon is defeated by Prussia and Sweden.
August 26 –Battle of Katzbach: Napoleon's troops are defeated by Prussia and Russia.
August 26–27 –Battle of Dresden: Napoleon's troops are victorious.
August 29–30 –First Battle of Kulm: French Marshal Vandamme defeated, captured by allied Coalition forces from Russia, Prussia and Austria.
August 30 –Creek War –Fort Mims massacre: A force of Creeks belonging to the Red Sticks faction kill hundreds of settlers in Fort Mims in Alabama.
August 31 –Peninsular War:
At the Battle of San Marcial, the Spanish Army of Galicia under Manuel Freire de Andrade turns back Marshal Soult's last major offensive against Wellington's allied army.
After besieging San Sebastián, allied troops in Spain rampage, ransack and burn down the town almost entirely.
September –Robert Southey becomes Poet Laureate of the United Kingdom.
September 6 –Battle of Dennewitz: The armies of Napoleon are again defeated by Prussia and Russia.
September 10 –War of 1812 –Battle of Lake Erie: An American squadron under Commodore Oliver Hazard Perry defeats a British squadron, capturing 6 ships.
September 17 –Second Battle of Kulm: Allied Coalition victory, Napoleon forced to halt his advance on Teplitz and withdraw to Leipzig
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 –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.
Russian troops reach and take Berlin without a fight after the French garrison evacuates the city.
Mathieu Orfila publishes his groundbreaking Traité des poisons, formalizing the field of toxicology.
Charles Waterton begins the process of turning his estate at Walton Hall, West Yorkshire, England, into what is, in effect, the world's first nature reserve.
George Hamilton-Gordon serves as ambassador extraordinaire in Vienna.
Following the death of his father Wossen Seged, Sahle Selassie arrives at the capital Qundi before his other brothers, and is made Meridazmach of Shewa.
Supreme Council for the Northern Jurisdiction of the United States of America is founded.
Probable date –George E. Clymer invents the Columbian press, used to print newspapers worldwide.
The poem "She Walks in Beauty" is written by Lord Byron.
January 19 –Sir Henry Bessemer, English inventor (d. 1898)
January 21 –John C. Frémont, American soldier and 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 and 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 and pioneer of Epidemiology, ( d. 1858)
March 18 –Christian Friedrich Hebbel, German poet and playwright (d. 1863)
March 19 –David Livingstone, Scottish missionary and 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, U.S. Senator from Illinois and 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 8 –David Dixon Porter, American admiral (d. 1891)
June 24 –Henry Ward Beecher, American clergyman and 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 – Kreeta Haapasalo, Finnish kantele-player, singer and folk musician (d. 1893)
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)
John Miley, American Methodist theologian (d. 1895)
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)
Alexandre-Théodore Brongniart, French architect (b. 1739)
Antonio Cachia, Maltese architect, engineer and archaeologist (b. 1739)
June 17 –Charles Middleton, 1st Baron Barham, English sailor and politician (b. 1726)
July 17 (bapt.) – 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 and 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 and military engineer (b. 1752)
October 5 –Tecumseh, Shawnee leader (b. 1768)
October 19 –Józef Poniatowski, Polish prince and 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)
Nikolaos Koutouzis –Greek painter, poet and priest (b. 1741)
1813 (MDCCCXIII) was a common year starting on Friday (dominical letter C) of the Gregorian calendar and a common year starting on Wednesday (dominical letter E) 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.