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was a common year starting on Monday of the Gregorian calendar and a common year starting on Friday of the Julian calendar, the 1781st year of the Common Era (CE) and Anno Domini (AD) designations, the 781st year of the 2nd millennium, the 81st year of the 18th century, and the 2nd year of the 1780s decade. As of the start of 1781, the Gregorian calendar was
11 days ahead of the Julian calendar, which remained in localized use until 1923.
- January – William Pitt the Younger, later Prime Minister of Great Britain, enters Parliament, aged 21.
- January 1 – Industrial Revolution: The Iron Bridge opens across the River Severn in England.
- January 2 – Virginia passes a law ceding its western land claims, paving the way for Maryland to ratify the Articles of Confederation.
- January 5 – American Revolutionary War: Richmond, Virginia is burned by British naval forces, led by Benedict Arnold.
- January 6 – Battle of Jersey: British troops prevent the French from occupying Jersey in the Channel Islands.
- January 17 – American Revolutionary War – Battle of Cowpens: The American Continental Army, under Daniel Morgan, decisively defeats British forces in South Carolina.
- February 2 – The Articles of Confederation are ratified by Maryland, the 13th and final state to do so.
- February 3 – Fourth Anglo-Dutch War – Capture of Sint Eustatius: British forces take the Dutch Caribbean island of Sint Eustatius, with only a few shots fired. On November 26 it is retaken by Dutch-allied French forces.
- March – Riots break out in Socorro, Santander, and spread to other towns.
- March 1 – The United States Continental Congress implements the Articles of Confederation, forming its Perpetual Union as the United States in Congress Assembled.
- March 13 – Sir William Herschel discovers the planet Uranus. Originally he calls it Georgium Sidus (George's Star), in honour of King George III of Great Britain.
- March 15 – American Revolutionary War – Battle of Guilford Court House: American General Nathanael Greene loses to the British.
- April 6 – The rebellion by Túpac Amaru II, against the Spanish colonial government of Peru, is ended as Tupac, his wife and two of his sons are captured at Checacupe. 
- April 10 – Future U.S. President Andrew Jackson, age 14, is slashed by a British officer's sword at his home near Waxhaw, North Carolina, after refusing to clean the officer's boots, an event that leaves physical and psychological scars. 
- April 14 – The Continental Congress votes a resolution thanking U.S. Captain John Paul Jones for his services. 
- April 18 – Future New York mayor James Duane, North Carolina representative William Sharpe and future Connecticut governor Oliver Wolcott deliver the first report to the U.S. Continental Congress about the national debt and report it to be 24,057,157 and 2/5 dollars. 
- April 25 – The Battle of Hobkirk's Hill took place in Camden, South Carolina
- May 9 – General John Campbell, defender of the British colony of West Florida, surrenders the capital at Pensacola to Spanish forces commanded by Bernardo de Galvez. 
- May 18 – A Spanish army sent from Lima puts down the Inca rebellions, and captures and savagely executes Túpac Amaru II.
- June 4 – The commission agrees to the rebels' terms: reduction of the alcabala and of the Indians' forced tribute, abolition of the new taxes on tobacco, and preference for Criollos over peninsulares in government positions.
- October 12 – The first bagpipes competition is held in the Masonic Arms, Falkirk, Scotland.
- October 19 – American Revolution: Following the Siege of Yorktown, General Charles Cornwallis surrenders to General George Washington at Yorktown, Virginia, ending the armed struggle of the American Revolution.
- October 20 – A Patent of Toleration, providing limited freedom of worship, is approved in the Habsburg Monarchy.
- November 5 – John Hanson is elected President of the Continental Congress.
- November 29
- December – A school is founded in Washington County, Pennsylvania that will later be known as Washington & Jefferson College.
- December 12 – American Revolutionary War – Second Battle of Ushant: The British Royal Navy, commanded by Rear Admiral Richard Kempenfelt in HMS Victory, decisively defeats the French fleet in the Bay of Biscay.
- June 9 – George Stephenson, English engineer, designer of railway locomotives Locomotion No. 1, Rocket (d. 1848)
- June 21 – Siméon Denis Poisson, French mathematician, physicist (d. 1840)
- July 6
- July 25 – Merry-Joseph Blondel, French painter (d. 1853)
- July 27 – Mauro Giuliani, Italian composer (d. 1829)
- September 3 – Eugène de Beauharnais, French nobleman, son of Napoleon's wife Joséphine (d. 1824)
- September 5 – Anton Diabelli, Austrian music publisher, or, composer (d. 1858)
- October 1 – James Lawrence, U.S. Navy officer (d. 1813)
- October 5 – Bernard Bolzano, Czech philosopher, mathematician (d. 1848)
- November 1 – Joseph Karl Stieler, German painter (d. 1858)
- November 6
- November 20 – Karl Friedrich Eichhorn, German jurist (d. 1854)
- November 29 – Andrés Bello, Venezuelan poet, lawmaker, teacher, philosopher, sociologist (d. 1865)
- November 30 – Alexander Berry, Scottish adventurer, Australian pioneer (d. 1873)
- December 11 – Sir David Brewster, Scottish physicist (d. 1868)
- February 15 – Gotthold Ephraim Lessing, German author, philosopher (b. 1729)
- February 22 – Anna Magdalena Godiche, Danish book printer, publisher (b. 1721)
- February 23 – George Taylor, American signer of the Declaration of Independence
- February 24 – Edward Capell, English critic (b. 1713)
- March 17 – Johannes Ewald, Danish national dramatist, poet (b. 1743)
- March 18 – Anne-Robert-Jacques Turgot, Baron de Laune, French statesman, economist (b. 1727)
- April 23 – James Abercrombie, British general (b. 1706)
- April 28 – Cornelius Harnett, American delegate to the Continental Congress (b. 1723)
- May 8 – Richard Jago, English poet (b. 1715)
- May 16 – Giacomo Puccini (senior), Italian composer (b. 1712)
- May 18 – Túpac Amaru II, Peruvian indigenous rebel leader (b. 1742)
- May 18 – Micaela Bastidas Puyucahua, Peruvian indigenous rebel leader (b. 1745)
- May 27 – Giovanni Battista Beccaria, Italian physicist (b. 1716)
- July 18 – Padre Francisco Garcés, Spanish missionary (killed) (b. 1738)
- July 23 – John Joachim Zubly, Swiss-born Continental Congressman (b. 1724)
- September 12 – Peter Scheemakers, Flemish sculptor (b. 1691)
- September 28 – William Nassau de Zuylestein, 4th Earl of Rochford, British diplomat, statesman (b. 1717)
- October 16 – Edward Hawke, 1st Baron Hawke, British naval officer (b. 1705)
- November 4 – Johann Nikolaus Götz, German poet (b. 1721)
- ^ Williams, Hywel (2005). Cassell's Chronology of World History. London: Weidenfeld & Nicolson. pp. 333–334. ISBN 0-304-35730-8.
- ^ Penguin Pocket On This Day. Penguin Reference Library. 2006. ISBN 0-14-102715-0.
- ^ "The Rebellion of Tupac-Amaru II", in The Hispanic American Historical Review (February 1919) p20
- ^ William J. Bennett and John T.E. Cribb, The American Patriot's Almanac: Daily Readings on America (Thomas Nelson, Inc. 2013) p125
- ^ "John Paul Jones and Our First Triumphs on the Sea", in The American Monthly Review of Reviews" (July 1905) p42
- ^ Albert Bushnell Hart, ed., American History Told by Contemporaries (Macmillan, 1908) p600
- ^ Michael Lee Lannin, African Americans in the Revolutionary War (Citadel Press, 2005) p86
- ^ "BBC History British History Timeline". Archived from the original on September 9, 2007. Retrieved 2007-09-03.
- ^ "History & Facts". Washington & Jefferson College. Archived from the original on July 29, 2011. Retrieved September 10, 2010.