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1780 (MDCCLXXX) was a leap year starting on Saturday (dominical letter BA) of the Gregorian calendar and a leap year starting on Wednesday (dominical letter ED) of the Julian calendar, the 1780th year of the Common Era (CE) and Anno Domini (AD) designations, the 780th year of the 2nd millennium, the 80th year of the 18th century, and the 1st year of the 1780s decade. As of the start of 1780, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- July 11 – French soldiers arrive in Newport, Rhode Island to reinforce colonists in the American Revolutionary War.
- August 16 – American Revolutionary War – Battle of Camden: British troops inflict heavy losses on a Patriot army at Camden, South Carolina.
- August 9 – American Revolutionary War: Spanish admiral Luis de Córdova y Córdova captures a British convoy totalling 55 vessels amongst Indiamen, frigates and other cargo ships off Cape St. Vincent.
- August 24 – Louis XVI of France abolishes the use of torture in extracting confessions.
- September 21 – Benedict Arnold gives detailed plans of West Point to Major John André. Three days later, André is captured with papers revealing that Arnold was planning to surrender West Point to the British.
- September 25 – Benedict Arnold flees to British-held New York.
- October 2 – American Revolutionary War: In Tappan, New York, British spy John André is hanged by American forces.
- October 7 – American Revolutionary War – Battle of Kings Mountain: Patriot militia forces annihilate Loyalists under British Major Patrick Ferguson at Kings Mountain in South Carolina.
- October 10–October 16 – The Great Hurricane flattens the islands of Barbados, Martinique and Sint Eustatius: 22,000 dead.
- November 29 – Maria Theresa of Austria dies and her Habsburg dominions pass to her ambitious son, Joseph II, who has already been Holy Roman Emperor since 1765.
- December 16 – Emperor Kōkaku accedes to the throne of Japan.
- December 20 – Start of the Fourth Anglo-Dutch War.
- Jose Gabriel Kunturkanki, businessman and landowner, proclaims himself Inca Túpac Amaru II.
- The Duke of Richmond calls, in the House of Lords of Great Britain, for manhood suffrage and annual parliaments, which are rejected.
- Jeremy Bentham's Introduction to Principles of Morals and Legislation, presenting his formulation of utilitarian ethics, is printed (but not published) in London.
- Nikephoros Theotokis starts introducing Edinoverie, an attempt to integrate the Old Believers into Russia's established church.
- Woodford Reserve bourbon whiskey distillery begins operation in Kentucky.
- In Ireland, Lady Berry, who is sentenced to death for the murder of her son, is released when she agrees to become an executioner (retires 1810)
- The original Craven Cottage is built by William Craven, 6th Baron Craven, in London on what will become the centre circle of Fulham F.C.'s pitch.
- The amateur dramatic group Det Dramatiske Selskab in Christiania is founded in Norway.
- Western countries pay 16,000,000 ounces of silver for Chinese goods.
- c.9 million population in the Kingdom of Great Britain.
- January 13 – Pierre Jean Robiquet, French chemist (d. 1840)
- January 14 – Henry Baldwin, Associate Justice of the Supreme Court of the United States (d. 1844)
- February 1 – David Porter, American naval officer (d. 1843)
- February 19 – Richard McCarty, American politician (d. 1844)
- February 25 – John Sumner, Archbishop of Canterbury (d. 1862)
- March 25 – Joseph Ritner, American politician (d. 1869)
- April 7 – William Ellery Channing, Influential Unitarian theologian and minister (d. 1842)
- April 26 – Gotthilf Heinrich von Schubert, German naturalist (d. 1860)
- April 29 – Charles Nodier, French author (d. 1844)
- May 1 – John McKinley, American politician and Associate Justice of the Supreme Court of the United States (d. 1852)
- May 21 – Elizabeth Fry, British humanitarian (d. 1845)
- May 29 – Henri Braconnot, French chemist and pharmacist (d. 1855)
- June 1 – Carl von Clausewitz, Prussian military strategist (d. 1831)
- July 4 – Sofia Hjärne, Finnish baroness and writer (d. 1860)
- July 5 – François Carlo Antommarchi, French Physician (d. 1838)
- July 15 – Emilie Petersen, Swedish philanthropist (d. 1859)
- August 29
- February 14 – William Blackstone, English jurist (b. 1723)
- February 17 – Andreas Felix von Oefele, German historian and librarian (b. 1706)
- February 18 – Kristijonas Donelaitis, Lithuanian poet (b. 1714)
- March 17 – Elizabeth Butchill, English woman executed for the murder of her newborn child (b. ca. 1758)
- March 26 – Charles I, Duke of Brunswick-Wolfenbüttel (b. 1713)
- April 5 – Ulrika Strömfelt, Swedish courtier (b. 1724)
- May 18 – Charles Hardy, British governor of Newfoundland (b. c. 1714)
- June 3 – Thomas Hutchinson, American colonial governor of Massachusetts (b. 1711)
- July 4 – Prince Charles Alexander of Lorraine, Austrian military leader (b. 1712)
- July 14 – Charles Batteux, French philosopher (b. 1713)
- August 3 – Étienne Bonnot de Condillac, French philosopher (b. 1715)
- August 19 – Johann de Kalb, Bavarian-French military officer who served as a major general in the Continental Army during the American Revolutionary War (b. 1721)
- August 29 – Jacques-Germain Soufflot, French architect (b. 1713)
- September 4 – John Fielding, English magistrate and social reformer (b. 1721)
- September 8 – Enoch Poor, American Revolutionary general (b. 1736)
- September 23 – Marie Anne de Vichy-Chamrond, marquise du Deffand, French salon holder (b. 1697)
- October 2 – John André, British Army officer of the American Revolutionary War (executed) (b. 1750)
- October 17 – William Cookworthy, English chemist (b. 1705)
- November 26 – Sir James Steuart, Scottish economist (b. 1713)