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|Centuries:||17th century – 18th century – 19th century|
|Decades:||1760s 1770s 1780s – 1790s – 1800s 1810s 1820s|
|Years:||1788 1789 1790 – 1791 – 1792 1793 1794|
|1791 by topic:|
|Arts and Sciences|
|Archaeology – Architecture – Art – Literature (Poetry) – Music – Science|
|Australia – Canada – Great Britain – United States|
|Lists of leaders|
|Colonial governors – State leaders|
|Birth and death categories|
|Births – Deaths|
|Establishments and disestablishments categories|
|Establishments – Disestablishments|
|Ab urbe condita||2544|
|British Regnal year||31 Geo. 3 – 32 Geo. 3|
— to —辛亥年十二月初七日
|- Vikram Samvat||1847–1848|
|- Shaka Samvat||1713–1714|
|- Kali Yuga||4892–4893|
|- Ǹrí Ìgbò||791–792|
|Japanese calendar||Kansei 3
|Juche calendar||N/A (before 1912)|
|Julian calendar||Gregorian minus 11 days|
|Minguo calendar||121 before ROC
|Thai solar calendar||2334|
|Wikimedia Commons has media related to: 1791|
Year 1791 (MDCCXCI) was a common year starting on Saturday (link will display the full calendar) of the Gregorian calendar and a common year starting on Wednesday of the 11-day slower Julian calendar.
- January 12 – Holy Roman troops reenter Liège, heralding the end of the Liège Revolution and the restoration of its Prince-Bishops
- January 25 – The British Parliament passes the Constitutional Act of 1791, splitting the old province of Quebec into Upper and Lower Canada.
- March 2 – Long-distance communication speeds up with the unveiling of a semaphore machine in Paris.
- March 4 – Vermont is admitted as the 14th U.S. state.
- April 21 – The first of forty boundary stones delineating the borders of the new District of Columbia is laid at Jones Point Light, in Alexandria, Virginia.
- May 3 – The Sejm of the Polish–Lithuanian Commonwealth proclaims the Constitution of May 3, 1791, the first modern codified constitution in Europe.
- June 20 – The French Royal Family is captured when they try to flee in disguise.
- July 8 – Composer Joseph Haydn awarded an honorary doctorate of music at Oxford University.
- July 14 – The Priestley Riots break out in Birmingham, England.
- July 17 – The Champ de Mars Massacre occurs during the French Revolution.
- August 4 – The Treaty of Sistova is signed, ending the Ottoman-Habsburg wars.
- August 6 – The Brandenburg Gate in Berlin is finished.
- August 26 – John Fitch is granted a patent for the steamboat in the United States.
- August 22 – A slave rebellion breaks out in the French colony of Saint-Domingue.
- September 13 – Louis XVI of France accepts the final version of the completed constitution.
- September 25 – Mission Santa Cruz is founded by Father Fermín Francisco de Lasuén, becoming the 12th mission in the California mission chain.
- September 28 – Promulgation of the law on Jewish emancipation in France, the first such legislation in Europe.
- September 30 – Wolfgang Amadeus Mozart's singspiel The Magic Flute ("Die Zauberflöte") premieres at the Freihaus-Theater auf der Wieden in Vienna.
- October – The Legislative Assembly (France) convenes.
- October 9 – Mission Nuestra Señora de la Soledad is founded by Father Fermín Francisco de Lasuén, becoming the 13th mission in the California mission chain.
- December 4 – The first issue of The Observer, the world's first Sunday newspaper, is published in London.
- December 5 – Austrian composer Wolfgang Amadeus Mozart dies aged 35 at his home in Vienna, perhaps of acute rheumatic fever, and is buried two days later.
- December 15 – Ratification by the states of the first ten amendments to the United States Constitution is completed, creating the United States Bill of Rights. Two additional amendments remain pending, and one of these is finally ratified in 1992, becoming the Twenty-seventh Amendment.
Date unknown 
- The first American ship reaches Japan.
- A slave rebellion begins in Haiti; see Haitian Revolution.
- An ordinance is written barring the game of baseball within 80 yards of the Meeting House in Pittsfield, Massachusetts (first known reference to the game of baseball in North America).
- The metric system is adopted in France.
- January 15 – Franz Grillparzer, Austrian writer (d. 1872)
- January 28 – Louis Joseph Ferdinand Herold, French composer (d. 1833)
- February 12 – Peter Cooper, American industrialist, inventor and philanthropist (d. 1883)
- February 21
- April 23 – James Buchanan, 15th President of the United States (d. 1868)
- April 27 – Samuel Morse, American inventor (d. 1872)
- July 26 – Franz Xaver Wolfgang Mozart, Austrian composer and pianist (d. 1844)
- September 5 – Giacomo Meyerbeer, German composer (d. 1864)
- September 21 – István Széchenyi, Hungarian politician and writer (d. 1860)
- September 22 – Michael Faraday, British scientist (d. 1867)
- September 26 – Théodore Géricault, French painter (d. 1824)
- November 11 – Josef Munzinger, member of the Swiss Federal Council (d. 1855)
- December 7 – Ferenc Novák Hungarian Slovene writer (d. 1836)
- December 26 – Charles Babbage, British mathematician and inventor (d. 1871)
- date unknown – Anne Lister, A wealthy Lesbian from Halifax, famous for her openly lesbian life style and her extensive, coded diaries (d. 1840)
- January 11 – William Williams Pantycelyn, Welsh hymnist (b. 1717)
- March 2 – John Wesley, English founder of Methodism (b. 1703)
- March 14 – Johann Salomo Semler, German historian and Bible commentator (b. 1725)
- April 19 – Richard Price, Welsh philosopher (b. 1723)
- May 9 – Francis Hopkinson, American signer of the Declaration of Independence (b. 1737)
- June 5 – Frederick Haldimand, Swiss-born British colonial governor (b. 1718)
- June 10 – Toussaint-Guillaume Picquet de la Motte, French admiral (b. 1720)
- July 17 – Martin Dobrizhoffer, Austrian Jesuit missionary (b. 1717)
- July 25 – Isaac Low, American delegate to the Continental Congress (b. 1735)
- August 16 – Charles-François de Broglie, marquis de Ruffec, French soldier and diplomat (b. 1719)
- November 4 – Richard Butler (general), American soldier (b. 1743)
- September 25 – William Bradford, American printer (b. 1719)
- December 5 – Wolfgang Amadeus Mozart, Austrian composer (b. 1756)