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1795 (MDCCXCV) was a common year starting on Thursday of the Gregorian calendar and a common year starting on Monday of the Julian calendar, the 1795th year of the Common Era (CE) and Anno Domini (AD) designations, the 795th year of the 2nd millennium, the 95th year of the 18th century, and the 6th year of the 1790s decade. As of the start of 1795, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- January – England records its coldest ever month, in the CET records dating back to 1659.
- January 14 – The University of North Carolina opens to students at Chapel Hill, becoming the first state university in the United States.
- January 16 – The French occupy Utrecht, Netherlands.
- January 18 – Batavian Revolution in Amsterdam: William V, Prince of Orange, Stadtholder of the Dutch Republic, flees the country.
- January 19 – The Batavian Republic is proclaimed in Amsterdam.
- January 20 – French troops enter Amsterdam.
- January 21 – Capture of the Dutch fleet at Den Helder: The Dutch fleet, frozen in Zuiderzee, is captured by the French 8th Hussars.
- February 7 – The Eleventh Amendment to the United States Constitution is passed.
- March – English Benedictine monks expelled from Douai are permitted to proceed to England.
- April 5 – The Peace of Basel is signed, between France and Prussia.
- April 7 – The metric system is adopted in France.
- April 8 – George, Prince of Wales, marries Caroline of Brunswick.
- April 23
- May 1 – Battle of Nuʻuanu: Kamehameha I of the Island of Hawaii defeats the Oahuans, solidifying his control of the major islands of the archipelago and officially founding the Kingdom of Hawaii.
- May–June – The Battle of Richmond Hill is fought in the colony of New South Wales, between the Darug people and British colonial forces.
- June 5–7 – The Copenhagen Fire of 1795, starting in a naval warehouse, destroys 941 houses.
- June 8 – The Dauphin of France, would-be-Louis XVII, dies. Louis XVIII becomes titular King of France (he becomes the actual king on April 6, 1814).
- June 16–17 – French Revolutionary Wars – Cornwallis's Retreat: A British Royal Navy battle squadron commanded by William Cornwallis fends off a numerically superior French Navy fleet, off the coast of Brittany.
- June 24 – The United States Senate ratifies the Jay Treaty with Great Britain.
- June 28 – The French government announces that the heir to the French throne has died of illness (many doubt the statement).
- June 27
- September 11 – Battle of Krtsanisi: The Persian emperor Agha Mohammad Khan Qajar defeats the forces of Heraclius II of Georgia.
- September 15 – French Revolutionary Wars – Invasion of the Cape Colony: British forces capture Cape Town in the Dutch Cape Colony, to use its strategic facilities against the French Navy.
- September 21 – Battle of the Diamond: Protestant forces defeat Catholic troops in Loughgall, Ireland, leading to the foundation of the Orange Order.
- September 28 – The Alliance of St Petersburg is formed between Britain, Russia and Austria against France.
- October 1 – The Austrian Netherlands is annexed to the French Republic, as the Belgian departments.
- October 2 – British forces capture the Île d'Yeu off the coast of Brittany.
- October 5 – 13 Vendémiaire: Royalist riots in Paris are crushed by troops under Paul Barras, and newly reinstalled artillery officer Napoleon Bonaparte.
- October 20 – The United States signs a treaty with Spain, opening commerce along the Mississippi River to the Gulf of Mexico, and establishing boundaries between U.S. territory and Spanish Florida.
- October 24 – The Third Partition of Poland is made, dividing the territory of the Commonwealth of Poland between the Habsburg Monarchy, Prussia and the Russian Empire. On November 25, Stanisław August Poniatowski formally abdicates as last King of Poland.
- October 27 – The United States and Spain sign the Treaty of Madrid, which establishes the boundaries between Spanish colonies and the U.S.
- November 2 – French Revolution: The French Directory takes power; the influence of the Sans-culottes declines.
- December 13 – Wold Newton meteorite: A meteorite falls at Wold Newton, a hamlet in Yorkshire in England. This meteorite fall is subsequently used as a literary premise by science fiction writer Philip José Farmer, as the basis for the Wold Newton family.
- December 28 - Construction of Yonge Street, formerly recognized as the longest street in the world, begins in York, Upper Canada (present-day Toronto).
- January 6 – Anselme Payen, French chemist (d. 1878)
- January 18 – Anna Pavlovna of Russia, Dutch queen (d. 1865)
- January 26 – Policarpa Salavarrieta, Colombian spy, revolutionary heroine who worked for the independence of Colombia (d. 1817)
- February 3 – Antonio José de Sucre, Venezuelan revolutionary leader, general and statesman (d. 1830)
- February 8 – Friedlieb Ferdinand Runge, German chemist (d. 1867)
- February 18 – George Peabody, American businessman; "Father of modern philanthropy" (d. 1869)
- February 16 – Sarah Ann Gill, Barbadian national heroine (d. 1866)
- March 12 – William Lyon Mackenzie, Scottish journalist, 1st Mayor of Toronto (d. 1861)
- May 4 – Annestine Beyer, Danish reform pedagogue (d. 1884)
- May 19 – Johns Hopkins, American businessman, philanthropist (d. 1873)
- May 23 – Charles Barry, English architect (d. 1860)
- June 11 – Sara Torsslow, Swedish actor (d. 1859)
- June 13 – Thomas Arnold, English school reformer (d. 1842)
- June 19 – James Braid, Scottish surgeon, hypnotism pioneer (d. 1860)
- June 21 – José María Pinedo, Argentinian naval commander (d. 1885)
- June 24 – Ernst Heinrich Weber, German physician, psychologist (d. 1878)
- July 5 – Georg Ernst Ludwig Hampe, German pharmacist, botanist and bryologist (d. 1880)
- September 1 – James Gordon Bennett, American newspaper publisher (d. 1872)
- September 6 – Achille Baraguey d'Hilliers, Marshal of France (d. 1878)
- September 7 – John William Polidori, English writer and physician (d. 1821)
- September 16 – Saverio Mercadante, Italian composer (d. 1870)
- September 18 – Kondraty Ryleyev, Russian poet, Decembrist (d. 1826)
- October 13 – James McDowell, American politician (d. 1851)
- October 15 – King Frederick William IV of Prussia (d. 1861)
- October 16 – William Buell Sprague, American clergyman, author (d. 1876)
- October 26 – Nikolaos Mantzaros, Greek composer (d. 1872)
- October 31 – John Keats, English poet (d. 1821)
- November 2 – James K. Polk, 11th President of the United States (d. 1849)
- November 12 – Thaddeus William Harris, American naturalist (d. 1856)
- December 2 – Guillermo (William) Miller, English-born military leader in Peru (d. 1861)
- December 3 – Rowland Hill, English teacher, inventor and social reformer (d. 1879)
- December 4 – Thomas Carlyle, Scottish writer, historian (d. 1881)
- December 10 – Matthias W. Baldwin, American locomotive manufacturer (d. 1866)
- December 21 – Leopold von Ranke, German historian (d. 1886)
- January 3 – Josiah Wedgwood, English potter, entrepreneur (b. 1730)
- January 5 – Jacobo Fitz-James Stuart, 6th Duke of Liria and Jérica, second surviving son of the Jacobo Fitz-James Stuart (b. 1792)
- January 10 – David Blackburn, Royal Navy officer (b. 1753)
- January 19 – Thomas Balguy, English churchman (b. 1716)
- January 21 – Samuel Wallis, English navigator
- January 22 – Richard Clinton, officer in the Continental Army during the American Revolution (b. 1741)
- January 23 – John Sullivan, American General in the American Revolutionary War, delegate in the Continental Congress (b. 1740)
- January 26 – Johann Christoph Friedrich Bach, German harpsichordist, composer (b. 1732)
- February 3 – Richard Edwards (b. c. 1715)
- February 7 – Antoine Polier, Swiss adventurer (b. 1741)
- February 11 – Carl Michael Bellman, Swedish poet (b. 1740)
- February 14 – Samuel Cook Silliman, member of the Connecticut House of Representatives from Norwalk (b. 1741)
- February 27 – Tanikaze Kajinosuke (b. 1750)
- March 4 – John Collins, third Governor of the U (b. 1717)
- March 9 – John Armstrong, Sr., American civil engineer and major general during the Revolutionary War (b. 1717)
- March 15 – Louisa Catharina Harkort, German ironmaster (b. 1718)
- March 18 – Jonathan Buck, Bucksport (b. 1719)
- March 21
- April 1 – Charles II August, Duke of Zweibrücken (b. 1746)
- April 6 – George Collier, officer of the Royal Navy who saw service during the Seven Years' War (b. 1738)
- April 12 – Johann Kaspar Basselet von La Rosée, Bavarian general (b. 1710)
- May 6 – Pieter Boddaert (b. 1730)
- May 7 – Antoine Quentin Fouquier-Tinville, French revolutionary leader (executed) (b. 1746)
- May 12 – Ezra Stiles (b. 1727)
- May 18 – Robert Rogers, American colonial frontiersman (b. 1731)
- May 19 – Josiah Bartlett, signer of the American Declaration of Independence (b. 1729)
- May 20
- May 27 – Thomas-Laurent Bédard, priest (b. 1747)
- May 28 – Jeremiah Dencke (b. 1725)
- June 1 – Pierre-Joseph Desault, French anatomist and surgeon (b. 1744)
- June 8 – King Louis XVII of France (b. 1785)
- June 13 – Stephen Popham, British politician and solicitor who is remembered for improving the residential locality of Georgetown (b. 1745)
- June 17 – Gilbert Romme, French politician and mathematician who developed the French Republican Calendar (b. 1750)
- June 23 – James Craig, Scottish architect who worked mostly in lowlands of the country and especially his native city of Edinburgh (b. 1739)
- June 24 – William Smellie, encyclopedist (b. 1740)
- July 3
- July 9 – Henry Seymour Conway, British general and statesman (b. 1721)
- July 10 – Omar Ali Saifuddin I, Sultan of Brunei from 1740 until his death in 1795 (b. 1711)
- July 12 – Archduke Alexander Leopold of Austria (b. 1772)
- July 27 – Louis Grégoire Deschamps Destournelles, French politician who was Minister of Finance during the French Revolution (b. 1744)
- July 28 – Zebulon Butler, soldier and politician from Connecticut who served with the Continental Army during the American Revolutionary War (b. 1731)
- July 31
- August 4 – Timothy Ruggles, American-born Tory politician (b. 1711)
- August 5 – William Fleming, physician (b. 1729)
- August 14
- August 19 – Friedrich Hartmann Graf, German flautist and composer (b. 1727)
- August 20 – William Jones, Welsh antiquary (b. 1726)
- August 23 – William Bradford, lawyer and judge from Philadelphia (b. 1755)
- August 26 – Alessandro Cagliostro, Italian Freemason (b. 1743)
- August 31 – François-André Danican Philidor, French composer and chess player (b. 1726)
- September 30 – George Butt, British poet (b. 1741)
- October 8 – Andrew Kippis, English non-conformist clergyman and biographer (b. 1725)
- October 10
- October 13
- October 27 – Madhavrao II (b. 1774)
- November 3 – Sir John Hotham, 9th Baronet (b. 1734)
- November 11 – George Dixon, English sea captain (b. 1748)
- November 15 – Charles-Amédée-Philippe van Loo, French painter (b. 1719)
- November 17 – Samuel Bishop, poet born in London (b. 1731)
- November 18 – Jan August Cichocki, Polish military officer and a general of the Polish Army (b. 1750)
- December 4 – Prince Eugene of Saxe-Hildburghausen, Prince of Saxe-Hildburghausen (b. 1730)
- December 10 – John Johnstone, East India Company (b. 1734)
- December 23 – Henry Clinton, British general (b. 1730)
- December 26 – Antonio Zucchi (b. 1726)
- December 28 – Eugenio Espejo, Ecuadorian scientist (b. 1747)
- Date unknown - Marie Marguerite Bihéron, French anatomist (b. 1719)