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1775 was a common year starting on Sunday of the Gregorian calendar and a common year starting on Thursday of the Julian calendar, the 1775th year of the Common Era (CE) and Anno Domini (AD) designations, the 775th year of the 2nd millennium, the 75th year of the 18th century, and the 6th year of the 1770s decade. As of the start of 1775, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
The American Revolution begins this year, with the first military engagement being the April 19 Battles of Lexington and Concord on the day after Paul Revere's now-epic ride. The Second Continental Congress takes various steps toward organizing an American government, appointing George Washington commander-in-chief (June 14), Benjamin Franklin postmaster general (July 26) and creating a Continental Navy (October 13) and a Marine force (November 10) as landing troops for it, but as yet the 13 colonies have not declared independence, and both the British (June 12) and American (July 15) governments make laws. On July 6, Congress issues the Declaration of the Causes and Necessity of Taking Up Arms, and on August 23, King George III of England declares the American colonies in rebellion, announcing it to Parliament on November 10. On June 17, two months into the colonial siege of Boston, at the Battle of Bunker Hill, just north of Boston, British forces are victorious, but only after suffering severe casualties and after Colonial forces run out of ammunition, Fort Ticonderoga is taken by American forces in New York Colony's northern frontier, and American forces unsuccessfully invade Canada, with an attack on Montreal defeated by British forces on November 13 and an attack on Quebec repulsed December 31.
Human knowledge and technology advances when James Watt builds a successful prototype of a steam engine, and a scientific expion continues as Captain James Cook claims the South Georgia and South Sandwich Islands in the south Atlantic Ocean for Britain. Nature's power over humanity is dramatically demonstrated when the Independence Hurricane (August 29 – September 13) devastates the east coast of North America, killing 4,173, and when a smallpox epidemic begins in New England.
- January – The Habsburg Monarchy forces the Ottoman Empire to cede Bukovina to its rule.
- January 5 – Wolfgang Amadeus Mozart finishes a Sonata for Keyboard in C.
- January 16–20 – Second voyage of James Cook: Captain James Cook circumnavigates, makes the first landing on and (on January 17) takes possession of South Georgia in the southern Atlantic Ocean, for the Kingdom of Great Britain. The following month he discovers the South Sandwich Islands.
- February 9 – American Revolution: The Parliament of Great Britain declares the Province of Massachusetts Bay to be in rebellion.
- February 15 – Pope Pius VI succeeds Pope Clement XIV, as the 250th pope.
- March 6 – Raghunathrao, Peshwa of the Maratha Empire in India, signs the Treaty of Surat with British Governor-General Warren Hastings in Bombay, ceding the territories of Salsette and Bassein to the British East India Company, along with part of the revenues from Surat and Bharuch districts, in return for military assistance. This leads to the First Anglo-Maratha War, fought between the British and the Marathas, ending with the Treaty of Salbai in 1782.
- March 17 – Catherine the Great of Russia issues a manifesto, prohibiting freed serfs from being returned to serfdom.
- March 23 – American Revolution: Patrick Henry, a delegate to the Second Virginia Convention after the Virginia House of Burgesses was disbanded by the Royal Governor, delivers his Give me liberty, or give me death! speech at St. John's Church in Richmond, Virginia.
- April 18 – American Revolution: Paul Revere and William Dawes, instructed by Dr. Joseph Warren, ride from Boston to Lexington, to warn John Hancock and Sam Adams that British forces are coming to take them prisoner, and to seize colonial weapons and ammunition in Concord.
- April 19 – American Revolution – Battles of Lexington and Concord: Hostility between Britain and its American colonies explodes into bloodshed,  igniting the American Revolution.
- May 9 – American Revolution: Brunswick militiamen commanded by Samuel Thompson capture Henry Mowat, captain of HMS Canceaux.
- May 10
- May 14 – American Revolution – Battle off Fairhaven: In the first naval engagement of the American Revolutionary War, Patriots recover two Patriot vessels, and capture 13 Royal Navy sailors as prisoners of war.
- May 17 – American Revolution: The Continental Congress bans trade with Canada.
- May 20
- American Revolution – Battle of Lexington: American militiamen drive British troops back to Boston.
- The Committee of Mecklenburg County, North Carolina ratifies the Mecklenburg Declaration of Independence, dissolving allegiance to the Royal Crown of England, becoming the first collective to declare sovereignty in the Royal Colonies.
- June 11 – Battle of Machias: In the second naval engagement of the American Revolutionary War, American forces capture the schooner HMS Margaretta.
- June 12 – American Revolution:
- June 14 – American Revolution: The Continental Congress names George Washington as commander of the Continental Army.
- June 16 – The post of Chief Engineer of the Continental Army is created.
- June 17 – American Revolution: Two months into the colonial siege of Boston, British open fire on Breed's Hill on Charles Town Peninsula. After 3 charges, the British take the hill, in the misnamed Battle of Bunker Hill.
- June 19 – American Revolution: The post of Commanding General is created by the Continental Congress.
- June 25 – The Great Fire of Tartu, Governorate of Livonia, destroys most of the town.
- July 3 – American Revolution: George Washington takes command of the 17,000-man Continental Army at Cambridge.
- July 5 – American Revolution: The Continental Congress sends the Olive Branch Petition, hoping for a reconciliation.
- July 6 – American Revolution: The Continental Congress issues the Declaration of the Causes and Necessity of Taking Up Arms, which contains the words: "Our cause is just. Our union is perfect... being with one mind resolved to die freemen rather than to live slaves...".
- July 26 – The Second Continental Congress appoints Benjamin Franklin to be the first Postmaster General, of what later becomes the United States Post Office Department.
- July 30 – Second voyage of James Cook: HMS Resolution anchors off the south coast of England, Captain Cook having completed the first eastabout global circumnavigation.
- August 18 – Tucson is founded.
- August 21 – American Revolution – Siege of Fort St. Jean: American rebels launch an invasion of Canada.
- August 23 – American Revolution: Refusing to even look at the Olive Branch Petition, King George III issues a Proclamation of Rebellion against the American colonies.
- August 29–September 12 – The Independence Hurricane from South Carolina to Nova Scotia kills 4,170, mostly fishermen and sailors.
- September 8 – The unsuccessful Rising of the Priests takes place in Malta.
- September 25 – American Revolution – Siege of Fort St. Jean – Battle of Longue-Pointe: Thirteen Colonies revolutionary forces under Maj. Ethan Allen attack Montreal, Quebec, commanded by British General Guy Carleton. Allen's forces are defeated, and Allen himself is captured and held on British ships, until he is later released.
- October – The Sayre Plotters attempt to kidnap George III of Great Britain.
- October 13 – American Revolution: The Continental Congress orders the establishment of the Continental Navy (later the United States Navy).
- October 18 – American Revolution: Burning of Falmouth by ships of the Royal Navy commanded by Henry Mowat, who had been humiliated by local militiamen on May 9.
- October 26 – American Revolution: George III announces to Parliament that the American colonies are in an uprising, and must be dealt with accordingly.
- November – American Revolution: Colonel Richard Richardson's South Carolina revolutionaries march through Ninety-Six District, in what becomes known as the Snow Campaign, effectively ending all major support for the Loyalist cause in the backcountry of South Carolina.
- November 7 – Dunmore's Proclamation: Lord Dunmore, colonial governor of Virginia, signs a proclamation promising freedom for slaves of Patriots if they join Loyalist forces, thus losing the support of slaveowning planters.
- November 10 – American Revolution: The Continental Congress passes a resolution creating the Continental Marines, to serve as landing troops for the recently created Continental Navy (the Marines are disbanded at end of the war in April 1783 but reformed on July 11, 1798 as the United States Marine Corps).
- November 13 – American Revolution – Battle of Montreal: American forces under Brigadier General Richard Montgomery capture Montreal. British General Guy Carleton escapes to Quebec.
- December 5 – American Revolution: Henry Knox begins his journey to Cambridge, Massachusetts with the artillery that has been captured from Fort Ticonderoga.
- December 9 – American Revolution – Battle of Great Bridge: Victory by the Continental Army and militia leads to withdrawal of the British from the Colony of Virginia.
- December 31 – American Revolution: Battle of Quebec: British forces repulse an attack by Continental Army generals Richard Montgomery and Benedict Arnold, at Quebec.
The Honourable Mrs Graham (1757–1792) painted by Gainsborough
- January 20 – André-Marie Ampère, French physicist, mathematician (d. 1836)
- January 21 – Manuel García, Spanish singer, teacher, composer (d. 1832)
- January 22 – Abraham H. Schenck, American politician (d. 1831)
- January 23
- January 27 – Friedrich Wilhelm Joseph Schelling, German philosopher (d. 1854)
- January 28 – Lady Charlotte Bury, English novelist (d. 1861)
- January 30 – Walter Savage Landor, English writer, poet (d. 1864)
- January 31 – John Richard Farre, English physician (d. 1862)
- March 3 – Henry Prittie, 2nd Baron Dunalley, British politician (d. 1854)
- March 4 – Cuthbert Powell, American politician (d. 1849)
- March 5 – Adam Elias von Siebold, German gynecologist (d. 1828)
- March 10 – Marc-Antoine Jullien de Paris, French journalist (d. 1848)
- March 11 – Nils Landmark, Norwegian politician (d. 1859)
- March 12
- March 14 – Samuel Street, Jr., Upper Canada businessman (d. 1844)
- March 15 – Juan Bautista Arismendi, general in the Venezuelan War of Independence (d. 1841)
- March 17 – Ninian Edwards, Governor of and Senator from Illinois (d. 1833)
- March 19 – Ramsay Richard Reinagle, English painter (d. 1862)
- March 22
- March 23 – William Haseldine Pepys, English scientist (d. 1856)
- March 24
- March 25 – John Johnston, United States Indian agent (d. 1861)
- March 26 – Thomas Monteagle Bayly, American politician (d. 1834)
- March 28 – Johann Heinrich Gossler, Hamburg banker, grand burgher (d. 1842)
- March 30 – Hieronymus Karl Graf von Colloredo-Mansfeld, Austrian corps commander during the Napoleonic Wars (d. 1822)
- April 2 – Calvin Jones, American politician (d. 1846)
- April 4 – Dutch Sam, British boxer (d. 1816)
- April 5 – Johann Nepomuk Rust, Austrian surgeon (d. 1840)
- April 7
- April 8
- April 10 – Carl Wigand Maximilian Jacobi, German psychiatirst (d. 1858)
- April 12
- April 13 – Adolph Henke, German physician (d. 1843)
- April 14
- April 16 – Charles Stewart, British bishop (d. 1837)
- April 19 – Samuel King, American minister (d. 1842)
- April 21
- April 22
- April 23 – J. M. W. Turner, English Romantic landscape painter, watercolourist and printmaker (d. 1851)
- April 25
- April 27 – Pietro Ostini, Italian Catholic cardinal (d. 1849)
- April 28
- April 30
- May 5
- May 6
- May 8 – George Gwilt the younger, English architect (d. 1856)
- May 10
- May 12 – George Whitmore, British Army general (d. 1862)
- May 14 – Micah Brooks, United States general (d. 1857)
- May 17
- May 19 – Antonín Jan Jungmann, Czech physician (d. 1854)
- May 21 – Lucien Bonaparte, French statesman (d. 1840)
- May 24
- May 25 – Pelagio Palagi, Italian painter (d. 1860)
- May 28 – Thomas Graves, 2nd Baron Graves, British politician (d. 1830)
- May 31 – Charles Jackson, United States lawyer, jurist (d. 1855)
- June 4 – Francesco Molino, Italian guitarist (d. 1847)
- June 8 – Henry Boehm, American clergyman, pastor (d. 1875)
- June 9 – Georg Friedrich Grotefend, German epigraphist, philologist (d. 1853)
- June 10 – James Barbour, American politician (d. 1842)
- June 12
- June 13 – Antoni Radziwiłł, Polish politician (d. 1833)
- June 14 – André Bruno de Frévol de Lacoste, French general of the First Empire (d. 1809)
- June 15
- June 16 – Judah Touro, American businessman (d. 1854)
- June 18 – Orsamus Cook Merrill, American politician (d. 1865)
- June 19 – Friedrich August Peter von Colomb, German general (d. 1854)
- June 22 – Johannes Flüggé, German botanist and physician (d. 1816)
- June 24 – John Kempthorne, English clergyman and hymnwriter (d. 1838)
- June 26
- June 29 – Thomas Boyle, Sailing Master, United States Navy (War of 1812) (d. 1825)
- June 30 – William Thompson, Irish philosopher (d. 1833)
- July 1 – Cephas Thompson, American artist (d. 1856)
- July 2 – Aaron Peasley American button maker (d. 1837)
- July 3 – Antoine Philippe, Duke of Montpensier (d. 1807)
- July 5 – William Crotch, English composer, organist and artist (d. 1847)
- July 8
- July 9 – Matthew Lewis, British politician (d. 1818)
- July 11 – Joseph Blanco White Spanish theologian, poet (d. 1841)
- July 14
- July 15 – Richard Westmacott, British sculptor (d. 1856)
- July 17 – Domingo Eyzaguirre, Chilean politician (d. 1854)
- July 18 – Karl von Rotteck, German historian (d. 1840)
- July 19
- July 21
- July 23
- July 25 – Anna Harrison, First Lady of the United States (d. 1864)
- July 27 – Teréz Brunszvik Hungarian noble, pedagogue (d. 1861)
- July 28 – Hussey Vivian, 1st Baron Vivian, British Army general (d. 1842)
- July 31 – Emmanuel Dupaty, French singer, writer (d. 1851)
- August 2
- August 6
- August 7
- August 8 – Richard Blakemore, English politician (d. 1855)
- August 9 – Jacob Brown, American general (d. 1828)
- August 14 – Pieter Adrianus Ossewaarde, Dutch politician (d. 1853)
- August 15
- August 16
- August 18 – Johann Leonhard Pfaff, Bischof von Fulda (d. 1848)
- August 20
- August 22 – August von Vécsey, Austro-Hungarian general (d. 1857)
- August 23 – Mark Cubbon, British army officer (d. 1861)
- August 25 – Karl Joseph Hieronymus Windischmann, German philosopher, anthropologist (d. 1839)
- August 26 – William Joseph Behr, German publicist, writer (d. 1851)
- August 27 – Frederick Graff, American hydraulic engineer (d. 1847)
- August 28
- August 29 – Niels Wulfsberg, Norwegian publisher (d. 1852)
- August 31
- September 1 – Honoré Charles Reille, French general, Marshal of France (d. 1860)
- September 4 – Jean-François Le Gonidec, Linguist and translator of the bible (d. 1838)
- September 6 – Aleksey Greig, Russian admiral (d. 1845)
- September 7 – John Jebb, Irish writer (d. 1833)
- September 8
- September 9 – Francisco Ramón Vicuña, President of Chile (d. 1849)
- September 10
- September 11 – Narciso Fernández de Heredia, 2nd Count of Heredia-Spínola, Prime Minister of Spain (d. 1847)
- September 13
- September 14
- September 15 – William A. Griswold, American politician (d. 1846)
- September 16 – Hermano José Braamcamp de Almeida Castelo Branco, Portuguese nobleman and politician (d. 1846)
- September 17
- September 19 – José Félix Ribas, hero of the Venezuelan War of Independence (d. 1815)
- September 22 – Philip Milledoler, American minister, fifth President of Rutgers College (d. 1852)
- September 23 – Jens Christian Berg, Norwegian lawyer and historian (d. 1852)
- September 24 – Nathan Heald, officer in the United States Army during the War of 1812 (d. 1832)
- September 25 – Pierre Flor, Norwegian politician (d. 1848)
- September 26 – James Grimston, 1st Earl of Verulam, British peer and Member of Parliament (d. 1845)
- September 29
- September 30 – Robert Adrain, Irish-born American mathematician, scientist (d. 1843)
- October 6 – Johann Anton André, German composer, music publisher (d. 1842)
- October 7 – Ramón Power y Giralt, Puerto Rican politician and Spanish admiral (d. 1813)
- October 9
- October 12
- October 13 – John Wentworth Loring, British Royal Navy admiral (d. 1852)
- October 14 – Godfrey Macdonald, 3rd Baron Macdonald of Slate, British general (d. 1832)
- October 15
- October 17 – Ole Paulssøn Haagenstad, Norwegian politician (d. 1866)
- October 18
- October 19
- October 21
- October 23 – Gottlob Friedrich Thormeyer, German architect (d. 1842)
- October 24 – Bahadur Shah II, Mughal emperor (d. 1862)
- October 26
- October 30 – Catterino Cavos, Russian composer (d. 1840)
- November 1 – Christian Adolph Diriks, Norwegian lawyer, statesman (d. 1837)
- November 2 – Jeromus Johnson, American politician (d. 1846)
- November 6 – August Wilhelm Hartmann, Danish composer (d. 1850)
- November 8
- November 9 – Daniel Waldron, American businessman (d. 1821)
- November 10 – James Elliot, American politician (d. 1839)
- November 13
- November 14 – Paul Johann Anselm Ritter von Feuerbach, German legal scholar (d. 1833)
- November 15 – James Carnahan, American clergyman and educator, ninth President of Princeton University (d. 1859)
- November 19 – Johann Karl Wilhelm Illiger, German biologist (d. 1813)
- November 21
- November 23
- November 25
- November 27 – Lauritz Weidemann, Norwegian politician (d. 1856)
- November 28
- January 8 – John Baskerville, English printer (b. 1706)
- January 13 – Johann Georg Walch, German theologian (b. 1693)
- February 2 – Sir John Rushout, 4th Baronet, England (b. 1685)
- February 5 – Eusebius Amort, German Catholic theologian (b. 1692)
- February 6 – William Dowdeswell, English politician (b. 1721)
- February 15 – Peter Dens, Belgian Catholic theologian (b. 1690)
- April 27 – Col. Thomas Gardner, American politician, heroic soldier (b. 1724)
- May 10 – Marie Magdalene Charlotte Ackermann, German actress (b. 1757)
- June 17
- June 23 – Karl Ludwig von Pöllnitz, German adventurer, writer (b. 1692)
- July 11 – Simon Boerum, American Continental Congressman (b. 1724)
- August 27 – James Burgh, British Whig politician, writer (b. 1714)
- September 6 – Jean-Baptiste Bullet, French writer (b. 1669)
- September 16 – Allen Bathurst, 1st Earl Bathurst, English privy councillor (b. 1684)
- October 2 – Fukuda Chiyo-ni, Japanese poet (b. 1703)
- October 18 – Christian August Crusius, German philosopher, theologian (b. 1715)
- October 21 – Peyton Randolph, American President of the Continental Congress (b. 1721)
- November 9 – Francisco Ximenes de Texada, Spanish-born 69th Grandmaster of the Knights Hospitaller (b. 1703)
- November 21 – John Hill, English writer
- November 24 – Lorenzo Ricci, Italian Jesuit leader (b. 1703)
- December 7 – Charles Saunders, British admiral
- December 31 – Richard Montgomery, American general (killed in battle) (b. 1738)
- date unknown – Barbe de Nettine, politically influential banker in the Austrian Netherlands (b. 1706)