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1771 was a common year starting on Tuesday of the Gregorian calendar and a common year starting on Saturday of the Julian calendar, the 1771st year of the Common Era (CE) and (AD) designations, the 771st year of the Anno Domini 2nd millennium, the 71st year of the 18th century, and the 2nd year of the 1770s decade. As of the start of 1771, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
January 5 – The Great Kalmyk ( Torghut) Migration is led by Ubashi Khan, from the east bank of the Lower Volga River back to the homeland of Dzungaria, at this time under Qing Dynasty rule.
January 9 – Emperor Go-Momozono accedes to the throne of Japan, following his aunt's abdication.
February 12 – Upon the death of Adolf Frederick, he is succeeded as King of Sweden by his son Gustav III. At the time, however, Gustav is unaware of this, since he is abroad in Paris. The news of his father's death reaches him about a month later.
March – War of the Regulation: North Carolina Governor William Tryon raises a militia, to put down the long-running uprising of backcountry militias against North Carolina's colonial government.
March 12 – The North Carolina General Assembly establishes Wake County (named for Margaret Wake, the wife of North Carolina Royal Governor William Tryon) from portions of Cumberland, Johnston and Orange counties. Bloomsbury (later known as Wake Courthouse) is made the informal county seat.
March 15 – The Smeatonian Society of Civil Engineers first meets in London, the world's oldest engineering society.  
May 11 – War of the Regulation: North Carolina Governor William Tryon marches his military out of Hillsborough, to come to the aid of General Hugh Waddell's beleaguered forces. Tryon's army stops at Alamance Creek, 5 miles (8.0 km) away from the Regulator army.
May 16 – War of the Regulation – Battle of Alamance: Regulators reject an appeal by Governor Tryon to peacefully disperse. Governor Tryon's forces crush the rebellion, causing many Regulators to move to frontier areas outside of North Carolina.
May 23 – Battle of Lanckorona: A force of 4,000 Russians under Alexander Suvorov defeat a Polish formation of 1,300 men.
May – Three battles of Sarbakusa: An alliance of three of the most powerful aristocrats of Ethiopia (Goshu of Amhara, Wand Bewossen, and Fasil of Damot) defeats Ras Mikael Sehul and Emperor Tekle Haymanot I, taking control of Ethiopia.
July 13 – Russo-Turkish War (1768–74): Russian forces occupy the Crimea, under Prince Vasily Dolgorukov. 
July 17 – Bloody Falls massacre: Chipewyan chief Matonabbee, traveling as the guide to Samuel Hearne on his Arctic overland journey, massacres a group of unsuspecting Inuit.
August 8 – The first recorded town cricket match is played, at Horsham, England. 
September 8 – In California, Fathers Pedro Cambon and Angel Somera found Mission San Gabriel Arcángel, in what is now San Gabriel, California.
September 15– 17 – The Moscow plague riot results from an outbreak of bubonic plague, which kills 57,000.
October 9 – The Dutch merchant ship sinks off the coast of Finland; Captain Raymund Lourens and his crew escape unharmed. Vrouw Maria
October 17 – The opera by Ascanio in Alba Wolfgang Mozart, age 15, premieres in Milan.
November 16 – During the night the River Tyne, England, floods, destroying many bridges and killing several people; the replacement main bridge at Newcastle upon Tyne will not be completed until 1781.
The territory of
Baden-Baden is inherited by Charles Frederick, Margrave of Baden-Durlach, reunifying the territories of Baden. The trade monopoly with
Iceland is transferred to the Danish crown. The North Carolina General Assembly passes an act establishing the town of
Martinsborough, named for Royal Governor Josiah Martin, on the land of Richard Evans, which will serve as the seat of Pitt County. Construction of the
Putuo Zongcheng Temple complex in Chengde, China is completed during the reign of the Qianlong Emperor.
Limoges porcelain manufacture is established in France.
Slovene literature: István Küzmics, the Hungarian Slovene writer and evangelical pastor, publishes (in Halle) the , a translation of the Nouvi Zákon New Testament into the Prekmurje Slovene language, with discrete South Slavic artwork.
February 14 – Hanne Tott, Danish circus artist, circus manager (d. 1826)
March 16 – Antoine-Jean Gros, French painter (d. 1835)
March 20 – Heinrich Clauren, German author (d. 1854)
March 25 – Germanos III of Old Patras, Greek Metropolitan Bishop of Patras (d. 1826)
April 3 – Hans Nielsen Hauge, Norwegian revivalist, entrepreneur (d. 1824)
April 13 – Richard Trevithick, English inventor (d. 1833)
April 18 – Karl Philipp, Prince of Schwarzenberg, Austrian field marshal (d. 1820)
April 27 – Jean Rapp, French general (d. 1821)
May 1 – Cajsa Wahllund, Finnish restaurateur (d. 1843)
May 11 – Laskarina Bouboulina, Greek independence heroine (d. 1825)
May 14 – Robert Owen, Welsh social reformer (d. 1858)
May 16 – Louis Henri Loison, French general (d. 1816)
June 5 – Ernest Augustus I of Hanover (d. 1851)
June 24 – Éleuthère Irénée du Pont, French-American chemist, industrialist (d. 1834)
August 15 – Sir Walter Scott, Scottish novelist, poet (d. 1832)
September 5 – Archduke Charles of Austria, Austrian general, statesman (d. 1847)
September 11 – Mungo Park, Scottish explorer (d. 1806)
September 17 – Johann August Apel, German writer, jurist (d. 1816)
September 23 – Emperor Kōkaku of Japan (d. 1840)
October 9 – Frederick William, Duke of Brunswick-Wolfenbüttel (d. 1815)
October 23 – Jean-Andoche Junot, French general (d. 1813)
November 14 – Marie François Xavier Bichat, French anatomist and physiologist (d. 1802)
December 14 – Regina von Siebold, German physician and obstetrician (d. 1849)
December 27 – William Johnson, Associate Justice of the Supreme Court of the United States (d. 1834) Unknown –
William Lloyd, Welsh Anglican priest turned schoolteacher and Methodist preacher (d. 1841)
January 5 – John Russell, 4th Duke of Bedford, British statesman (b. 1710)
January 11 – Jean-Baptiste de Boyer, Marquis d'Argens, French writer (b. 1704)
January 23 – Jean Charles de Saint-Nectaire, French general (b. 1685)
February 12 – Adolf Frederick, King of Sweden (b. 1710)
February 20 – Jean-Jacques d'Ortous de Mairan, French geophysicist (b. 1678)
March 8 – Louis August le Clerc, French-born sculptor (b. 1688)
May 21 – Christopher Smart, English poet (b. 1722)
June 8 – George Montagu-Dunk, 2nd Earl of Halifax, English statesman (b. 1716)
July 14 – Chen Hongmou, Chinese scholar and philosopher (b. 1696)
July 30 – Thomas Gray, English writer (b. 1716)
September 17 – Tobias Smollett, Scottish novelist (b. 1721)
November 6 – John Bevis, English physician, astronomer (b. 1695)
November 13 – Konrad Ernst Ackermann, German actor (b. 1712)
December 6 – Giovanni Battista Morgagni, Italian anatomist (b. 1682)
December 23 – Marie-Marguerite d'Youville, Canadian saint (b. 1701)
December 26 – Claude Adrien Helvétius, French philosopher (b. 1715)
December 27 – Henri Pitot, Italian-born French engineer (b. 1695)