|Covid-19|January 14 – Third Battle of Panipat: Ahmad Shah Durrani and his coalition decisively defeat the Maratha Confederacy and restore the Mughal Empire to Shah Alam II.
January 16 – The British capture Pondichéry, India from the French.
February 8 – An earthquake in London breaks chimneys in Limehouse and Poplar.
March 8 – A second earthquake occurs in North London, Hampstead and Highgate.
March 31 – Earthquake in Lisbon, Portugal.
June 6 – A transit of Venus occurs, and is observed from 120 locations around the Earth. Mikhail Lomonosov discovers atmosphere of Venus.
July 17 - The first section of the Bridgewater Canal is opened, for the transportation of coal from local mines to Manchester.
September 8 – King George III of Great Britain marries Charlotte of Mecklenburg-Strelitz (Queen Charlotte).
September 19 – The slave trade to and within Portugal is forbidden.
September 22 – King George III and Queen Charlotte are crowned.
December 16 – Seven Years' War: After four months of siege, the Russians under Pyotr Rumyantsev take the Prussian fortress of Kolberg.
In Dutch Guyana, a "state" formed by escaped slaves signs a treaty with the local governor.
Matthew Boulton's Soho Manufactory opens.
The tune to Twinkle Twinkle Little Star is published in France.
Faber-Castell Company was founded by Kasper Faber in Nuremberg, Germany.
Johann Heinrich Lambert found a proof that π is irrational.
l'Ordre des Chevaliers Maçons Élus Coëns de l'Univers is founded.
January 17 – James Hall, Scottish geologist (d. 1832)
February 1 – Christian Hendrik Persoon, South African mycologist (d. 1836)
February 3 – Dorothea von Medem, Latvian diplomat and duchess of Courland (d. 1821)
February 16 – Charles Pichegru, French general (d. 1804)
February 22 – Erik Tulindberg, Finnish composer (d. 1814)
March 6 – Antoine-Francois Andreossy, French general (d. 1828)
May 3 – August von Kotzebue, German dramatist (d. 1819)
May 14 – Samuel Dexter, American lawyer and politician, 4th United States Secretary of War, 3rd United States Secretary of the Treasury (d. 1816)
June 3 – Henry Shrapnel, British Army officer and inventor (d. 1842)
June 7 – John Rennie the Elder, Scottish-born civil engineer (d. 1821)
October 21 – Louis Albert Guislain Bacler d'Albe, French painter and cartographer (d. 1824)
October 27 – Matthew Baillie, Scottish physician and pathologist (d. 1823)
November 4 – Bertrand Andrieu, French engraver of medals (d. 1822)
November 13 – John Moore, British general (d. 1809)
November 20 – Pope Pius VIII (d. 1830)
December 1 – Marie Tussaud, French wax modeller (d. 1850)
December 24 – Jean-Louis Pons, French astronomer (d. 1831)
December 27 – Michael Andreas Barclay de Tolly, Russian military commander (d. 1818)
January 4 – Stephen Hales, English physiologist, chemist, and inventor (b. 1677)
January 7 – Darkey Kelly, Irish madam and serial murderer, executed by burning
January 10 – Edward Boscawen, British admiral (b. 1711)
February 1 – Pierre François Xavier de Charlevoix, French historian (b. 1682)
April 4 – Theodore Gardelle, Swiss painter and enameler (b. 1722)
April 9 – William Law, English minister (b. 1686)
April 15 – Archibald Campbell, 3rd Duke of Argyll, Scottish politician (b. 1682)
April 17 – Thomas Bayes, English mathematician (b. c. 1702)
May 14 – Thomas Simpson, English mathematician (b. 1710)
June 2 – Jonas Alströmer, Swedish industrialist (b. 1685)
July 4 – Samuel Richardson, English writer (b. 1689)
July 9 – Carl Gotthelf Gerlach, German organist (b. 1704)
July 13 – Tokugawa Ieshige, Japanese shogun (b. 1712)
August 3 – Johann Matthias Gesner, German classical scholar (b. 1691)
September 8 – Bernard Forest de Bélidor, French engineer (b. 1698)
November 30 – John Dollond, English optician (b. 1706)
December 9 – Tarabai, Indian queen regent of the Maratha Empire (b. 1675)
December 23 – Alestair Ruadh MacDonnell, Scottish Jacobite spy (b. c. 1725)
December 25 – Dorothea of Schleswig-Holstein-Sonderburg-Beck, Margravine of Brandenburg-Bayreuth-Kulmbach (b. 1685)
1761 (MDCCLXI) was a common year starting on Thursday (dominical letter D) of the Gregorian calendar and a common year starting on Monday (dominical letter G) of the Julian calendar, the 1761st year of the Common Era (CE) and Anno Domini (AD) designations, the 761st year of the 2nd millennium, the 61st year of the 18th century, and the 2nd year of the 1760s decade. As of the start of 1761, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.