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1770 (MDCCLXX) was a common year starting on Monday (dominical letter G) of the Gregorian calendar and a common year starting on Friday (dominical letter C) of the Julian calendar, the 1770th year of the Common Era (CE) and Anno Domini (AD) designations, the 770th year of the 2nd millennium, the 70th year of the 18th century, and the 1st year of the 1770s decade. Note that the Julian day for 1770 is 11 calendar days difference, which continued to be used from 1582 until the complete conversion of the Gregorian calendar was entirely done in 1929.
- January 1 – Foundation of Fort George, Bombay laid by Colonel Keating, principal engineer, on the site of the former Dongri Fort.
- March 5 – Boston Massacre: Eleven Americans are shot, five fatally, by British troops in an event that helps start the American Revolutionary War five years later.
- March 26 – First voyage of James Cook: English explorer Captain James Cook and his crew aboard HMS Endeavour complete the circumnavigation of New Zealand.
- April 18 (April 19 by Cook's log) 18:00 – First voyage of James Cook: English explorer Captain James Cook and his crew become the first recorded Europeans to encounter the eastern coastline of the Australian continent.
- April 20 – Georgian king Erekle II defeats the Ottoman forces in the battle of Aspindza, despite being abandoned by an ally, Russian General Totleben.
- April 29 – First voyage of James Cook: Captain Cook drops anchor on HMS Endeavour in a wide bay about 16 km (10 mi) south of the present city of Sydney, Australia. Because the young botanist on board the ship, Joseph Banks, discovers 30,000 specimens of plant life in the area, 1,600 of them unknown to European science, Cook names the place Botany Bay on May 7.
- May 7 – Fourteen-year-old Marie Antoinette arrives at the French court.
- May 16
- February 21 – Georges Mouton, Marshal of France (d. 1838)
- March 2 – Louis-Gabriel Suchet, Marshal of France (d. 1826)
- March 20 – Friedrich Hölderlin, German writer (d. 1843)
- April 3 – Theodoros Kolokotronis, Greek general (d. 1843)
- April 7 – William Wordsworth, English poet (d. 1850)
- April 8 – John Campbell, Australian public servant and politician (d. 1830)
- April 11 – George Canning, Prime Minister of the United Kingdom (d. 1827)
- April 25 – Georg Sverdrup, Norwegian philologist (d. 1850)
- April 30 – David Thompson, English-Canadian explorer (d. 1857)
- May 10 – Louis-Nicolas Davout, Marshal of France (d. 1823)
- May 15 – Ezekiel Hart, Canadian entrepreneur & politician (d. 1843)
- May 29 – Charles Adams, second son of President John Adams (1735–1826) (d. 1800)
- June 1 – Friedrich Laun, German author (d. 1849)
- June 3 – Manuel Belgrano, Argentine politician and general in the Independence War (d. 1820)
- June 7 – Robert Jenkinson, 2nd Earl of Liverpool, Prime Minister of the United Kingdom (d. 1828)
- June 20 – Moses Waddel, American educator/minister and bestselling author (d. 1840)
- August 1 – William Clark, explorer, Governor of Missouri Territory, and Superintendent of Indian Affairs (d. 1838)
- August 3 – King Frederick William III of Prussia (d. 1840)
- August 27 – Georg Wilhelm Friedrich Hegel, German philosopher (d. 1831)
- October 10 – Adam Johann von Krusenstern, Baltic German explorer who lead the First Russian circumnavigation (d. 1846)
- December 17 – Ludwig van Beethoven, German composer] (d. 1827)
- December 18 – Nicolas Joseph Maison, Marshal of France and Minister of War (d. 1840)
- January 7 – Carl Gustaf Tessin, Swedish politician (b. 1695)
- January 20 – Charles Yorke, Lord Chancellor of Great Britain (b. 1722)
- February 26 – Giuseppe Tartini, Italian composer and violinist (b. 1692)
- March 5 – Crispus Attucks, African-American, first to die in the Boston Massacre (b. 1723)
- March 27 – Giovanni Battista Tiepolo, Venetian artist (b. 1696)
- April 25 – Jean-Antoine Nollet, French abbot and physicist (b. 1700)
- May 30 – François Boucher, French painter (b. 1703)
- June 23 – Mark Akenside, English poet and physician (b. 1721)
- July 27 – Robert Dinwiddie, British colonial Governor of Virginia (b. 1693)
- August 24 – Thomas Chatterton, English poet (b. 1752)
- September 30
- October 14 – Benning Wentworth, colonial governor of New Hampshire (b. 1696)
- October 18 – John Manners, Marquess of Granby, British soldier (b. 1721)
- November 9 – John Campbell, 4th Duke of Argyll, Scottish politician
- November 13 – George Grenville, Prime Minister of the United Kingdom (b. 1712)
- November 24 – Charles-Jean-François Hénault, French historian (b. 1685)
- December 5 – James Stirling, Scottish mathematician (b. 1692)