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1786 (MDCCLXXXVI) was a common year starting on Sunday (dominical letter A) of the Gregorian calendar and a common year starting on Thursday (dominical letter D) of the Julian calendar, the 1786th year of the Common Era (CE) and Anno Domini (AD) designations, the 786th year of the 2nd millennium, the 86th year of the 18th century, and the 7th year of the 1780s decade. As of the start of 1786, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- August 11 – Captain Francis Light acquired the island of Penang from the Sultan of Kedah on behalf of the British East India Company, renaming it Prince of Wales Island in honour of the heir to the British throne, the first colony of the British Empire in Southeast Asia.
- August 17 : The paternal nephew of Frederick the Great, Frederick William, became King of Prussia, as Frederick William II.
- August 18 : The Kingdom of Denmark–Norway chartered six settlements in Iceland to trade with it, thus ending the Danish–Icelandic Trade Monopoly and founding Reykjavík.
- August 29 – Shays' Rebellion began in Massachusetts.
- September–December – Goethe undertook his Italian Journey (published in 1817).
- September 2 – A hurricane struck Barbados.
- September 11–14 – Annapolis Convention was held, resulting in scheduling of the Philadelphia Convention.
- September 26 – Eden Agreement: Commercial treaty was signed between the Kingdoms of Great Britain and France.
- November 7 – The oldest musical organization in the United States, the Stoughton Musical Society, was founded.
- November 30 – Peter Leopold Joseph of Habsburg-Lorraine, Grand Duke of Tuscany, promulgated a penal reform making his country the first state to abolish the death penalty. November 30 is therefore commemorated by 300 cities around the world as Cities for Life Day.
- December 4 – Mission Santa Barbara was founded by Padre Fermín Lasuén as the tenth of the Spanish missions in California.
- December 20 – Robert Burns' "Address to a Haggis" first published, in Edinburgh.
- January 7 – John Catron, Associate Justice of the Supreme Court of the United States (d. 1865)
- January 8 – Nicholas Biddle, President of the Second Bank of the United States (d. 1844)
- January 12 – Sir Robert Inglis, Bt, English politician (d. 1855)
- January 23 – Auguste de Montferrand, French architect (d. 1858)
- February 16 – Maria Pavlovna of Russia, Grand duchess of Saxe-Weimar Eisenach (d. 1859)
- February 24 – Martin W. Bates, U.S. Senator from Delaware (d. 1869)
- February 26 – François Arago, French astronomer, physicist and politician (d. 1853)
- February 24 – Wilhelm Grimm, German philologist and folklorist (d. 1859)
- March 4 – Agustina de Aragón, Spanish heroine (d. 1857)
- March 22 – Joachim Lelewel, Polish historian (d. 1861)
- March 25 – Giovanni Battista Amici Italian astronomer, microscopist, and botanist (d. 1863)
- April 7 – William R. King, 13th Vice President of the United States (d. 1853)
- April 16 – John Franklin, British naval officer and explorer (d. 1847)
- April 28 – Elizabeth Andrew Warren, Cornish botanist and marine algolologist (d. 1864)
- May 12 – Jean-François Barrière, French historian (d. 1868)
- May 29 – Alexander Bryan Johnson, American philosopher (d. 1867)
- June 13 – Winfield Scott, American general and Presidential candidate (d. 1866)
- August 17
- August 25 – King Ludwig I of Bavaria (d. 1868)
- August 31 – Michel Eugène Chevreul, French chemist (d. 1889)
- September 10 – William Mason, American politician (d. 1860)
- September 11 – Friedrich Kuhlau, German composer (d. 1832)
- September 18
- September 24 – Charles Bianconi, Italian-Irish entrepreneur (d. 1875)
- September 29 – Guadalupe Victoria, 1st President of Mexico (d. 1843)
- November 18
- December 12 – William L. Marcy, American statesman (d. 1857)
- January 4 – Moses Mendelssohn, Jewish philosopher (b. 1729)
- January 7 – Jean-Étienne Guettard, French physician and scientist (b. 1715)
- January 11 – Joseph Jackson Lister, English opticist and physician (d. 1869)
- January 14 – Meshech Weare, Governor of New Hampshire (b. 1713)
- February 28 – John Gwynn, English architect and engineer (b. 1713)
- March 11 – Charles Humphreys, American delegate to the Continental Congress (b. 1714)
- April 10 – John Byron, British naval officer (b. 1723)
- May 2 – Petronella Johanna de Timmerman, Dutch poet and scientist (b. 1723)
- May 15 – Eva Ekeblad, Swedish scientist and agronomist, first female member of the Royal Swedish Academy of Sciences (b. 1724)
- May 19 – John Stanley, English composer (b. 1712)
- May 21 – Carl Wilhelm Scheele, Swedish chemist (b. 1742)
- May 25 – Pedro III of Portugal, consort of Queen Maria I of Portugal (b. 1717)
- June 19 – Nathanael Greene, major general in the Continental Army, 3rd Quartermaster General (b. 1742)
- August 17 – King Frederick II of Prussia ("Frederick the Great") (b. 1712)
- September 5 – Jonas Hanway, English merchant, traveler, and philanthropist (b. 1712)
- October 2 – Augustus Keppel, 1st Viscount Keppel, British admiral (b. 1725)
- October 17 – Johann Ludwig Aberli, Swiss artist (b. 1723)
- October 20 – Humphrey Sturt, British architect (b. 1725)
- November 30 – Bernardo de Gálvez, Spanish military leader who aided the United States in its quest for independence in the American Revolutionary War (b. 1746)
- December 26 – Gasparo Gozzi, Italian critic and dramatist (b. 1713)