January–March

• January 1
  • The Burmese Konbaung Dynasty annexes the Mrauk U Kingdom of Arakan.
  • The first issue of the Daily Universal Register, later known as The Times, is published in London.
• January 7 – Frenchman Jean-Pierre Blanchard and American John Jeffries travel from Dover, England to Calais, France in a hydrogen gas balloon, becoming the first to cross the English Channel by air.
• January 11 – Richard Henry Lee is elected as President of the U.S. Congress of the Confederation.^[1]
• January 20 – Battle of Rạch Gầm-Xoài Mút: Invading Siamese forces, attempting to exploit the political chaos in Vietnam, are ambushed and annihilated at the Mekong River, by the Tây Sơn.
• January 27 – The University of Georgia in the United States is chartered by the Georgia General Assembly meeting in Savannah. The first students are admitted in Athens, Georgia in 1801.
• February 9 – Sir Warren Hastings, who has been governing India on behalf of King George III as the Governor-General of the Presidency of Fort William (later British India), resigns. Sir John Macpherson administers British India until General Charles Cornwallis arrives 19 months later.^[2]
• February 27 – The Confederation Congress votes an $80,000 expense to establish diplomatic relations with Morocco.^[3]
• March 7 – Scottish geologist James Hutton first presents his landmark work, Theory of the Earth; or an Investigation of the Laws observable in the Composition, Dissolution, and Restoration of Land upon the Globe to the Royal Society of Edinburgh.^[4]
• General Henry Knox is appointed as the Confederation Congress's Secretary of War, with added duties as the Secretary of Navy, both functions now of the U.S. Department of Defense.^[1]
• March 10
  • American engineer James Rumsey sends a letter to George Washington informing of his plans to create a successful steamboat.^[5]
  • Thomas Jefferson is appointed the new U.S. Minister to France, and Benjamin Franklin's request for permission to return home is accepted.^[1]

April–June

• April 19 – The Commonwealth of Massachusetts cedes all of its claims to territory west of New York State to the United States Confederation Congress. The area will become the southern portions of Michigan and Wisconsin.^[6][1]
• April 21 – The Empress Catherine the Great of the Russian Empire issues the Charter to the Towns, providing for "a coherent, unified system of administration" for new governments organized in Russia.
• April 26 – John Adams is appointed as the U.S. ambassador to the United Kingdom, and Thomas Jefferson as ambassador to France.^[7]
• April 28 – Astronomer William Herschel begins his second series of surveys of the stars, published in 1789.^[8]
• May 10 – A hot air balloon crashes in Tullamore, Ireland, causing a fire that burns down about 100 houses, making it the world's first aviation disaster (by 36 days).^[9]
• May 20 – The Northwest Ordinance of 1785, setting the rules for dividing the U.S. Northwest Territory (later Ohio, Indiana, Illinois, Wisconsin and Michigan) into townships of 36 square miles apiece, is passed by the Confederation Congress. Walter G. Robillard and Lane J. Bouman, Clark on Surveying and Boundaries (LexisNexis, 1997) The survey system will later be applied to the continent west of the Mississippi River.^[1]
• June 3 – The Continental Navy is disbanded.
• June 15 – After several attempts, Jean-François Pilâtre de Rozier and his companion, Pierre Romain, set off in a balloon from Boulogne-sur-Mer, but the balloon suddenly deflates (without the envelope catching fire) and crashes near Wimereux in the Pas-de-Calais, killing both men, making it the first fatal aviation disaster.

July–September

• July 2 – Don Diego de Gardoqui arrives in New York City as Spain's first minister to the United States.^[1]
• July 6 – The dollar (and a decimal currency system) is unanimously chosen as the money unit for the United States by the Congress of the Confederation.^[10]
• July 16 – The Piper-Heidsieck Champagne house is founded by Florens-Louis Heidsieck in Reims, France.
• August 1 – The fleet of French explorer Jean-François de Galaup, comte de Lapérouse leaves Paris for the circumnavigation of the globe.
• August 15 – Cardinal de Rohan is arrested in Paris; the Necklace Affair comes into the open.
• September 10 – The United States and the Kingdom of Prussia sign a Treaty of Amity and Commerce.^[11]
• September 13
  • The Bank of North America, central bank for the Confederation Congress government, loses its charter.^[12]
  • Benjamin Franklin returns to Philadelphia after seven years as the U.S. Ambassador to France and prepares to take office as the new Governor of Pennsylvania.^[13]

October–December

• October 5 – Vincenzo Lunardi of Italy becomes the first person to pilot a balloon over Scotland.^[14]
• October 13
  • The first newspaper in British India, the English-language Madras Courier, is published. It continues publication as a weekly until 1794.^[15]
  • France mints new Louis d'or coins, with the image of King Louis XVI on the obverse, and one-sixth less gold than the coins with King Louis XV's image.^[16]
• October 17 – The Commonwealth of Virginia stops the importation of new African slaves by declaring that "No persons shall henceforth be slaves within this commonwealth, except such as were so on the seventeenth day of October, 1785, and the descendants of the females of them." ^[17]
• October 18 – Benjamin Franklin takes office as the new President of the Supreme Council of Pennsylvania, at the time the equivalent of a republic as one of the 13 independent governments of the United States of America under the Articles of Confederation.^[13]
• November 23 – John Hancock of Massachusetts, the former President of the Continental Congress, is selected as the new President of the Congress of the Confederation, but is unable to take office because of illness.^[1]
• November 28 – The Treaty of Hopewell is signed between the United States of America and the Cherokee Nation.
• December 11 – An edict is issued limiting Masonic lodges throughout the Holy Roman Empire by Emperor Joseph II. With the exception of Vienna, Budapest and Prague, no Empire province may have more than one lodge.^[18]

Date unknown

• The University of New Brunswick is founded in Fredericton, New Brunswick.
• Coal gas is first used for illumination.
• Louis XVI of France signs a law that a handkerchief must be square.
• The British government establishes a permanent land force in the Eastern Caribbean, based in Barbados.
• Belfast Academy (later Belfast Royal Academy) is founded by Rev. James Crombie in Belfast, Northern Ireland.
• Friedrich Heinrich Jacobi publishes Letters on the Teachings of Spinoza, and starts the Pantheism controversy.
• Napoleon Bonaparte becomes a lieutenant in the French artillery.
• Cabinet des Modes, the first fashion magazine, is published in France.
• Mozart's "Haydn" String Quartets are published, as is his collaboration with Salieri and Cornetti, Per la ricuperata salute di Ofelia.

• Charles Adams, John Adams’ son and John Quincy Adams's brother enters Harvard in August, at age 15. A few months later, he starts to drink often and would get into trouble, and was almost expelled from Harvard when he was caught running naked through the Campus while drunk with other boys.