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|Ab urbe condita||2093|
|Balinese saka calendar||1261–1262|
|English Regnal year||13 Edw. 3 – 14 Edw. 3|
|Chinese calendar||己卯年 (Earth Rabbit)|
4036 or 3976
— to —
庚辰年 (Metal Dragon)
4037 or 3977
|- Vikram Samvat||1396–1397|
|- Shaka Samvat||1261–1262|
|- Kali Yuga||4440–4441|
|Japanese calendar||Ryakuō 3|
|Minguo calendar||572 before ROC|
|Thai solar calendar||1882–1883|
1466 or 1085 or 313
— to —
1467 or 1086 or 314
|Wikimedia Commons has media related to 1340.|
- January 26 – King Edward III of England is declared King of France.
- April 8 – The Marinid galleys, under the command of Muhammad ibn Ali al-Azafi, rout the Castellan fleet, off the coast of Algeciras.
- April–July – An abortive uprising occurs against Irene Palaiologina of Trebizond, the first of a number of coups, revolts, and succession disputes in the Trapezuntine Civil War (1340–1349).
- June 7 – Rotterdam is officially declared a city.
- June 24
- The Battle of Sluys is fought between the naval fleets of England and France. The former is under the command of Edward III of England, and the latter under that of Admiral Hugues Quiéret and treasurer Nicolas Béhuchet, assisted by Genoese mercenary galleys under Egidio Bocanegra. The French fleet is virtually destroyed, and both of its commanders are killed.
- Valdemar IV of Denmark, son of deceased King Christopher II, is elected to the throne, following 8 years of interregnum.
- September 25 – Hundred Years' War: The temporary Truce of Espléchin is signed between England and France.
- October 30 – Battle of Río Salado in Spain: The kings of Castile and Portugal defeat the Nasrid ruler of Granada, and his Moroccan allies.
- Europe has about 74 million inhabitants.
- March 5 – Cansignorio della Scala, Lord of Verona (d. 1375)
- March 6 – John of Gaunt, 1st Duke of Lancaster (d. 1399)
- August – Haakon VI, king of Norway 1355–1380 and of Sweden 1362–1364 (d. 1380)
- October – Geert Groote, Dutch founder of the Brethren of the Common Life (d. 1384)
- November 30 – John, Duke of Berry, son of John II of France (d. 1416)
- date unknown
- March 31 – Ivan I of Moscow (b. 1288)
- April 5 – William Melton, English archbishop
- April 6 – Emperor Basil Megas Komnenos of Trebizond
- April 7 – Bolesław Jerzy II of Mazovia (b. 1308)
- December 2 – Geoffrey le Scrope, Chief Justice of King Edward III of England
- December 4 – Henry Burghersh, English bishop and chancellor (b. 1292)
- December 20 – John I, Duke of Bavaria (b. 1329)
- date unknown – Simonida, queen consort of Serbia (b. 1294)