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|Ab urbe condita||2096|
|Balinese saka calendar||1264–1265|
|English Regnal year||16 Edw. 3 – 17 Edw. 3|
|Chinese calendar||壬午年 (Water Horse)|
4039 or 3979
— to —
癸未年 (Water Goat)
4040 or 3980
|- Vikram Samvat||1399–1400|
|- Shaka Samvat||1264–1265|
|- Kali Yuga||4443–4444|
|Japanese calendar||Kōei 2|
|Minguo calendar||569 before ROC|
|Thai solar calendar||1885–1886|
1469 or 1088 or 316
— to —
1470 or 1089 or 317
|Wikimedia Commons has media related to 1343.|
- January 14 – Arnošt of Pardubice becomes the last bishop of Prague and, subsequently, the first Archbishop of Prague
- January 27 – Pope Clement VI issues his bill Unigenitus, defining the doctrine of "The Treasury of Merits" or "The Treasury of the Church" as the basis for the issuance of indulgences by the Catholic Church.
- April 23 – The St. George's Night Uprising begins in Estonia.
- May 4 – St. George's Night Uprising: The "Four Estonian kings" are murdered at the negotiations with the Livonian Order.
- August 15 – Magnus IV of Sweden abdicates from the throne of Norway in favor of his son Haakon VI of Norway. However, Haakon is still a minor, allowing Magnus to remain de facto ruler.
- August 31 – A naval league is formed between the Pope, the Republic of Venice, the Knights Hospitaller and the Kingdom of Cyprus, to prepare the Smyrniote Crusades.
- November 25 – A tsunami, caused by an earthquake, devastates the Maritime Republic of Amalfi, among other places.
Tsar Dušan conquers Albania
- December 19 – William I, Margrave of Meissen (d. 1407)
- date unknown
- Emperor Chōkei of Japan (d. 1394)
- Constance of Aragon, queen consort of Sicily (d. 1363)
- Thomas Percy, 1st Earl of Worcester, English rebel (d. 1403)
- Nang Keo Phimpha, queen of Lan Xang (d. 1438)
- Tommaso Mocenigo, doge of Venice (d. 1423)
- Paolo Alboino della Scala, lord of Verona (d. 1375)
- Alexander Stewart, 1st Earl of Buchan (d. 1394)
- probable – Geoffrey Chaucer, English poet (approximate date) (d. 1400)
- January 20 – Robert of Naples (b. 1275)
- May 29 – Francesco I Manfredi, lord of Faenza
- June 22 – Aimone, Count of Savoy (b. 1291)
- June 23 – Giacomo Gaetani Stefaneschi, Italian cardinal (b. c. 1270)
- September 16 – Philip III of Navarre (b. 1306)
- December 15 – Hasan Kucek, Chobanid prince (b. c. 1319)
- date unknown