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Year 413 (CDXIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Herclianus and Lucius (or, less frequently, year 1166 Ab urbe condita). The denomination 413 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.
|Ab urbe condita||1166|
|Balinese saka calendar||334–335|
|Chinese calendar||壬子年 (Water Rat)|
3109 or 3049
— to —
癸丑年 (Water Ox)
3110 or 3050
|- Vikram Samvat||469–470|
|- Shaka Samvat||334–335|
|- Kali Yuga||3513–3514|
|Iranian calendar||209 BP – 208 BP|
|Islamic calendar||215 BH – 214 BH|
|Minguo calendar||1499 before ROC|
|Seleucid era||724/725 AG|
|Thai solar calendar||955–956|
539 or 158 or −614
— to —
540 or 159 or −613
- Heraclianus, Roman usurper, lands in Italy with a large army to fight emperor Honorius. He is defeated in Umbria and flees to Carthage, where he is put to death by envoys of Honorius.
- May 8 – Honorius signs an edict providing tax relief for the Italian provinces Tuscia, Campania, Picenum, Samnium, Apulia, Lucania and Calabria, which were plundered by the Visigoths.
- The Visigoths, led by King Ataulf, conquer the towns of Toulouse and Bordeaux by force of arms. After a successful siege of Valence, he captures the usurper Jovinus and his brother Sebastianus. In Narbonne they are executed and their heads are sent to Honorius' court at Ravenna.
- Kumaragupta I succeeds his father Chandragupta II as emperor of the Gupta Empire (India).
- Jangsu becomes ruler of the Korean kingdom of Goguryeo.
- Augustine of Hippo, age 59, begins to writes his spiritual book De Civitate Dei (City of God) as a reply to the charge that Christianity was responsible for the decline of the Roman Empire.
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- March 7 – Heraclianus, Roman usurper
- September 13 – Marcellinus of Carthage, martyr and saint
- Chandragupta II, emperor of the Gupta Empire
- Gwanggaeto the Great, king of Goguryeo (b. 374)
- Jovinus, Roman usurper of Gaul
- Kumarajiva, Buddhist monk and translator (b. 344)
- Prudentius, Roman Christian poet (b. 348)
- Sebastianus, Roman usurper and brother of Jovinus
- Qiao Zong, warlord and prince of Chengdu