|Centuries:||5th century – 6th century – 7th century|
|Decades:||480s 490s 500s – 510s – 520s 530s 540s|
|Years:||510 511 512 – 513 – 514 515 516|
|513 by topic|
|State leaders – Sovereign states|
|Birth and death categories|
|Births – Deaths|
|Establishment and disestablishment categories|
|Establishments – Disestablishments|
|Ab urbe condita||1266|
|Bahá'í calendar||-1331 – -1330|
|English Regnal year||N/A|
|Chinese calendar||壬辰年 (Water Dragon)
3209 or 3149
— to —
癸巳年 (Water Snake)
3210 or 3150
|- Vikram Samvat||569–570|
|- Shaka Samvat||435–436|
|- Kali Yuga||3614–3615|
|Igbo calendar||-487 – -486|
|Iranian calendar||109 BP – 108 BP|
|Islamic calendar||112 BH – 111 BH|
|Minguo calendar||1399 before ROC
|Thai solar calendar||1056|
|Wikimedia Commons has media related to 513.|
Year 513 (DXIII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Clementinus (or, less frequently, year 1266 Ab urbe condita). The denomination 513 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.
- Revolt of Vitalian: Vitalian, Byzantine general, revolts against emperor Anastasius I and conquers a large part of the Diocese of Thrace. He gains the support of the local people and assembles an army of 50,000–60,000 men.
- Anastasius I reduces taxes in the provinces of Bithynia and Asia to prevent them from joining the rebellion. Vitalian marched to Constantinople and encamps at the suburb of Hebdomon (modern Turkey).
- Anastasius I sends an embassy under the former consul Patricius to start negotiations. Vitalian declares his aims: restoration of Chalcedonian Orthodoxy and the settling of the Thracian foederati.
- Vitalian accepts a agreement and returns with his army to Lower Moesia. After a few inconclusive skirmishes, Anastasius I sends an Byzantine army (80,000 men) under his nephew Hypatius.
- Vitalian defeats the Byzantines at Acris (Bulgaria) on the Black Sea coast. He attacks their fortified Laager in darkness and in a crushing defeat kills a large part of the imperial army.
- King Kavadh I adopts the doctrine of the Mazdakites and breaks the influence of the magnates (nobility). 
- The Jewish community revolt at Ctesiphon against Mazdakism and establish an independent Jewish kingdom that last for seven years.
- Vigor becomes bishop of Bayeux. He opposes paganism and found a monastery later known as Saint-Vigor-le-Grand (Normandy).
- Gesalec, king of the Visigoths (approximate date)
- Shen Yue, Chinese historian and statesman (b. 441)
- Martindale, Jones & Morris 1980, p. 840
- Richard Nelson Frye, The History of Ancient Iran, Vol.3, (Beck'sche Verlangbuchhandlung, 1984), p. 323