Battle of Roncevaux Pass: The Basques and Banu Qasi defeat a Frankish expedition, led by Counts Aznar and Ebles, in the Pyrenees.
Iñigo Arista revolts against the Frankish Empire, and establishes the Kingdom of Pamplona, with the support of the Caliphate of Córdoba.
November 11 – The Constitutio Romana establishes the authority of the Holy Roman Emperors over the papacy of Rome.
Vikings raid Bangor (modern Wales) for the second time, and plunder the bishopric (approximate date).
Zenpuku-ji, one of the oldest Tokyo temples, is founded by the Japanese Buddhist monk Kūkai.
February 11 – Pope Paschal I dies after a 7-year reign, and is succeeded by Eugene II, as the 99th pope of the Catholic Church.
Al-Tirmidhi, Persian scholar and hadith compiler (d. 892)
Chen Tao, Chinese poet (d. 882)
Ibn Majah, Persian scholar and hadith compiler
Li Pu, prince of the Tang Dynasty (d. 828)
Muhammad ibn Abdallah, Muslim governor (or 825)
Zhao Chou, Chinese warlord (d. 889)
February 11 – Paschal I, pope of the Catholic Church
March 5 – Suppo I, Frankish nobleman
August 5 – Heizei, emperor of Japan (b. 773)
Adelard, duke of Spoleto (Italy)
Han Yu, Chinese philosopher and poet (b. 768)
Mauring, Frankish nobleman
Mu Zong, emperor of the Tang Dynasty (b. 795)
Óengus of Tallaght, Irish bishop
Ruthmael, Irish abbot and bishop
Sayyida Nafisa, Arab female scholar (b. 762)
Wetti of Reichenau, German scholar
Zhang Hongjing, Chinese chancellor (b. 760)
Year 824 (DCCCXXIV) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar.