What is the name of the Islamic calendar system used to determine Ramadan and Eid dates?

The Islamic calendar system used to determine Ramadan and Eid dates is the Hijri calendar.

The Hijri, or Islamic, calendar is a lunar calendar consisting of 12 months. Its era begins with the Hijra, Muhammad’s migration from Mecca to Medina in 622 CE. Because lunar months are shorter than the solar year, Islamic dates move earlier by roughly 10 to 12 days each year in the Gregorian calendar.

Ramadan is the ninth month of the Hijri calendar. Eid al-Fitr begins after Ramadan, while Eid al-Adha occurs during Dhu al-Hijjah, the month of pilgrimage. The start of a month may be determined through crescent observation or calculated astronomical methods, depending on the community.

The Hijri calendar is therefore not simply another name for the Gregorian calendar. The two systems measure time differently and are used together in many countries.