The Hijri era is calculated according to the Islamic lunar calendar and not the Julian or Gregorian solar one. It thus does not begin on January 1, 1 CE, but on the first day of the month of Muharram which occurred in 622 CE. Its Julian equivalent was April 19 but it is sometimes mistakenly placed on July 16. The error derives from the tabular Islamic calendar which was devised by later Islamic astronomers. This reckons time backwards according to the lunar calendar, which causes it to miss the three intercalary months (about 88 days) added to the then-lunisolar calendar between the time of the Hijra and AH 10, when Muhammad is recorded as having received a revelation prohibiting their use.
The date of the Hijra itself did not form the Islamic New Year. Instead, the system continues the earlier ordering of the months with the Hijra occurring around the 8th day of Rabi al-Awwal, 66 days into the first year.
there was already an Arabian lunar calendar with named months. The years of its calendar, however, used conventional names rather than numbers: for example, the year of Muhammad and Ammar ibn Yasir's birth (570 CE) was known as the "Year of the Elephant". The year of the Hijra (622-23 CE) was initially named the "Permission to Travel".
17 years after the Hijra, a complaint from Abu Musa Ashaari prompted the caliph Umar to abolish the practice of named years and to establish a new calendar era. Rejected proposals included dating from the year of Muhammad's birth or death. Tradition credits ʿAli with the proposal to date from the year during which the Muslims established a new community (Ummah) in Medina. The order of the months within the calendar was then debated. Rejected proposals included Rajab, which had been a sacred month in the pre-Islamic period; Ramadan, which is a sacred month for Muslims; and Dhu al-Hijjah, the month of the Hajj. Tradition credits Othman with the successful proposal, simply continuing the order of the months that had already been established, beginning with Muharram. Adoption of this calendar was then enforced by Umar.