Here is a calculator that converts Gregorian calendar date to Muslim calendar date.
Traditionally, here is some information(I've actually discovered all this just now).
Solar calendar — calendar, which is based on the tropical year.
Tropical year - the time interval between two successive passages of the Sun through the vernal equinox.
Duration of the tropical year - 365,242196 days
During the tropical year there is a complete change of seasons
Lunar calendar - calendar, which is based on the synodic month.
Synodic month - the period of the Moon revolution around the Earth between the two new moons.
Duration the synodical month - 29.53059 days
During the synodical month there is a complete change of phases of the moon.
Well-known Gregorian calendar is solar, but the Muslim calendar is lunar.
A year in the Muslim calendar consists of 12 months, the duration of which alternate between 30 and 29 days. The last month consist of 29 days and during a leap years is extended to 30 days.
Without the introduction of leap years, the average duration of the months of the year would be strictly 29.5 days, which would give us a big error. Leap years are following a 30-year cycle and falls on the 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29 year of the cycle. Thus, every 30 years contains 19 normal years of 354 days and 11 leap years of 355 days.Thus, the average length of the year will be approximately equal to 354.366(6) days, and the month will be equal to 29.5305(5) days, which is much closer to the length of the synodic month.
Since the calendar is based on the moon and the lunar year is shorter than the solar year, the month is not tied to the seasons, and each year they are shifting for about 11 days relative to the solar calendar.
Generally speaking, earlier, in pre-Islamic times, the Arabs used a solar-lunar calendar, and there was a 13 month, who introduced an amendment to the solar year, so that the month remained tied to the seasons.
However, in 631 AD, the Prophet Muhammad has forbidden to add these days and the Muslim year became strictly lunar. Therefore, for example, the month of Ramadan, whose name in Arabic means "to burn", may happen in the winter.
The beginning of chronology or the era(see Old Russian (Byzantine) system of chronology) in Muslim calendar is the date of the expulsion of Mohammed from Mecca to Medina, or Hidzhry (Hegiræ). The days of the Muslim calendar are counted from the sunset, so the sunset of the previous day started 1 day 1 month 1 year of exile (Anno Hegiræ, A.H.)
Дни в мусульманском календаре считаются от заката, таким образом, закат предыдущего дня начал 1 день 1 месяца 1 года от изгнания (Anno Hegiræ, A.H.)
In the Julian calendar (the Gregorian did not yet exist) was July 16, 622 A.D.
Calendar used by the calculator, is the most common in the Islamic world the secular (civil) calendar, the beginning of the month is determined astronomically. Traditionally, it is believed that the new month begins with the moment when for the first time after sunset the crescent of the new moon becomes visible, and it can be attested by the Islamic clerics. Thus, the beginning of the month may depend on the location of the observer, weather, visibility, etc.