The number of months in the sight of Allah is twelve (in a year) so ordained by Him the day He created the heavens and the earth; (9:36)

The starting date of the Muslim calendar is the Hijra or migration of the Prophet Muhammad صلى الله عليه و سلم, from Makkah to Yathrib (later known as Madinah), about 250 miles to the north. The Prophet Muhammad صلى الله عليه و سلم left Makkah on the date corresponding to 16 July 622 CE in the Julian calendar and arrived at Madinah on 22 September 622 CE. About seventeen years later, the Muslim calendar was introduced by the second Caliph, Umar ibn al-Khattab رضي الله عنه, who was faced with the practical problems of administering a rapidly expanding empire in which correspondence between distant places had to be accurately dated. The introduction of the new calendar also gave expression to the feelings of all Muslims that a new era began with the migration to Madinah. Caliph Umar رضي الله عنه ordered that the Muslim calendar should be held to have begun on the day the Prophet Muhammad صلى الله عليه و سلم left Makkah, i.e., 16 July 622 CE. In English this is usually abbreviated in the Latin form AH (Anno Hegirae: 'in the year of the Hijra)

The Muslim year is purely lunar, consisting of twelve months containing, in alternate sequence, thirty and twenty-nine days. Thus it is approximately eleven days shorter than the solar year, with the result that in each cycle of 32.5 years, the individual months pass through all the solar seasons. If, for example, the Hajj (which takes place in the last month of the Muslim calendar) occurs at the height of summer, it will occur in the coolest season 16.25 years later, and the same time in summer again after another 16.25 years.

The twelve months forming the Muslim year are known as;

16 July 622 CE was officially declared as 1 Muharram AH 1.

Muharram Safar Rabi Awal Rabi Akyrah Jumada Awal Jumada Akyrah Rajab Shaaban Ramadan Shawwal Dhu-al-Qada Dhu-al-Hijja

The common year, therefore, has 354 days. But the mean length of a lunar year is 354 days, 8 hours, 48 minutes, 36 seconds, and the period of mean lunation is 29 days, 12 hours, 44 minutes, 3 seconds. This difference of 8 hours, 48 minutes, 36 seconds (which is almost equal to 11/30th of a day), by which the astronomical lunar year is the longer, is compensated by the intercalation of eleven days in every cycle of thirty years at the stated intervals. The most commonly used method of intercalation is to make years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 in the cycle into leap years, called kabisha. The intercalary day it self is always added to the twelfth month, i.e., the month of Dhu-al-Hijja which has twenty-nine days in the common year - in a kabisha year it has 30 days. Thus, to determine whether a Muslim year is common or kabisha, divide it by 30. If the remainder is 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 or 29, the year is kabisha, having 355 days; otherwise, it is a common year consisting of 354 days. For instance, AH 1400 gives a remainder 20 and is a common year. AH 1406 (remainder 26) is a kabisha year.

The day in the Muslim calendar is twenty-four hours in length. However, it is reckoned to commence not from midnight (as in the Christian calendar) but from the sunset preceding it, because the first day of the month is fixed by the first sight of the new moon observed at sunset. As a result, the Muslim and Christian days, though of the same length, do not cover exactly the same twenty-four hours, which can lead to an incorrect dating of an event if this difference is overlooked.

Although in modern times mathematically calculated calendars are widely available and used, some Muslims still use the ancient practice of actually observing the new moon to establish the beginning of a month, especially the fasting month of Ramadan and the following month of Shawwal.

When Rome emerged as a world power, the difficulties of making an accurate calendar were well known, but the Romans complicated their lives further because of their superstition that even numbers were unlucky. Hence their months were 29 or 31 days long with the exception of February, which had 28 days. However, 4 months of 31 days, 7 months of 29 days, and 1 month of 28 days added up to only 355 days. Therefore, the Romans invented an extra month called Mercedonius of 22 or 23 days. It was added every second year.

In the Christian or Julian calendar, named after Julius Caesar (100 or 102-44 BCE), who introduced it at the suggestion of the Egyptian astronomer Sosigenes as a reform of the old Roman calendar, the years are reckoned from the birth of Christ, and so are known as years AD (Anno Domini: 'in the year of the Lord'), or simply CE (Common Era) as non-Christian usage in place of AD. It fixed the average length of the year as 365.25 days, each fourth year being a Leap year, making up the omitted quarters by having 366 days. Also, Caesar decreed the year began with the first of January, not with the vernal equinox in late March. The new calendar officially began on 1 January 45 BCE. It is still the calendar used by the Eastern Orthodox Church.

Since the time which the earth takes to complete its orbit is 365 days, 5 hours, 48 minutes and 46 seconds, in the Julian calendar a year was about eleven minutes longer than a solar year. The resulting cumulative error became about ten days by the close of the sixteenth century, which  was rectified in 1582 by Pope Gregory X111 (1502-85), who ordained that 5 October in that year be called 15 October. In order to prevent further accumulation of error, he also ordered that while each year divisible by four should contain 366 days, as in the Julian calendar, centenary years should be counted as Leap years only if they are divisible by 400. Thus, 1600 was a Leap year but not 1700, 1800 or 1900, while 2000 CE will be a Leap year. It is this modified version, known as the Gregorian calendar, which is in use now.

Different countries adopted the calendar at different times. Great Britain (including her Dominions), for instance, did not adopt it until 1752, by which time she found herself eleven days behind the rest of Europe which was rectified by 3 September being reckoned as 14 September. It was adopted by Italy, France, Spain, Portugal and Luxembourg in 1582, Poland in 1586, Japan in 1872, China in 1912, Turkey and Soviet Russia in 1918 and by Greece as late as 1923.

I have derived the following perpetual formulae to convert Christian calendar into Muslim calendar and vice versa. To ascertain an approximate date of the commencement of a given Christian year (CE) in relation to Hijra year (AH), subtract 621.5643 from CE and then multiply the resultant figure by 1.030684:

Likewise, to convert a Hijra to Christian year, multiply AH by 0.970229 and then add 621.5643 to it:

As an illustration on the use of the first formula, consider the year 1994 CE; 1.030684(1994-621.5643) = 1414.5475, giving the year AH 1414; 0.5475 x 12 = 6.57, gives six complete months; finally, to obtain the day in the seventh month (Rajab), multiply 0.57 by 30 (number of days in Rajab) which gives 17.1 (approximately 17). Thus, according to the formula, the year 1994 started on 17th Rajab AH 1414. The year 1994 CE, in fact, began on 19th Rajab AH 1414.

As an illustration of the second formula, consider the year AH 1408; 0.970229 x 1408 + 621.5643 = 1987.6467, giving the year 1987 CE. 0.6467 x 12 = 7.7604, gives seven complete months; 0.7604 x 31 = 23.6 which is approximately equal to 24 days in the eighth month (August), 31 being the number of days in August. This date of 24th August 1987 may be compared with the actual date of 26th August 1987 on which the year AH 1408 began.

Once the corresponding Muslim date (or Christian date) for 1st January of a CE year (for 1st Muharram of an AH year) has be calculated using the above formulae, any other date in that CE year (or AH year) can easily be worked out by adding the appropriate number of months and days.

Extensive tables for calculating such conversion of Muslim and Christian dates are available in the literature, the latest available cover the years up to 2222 CE. But the above formulae, though approximate by a few days, are easily usable and for perpetual use.