Calendar introduction

I. The problem: Specificities of the Islamic Calendar
In order to elaborate an Islamic calendar both scientifically exact and faithful to the Sharia it is necessary to take simultaneously into account certain astronomical facts and the teaching of the Prophet (saws).

I.1 The astronomical facts
The Islamic calendar is strictly lunar. This means that it follows the revolution of the moon around the earth and that of the earth around the sun.

The synodic month, that is, the duration after which the moon reverts to the same position with respect to the sun is 29.53 days. The phases of the moon and thus the Islamic calendar are linked to the synodic month.

We note that the sidereal month, that is, the duration after which the moon reverts to the same position with respect to the celestial sphere (the background of stars) is 27.31 days. The sidereal month is shorter than the synodic month because the earth drags the moon along with it in its orbit around the sun. Thus the moon reverts earlier to its position with respect to the background of fixed stars. The sidereal month is of no importance for the Islamic calendar.

The synodic month is a fraction of the number of days. Consequently, the months alternate between 29 and 30 days. Calculation allows us to predict whether a given month will have 29 or 30 days. It is known that, over a cycle of 30 years of the Islamic calendar, 19 years have 354 days and 11 years have 355 days (years of abundance). The rhythm obeys the moon cycles. The celestial clock is thus fashioned, thanks be to God.

I.2 The teaching of the Prophet (saws)
If you are asked about the phases of the moon, tell them: ‘They are marks in time, intended for men and for fixing the pilgrimage.'” (Koran, Surat 2, verse 189).

As stipulated by the Prophet (saws) in several Hadiths, the Hegirian month begins with the visibility of the new moon. A few are quoted below:

First Hadith
“We are an illiterate community. We neither write nor count. The months are sometimes like this and sometimes like that, i.e. sometimes with 29 days and sometimes with 30.” (Reported by Al Bukhari, vol. 5, p. 2485, according to the narration of the son of Omar, transmitted by Said Ibn Awz.)

Second Hadith
“Fast when you see the crescent and finish fasting when you see the crescent. If you do not perceive it, complete the month of Sha’ban with 30 days.” (Reported by Al Bukhari, vol. 5, p. 3476, according to the narration of Abu Hurayra, transmitted by Mohammed Ibn Ziyad.)

Third Hadith
“If you see it, fast, and if you see it (again), stop fasting. If you do not see it, determine it by calculation.” (Reported by Al Bukhari, vol. 5, p. 2467, according to the narration by the son of Omar.)

Calculation is thus necessary!

Fourth Hadith
(Transmitted by Kurayb, according to the narration by Abdullah Ibn Abbas.)

Kurayb said: “Umm Al-Fadhl, daughter of Harith, sent me on a mission to Mu’awiya in Damascus. I accomplished the mission and was still in Al Sham when Ramadan began. I saw the new moon there on a Friday evening. I returned to Medina and reached there towards the end of the month. I met Ibn Abbas who asked me: ‘When did you observe the new moon (of Ramadan)?’ I replied: ‘We saw it during the night of Friday?’ Ibn Abbas inquired: ‘Did you see it yourself?’ I replied: ‘Yes, I saw it and other people as well. Thus they started fasting and Mu’awiya fasted too.’ At this juncture Ibn Abbas said: ‘But we saw it during the night of Saturday, and either we see it (again), or otherwise we will pursue the fast on the thirtieth day.’ I asked: ‘Do you not accept the observation by Mu’awiya and his fast?’ Ibn Abbas replied: ‘No! It is thus that the Messenger of God has ordered us.’” (Reported by Muslim, vol. 7, p.178)

Wise commandment of the Prophet (saws).

Let us then imagine that the month of Ramadan in consideration here lasted 30 days in Medina. Had the observation in Damascus been taken into account, Ramadan would have been arbitrarily reduced to 29 days!

More generally, let us suppose that for a given country, say Algeria, the duration of Sha’ban and Ramadan are 30 days each in Algiers and 29 days each in some oasis in the Hoggar.

Algiers An Oasis in the Hoggar
Duration of Sha’ban 30 days 29 days
Duration of Ramadan 30 days 29 days

Let us admit that, based on an observation that confirms the month of Sha’ban at 30 days in Algiers, all of Algeria has been asked to start the fast. Let us further admit that the people in the oasis, having observed a month of Sha’ban shorter by one day, have started to fast one day ahead of the national territory.

Imagine that this striking anomaly is discovered in the very midst of the month of Ramadan. Intrigued, an Algerian national television team is sent to the Hoggar to interview the people of the oasis concerned by the event. The team remains until the end of the month in order to complete the story. It is quite possible that the reporters manage to see, to film and to diffuse on television the new moon of Shawwal. What is now to be done if the situation is as follows?

Algiers An Oasis in the Hoggar
1st of Ramadan 2nd of Ramadan
28th of Ramadan 29th of Ramadan (crescent filmed)
29th of Ramadan 1st of Shawwal

What is to be done? Follow what is really visible in the oasis and fast only 28 days in the national territory? Or ignore the fact of visibility and continue the fast in the oasis for 30 days?

Such a situation is, alas, not a purely imaginary one. We have often experienced this concretely not only in Algeria but in the rest of the Muslim world? The reason? The reason is simply that each point on the globe has it’s own calendar, a fact perfectly established by celestial mechanics.

We thus have the choice between observing the beginning of the Hegirian months from an agreed unique location – which seems rather difficult to admit – or, more broadly, by reference to a unique location.

Fifth Hadith
On a certain morning, the Prophet (saws) evoked the Impostor, the false Messiah, insisting on certain of his features… We asked him: “What is the length of his stay upon earth?” He answered: “40 days, with a day like an year, a day like a month, a day like a week, and, for the remaining days, following the example of your ordinary days.” We asked him again: “O, Messenger of God, as far as the day like an year is concerned, will it suffice for us to accomplish the prayer for a sole day? Non, he replied, calculate judiciously.”

(Reported by Muslim, vol. 2, p. 51 & 52, according to the narration of Annawas Ibn Sam’an.)

What can we conclude from this Hadith for the Hegirian calendar, if not that calculation is absolutely essential? Calculation corroborated by vision and vision guided by a forecasting calculation.

II. The pre-eminence of one calendar: that of Makkah
Amongst all the Islamic calendars applicable to the different countries of the world, that of Makkah is precious in order to determine the date of the annual pilgrimage.

downloadThe calendar of Makkah is not the universal Hegirian calendar. But its pre-eminence amongst all the other calendars led us to evolve – first of all – a methodology in order to establish a rigorously exact calendar for this holy city. Our site is named after this calendar. A generalisation of this methodology – developed and perfected in the course of years – now allows us to establish an exact calendar, respecting the precepts of Islam, for each and every country of the world, month after month.

In what follows, we will first describe our methodology for elaborating the Makkah calendar. We will then treat the question of the generalisation of this methodology to the other countries of the world.

II.1 How to calculate the calendar of Makkah?
The principle:The day of the birth of the new moon, let us scrutinise the heavens of Makkah after sunset, in order to perceive, if possible, the crescent. In case of failure, let us “slide” towards the West, towards Jeddah, towards the Red Sea, perhaps towards the Nubian Desert, perhaps even further…

But what if we fail here too? Where should one stop and at what time should one stop? It seems quite obvious that we dispose of the whole time span until Fajr in Makkah in order to scrutinise the sky, scrutinise it attentively further and further West until the terrestrial limit imposed by the time of the prayer of Fajr in Makkah.

What to do in practice: Following the above principle, after the new moon is born, we first look for the earliest crescent in the evening sky of Makkah. If it is visible, then the new month starts the next day. If not, we look further and further west until the time of Fajr in Makkah. If the crescent is visible anywhere to the west before Fajr in Makkah, then the new month starts on the next day, exactly as if the crescent had been visible in the evening in Makkah itself.

We call this concept that of extended visibility.

III. The tools for the calculation
We describe in detail below the tools that we use not only for establishing a rigorously exact calendar for Makkah, but for all the other countries of the world.

III.1 The basic tool: the visibility curves
At each new moon, we first trace the visibility curves for the crescent according to the method now well admitted by the Muslim community. Elaborated by the British mathematician B. D. Yallop, this method was much improved by Syed Khalid Shaukat. It is his visibility curves that we employ. The explanation of these curves can be found on his site For each point on earth between the latitudes 60° N and 60° S, the different curves give the probability of observing the young crescent. According to the classification of Yallop, we have:

– The green field meaning easy visibility with the naked eye
– The blue field meaning easy visibility with the naked eye under good atmospheric conditions
– The grey field meaning visibility with optical aid
– The red field meaning visibility with powerful optical aid
– The black field meaning no visibility possible

III.2 Choice of a reference point for calculating extended visibility
Once we have established the visibility curves for the beginning of each lunar cycle, we look for the point of reference within these curves that will serve for applying our concept of extended visibility. Looking at the curves, we notice that the first point of visibility with the naked eye is always situated within the blue zone that precedes the green one. It is thus logical to choose as reference point one within the blue zone.

However, we do not choose as point of reference the very first point of visibility at the tip of the blue zone, but another one within the blue zone at 3° further west than the tip, following the longitude of the tip. Let us call this point the point P. The choice within the blue zone is dictated by the following argument:

The blue zone represents naked eye visibility under perfect observational conditions. For an individual point, such as the first point of visibility, it is not certain that such conditions will be realized. But if we place ourselves within the blue zone, we take advantage of visibility not only at the selected point of observation, but also of the probability of observation in the whole of the blue zone situated to the east of our point of observation P. Indeed, to the east of P, the crescent will be visible before it is visible at the point P itself. If Fajr in a given locality is after visibility at the point P, it will be even more so if the visibility occurs earlier than at the point P.

Let us take an imaginary example in order to clarify this point. Let us say that the visibility at the point P occurs at 04H45 in universal time UTC. Let us say that Fajr in a given locality is at 04H50, also in UTC. Since Fajr is after visibility, Ramadan will start in the place under consideration. Now, as we said before, visibility to the east of the point P will occur before that at the point P itself. Let us say that visibility occurs at 04H40 UTC, somewhere to the east of the point P, always within the blue zone. Fajr in the place under consideration will still be after visibility. Ramadan will start in this place.

The detailed calculation shows that the blue zone towards the east of the point P covers an area of roughly 450 000 km2. This is almost 67 % of the surface area of France. Within such an extensive area, the probability of sighting the crescent with the naked eye within the blue zone is almost 100 %. The reader will find an example of such a calculation by clicking on the following link. This particular calculation refers to the end of Ramadan 1434, but, generally speaking, the same situation will repeat itself each month.

III.3 The best time of visibility of the crescent at the point of reference
In the same scientific article as the one in which B.D. Yallop develops his theory of the earliest visibility of the crescent (HM Nautical Almanac Office NAO, NAO Technical Note, Updated April 1998), he also gives the following empirical formula for calculating the best time for observing the young crescent after sunset in any given place:

Best time of visibility of the new moon = Sunset time + 4/9 * (Difference between sunset and moonset time)

This formula is precious for determining whether the month in a given country will start on the day next to the evening after the birth of the new moon, or not.

IV. Generalisation of the method for all countries in the world
The methodology used for calculating the beginning of the month in Makkah, as well as all the tools used in the calculation, can be applied to any other country of the world.

IV.1 The principle
For any given country, the month will begin the next day if: [A] the new moon is born [B] the young moon is visible in the evening sky in the country, or [C] if it is visible somewhere to the west of the country before the hour of the Fajr prayer in the same country. If the contrary is the case, the month will last a day longer.

IV.2 In practice
For each country in the world, we choose a point at the extreme east of the country. If Fajr at this point is after the visibility of the crescent (defined by the best time of visibility) at the point of reference in the blue zone, then the Islamic month will be considered as having begun in the country, just as if the moon had been visible in the country just after sunset. We choose the easternmost point in the country because if visibility is acquired before Fajr in the east, it will all the more be acquired further west, where Fajr is later. We recall that we have called this concept: “the concept of the extension of the visibility zone”, or “extended visibility”, for short.

We have to introduce a nuance in the choice of the easternmost point in each country. In fact, it happens that for some countries the easternmost point is lost in an uninhabited territory in the ocean, in the mountains, in virgin forest or in the desert. Thus, in practice, we define the easternmost point as the last inhabited and identified locality on a geographical map.

IV.3 The particular cases of very large countries: China, Russia, North America
China occupies a longitudinal spread from 74°E to 135°E. Although the country follows a single time zone (Beijing time), in practice the country functions differently in the east and in the west. Thus it seemed reasonable to us to define – for the frequent case where the totality of the country does not fall within a single visibility zone – two distinct calendars: for Eastern China and for Western China. Thus the reader will find two choices for China in the menu for the choice of various countries for downloading the country wise calendar. The cities we have retained for the Fajr calculations for the two zones are respectively Fuyuan County, Jiamisu, Heilongjiang (48.4°N, 134.3°E) for Eastern China and Chengdu (30.7°N, 104.1°E) for Western China.

Russia, the largest country in the world, covers longitudinally the whole of the eastern hemisphere from 20°E onwards. In addition, it juts into a part of the western hemisphere, crossing the International Date Line, until 170°W. Since October 2014, Russia functions with 11 different time zones. However, it would not be reasonable at all to define 11 different calendars for Russia. Thus we have opted for three calendars, for the cases where all of the country is not covered by a single visibility zone. These calendars are: Eastern, Central and Western Russia. The localities we have retained for the Fajr calculations are respectively: Uelen (66.2°N, 169.8°W) for Eastern Russia, Yakutsk (62.0°N, 129.7°E) for Central Russia and Nizhnevartovsk (61.0°N, 76.6°E) for Western Russia. The reader will thus find three options for Russia in the menu that gives the choice of countries.

The reasoning for China and for Russia does not apply to the two other very large countries of the world: USA and Canada. Our experience shows that, practically each month, both these countries fall within the extension of the zone of visibility in the Pacific Ocean. We will not fail to point out to our readers the cases that are not in conformity with this rule.

IV.4 Another special case: Saudi Arabia
The case of Saudi Arabia is again different. The very reason for the existence of our site, and its origin, lie in establishing an accurate calendar for Makkah. It so happens that the easternmost point of the country is in Shaybah (22.5°N 54.0°E). In practically all cases, the two calendars will be identical, Saudi Arabia not being a very big country. However, in the menu for the country selection, we have chosen a dual appellation for this country:Makkah/Saudi Arabia. In the rare cases where the two calendars are different we will publish both.

V. Our photo gallery
Whenever possible, we ask people in whom we have confidence – astronomical observatories or groups of astronomers in different countries of the world – to photograph the young crescent for us, according to our visibility predictions based on the visibility curve of the month. The photo gallery on our site bears testimony to the exactness of our predictions and the seriousness of our calculations. Month after month, we publish photographical evidence of the very young moon. We might add that all our photographs are without optical aid.

VI. Conclusion
In his days, Galileo established, against all current thought, that it is the earth that revolves around the sun, and not the contrary. In our days, science – celestial mechanics in particular – clearly establishes that every point on the globe has its own calendar so that, ipso facto, an arbitrary national calendar is neither justified nor legitimate. And this is all the better! The Fajr criterion is a powerful means for establishing an authentic calendar for each country in all rigour, so that such a calendar is no longer submitted to misguided ways and the shackles of national decisions. In addition, it links strongly between themselves the second and the fourth principles of Islam, i.e. prayer and fasting.

With the publication of reliable country specific calendars for the entire world, we hope to have taken a large step towards the unification of the Islamic world around the Word of God. The feat is particularly significant because we have already shown by strict combinatory analytics that the total and theoretical number of legitimate Islamic calendars in the world is 584 Please read more about it here. Is it not a grace to be able –with the same scientific rigour – to be able to reduce this number to just one calendar by country, calculated and published month after month.

May the Almighty guide our efforts in this direction! God has promised: “And who is more faithful to His promise than God?”(Surah 9, Verse 111). Further, “God has promised to those amongst you who believe and do righteous deeds, that He will surely establish them as His lieutenants on earth, as He has done for those who lived before them. He has promised to establish firmly the religion that he has chosen for them, and to change their fear in security and peace.”(Surah 24, Verse 55)