Posted by: Dawud Israel | May 18, 2016

The Mathematics of Fasting in Islam

Last year I had taken to fasting more often. As time went by I thought more and more about rewards for optional sunnah fasting and its benefits. The hadith on it are well known and we hear them every few months in Shaban, Dhul Hijjah, Ramadhan and Shawwal (for those unfamiliar see the links). But the more time passed, the more a pattern appeared to me.

  • Fasting the day of Ashura (10th of Muharram) + 9th or 11th of Muharram expiates for sins in the previous year (Sahih Muslim). That is 360 days.
  • Fasting Ramadhan and 6 days of Shawwal gives the reward for 1 year as well, as 30 days in Ramadhan + 6 days Shawwal are given 10 times the reward in Ibn Abbas’ ijtihad so 360.
  • Fasting Ayam al-Bid (the luminous nights) which are, 3 days every Islamic month, including Ramadhan by default, typically 13-15th (see here for a possible wisdom behind that) or the 1st Monday and next 2 Thursdays, that is 12 months is 36 days as well. Multipy 10 times the reward gives 360 again.
  • Fasting 10 days of Dhul Hijjah, significant as the 12th month of the year, specifically fasting the Day of Arafah forgives sins in the previous year and the year to come. Again 360 x 2 = 720.
  • Fasting the fast of Sayyidina Dawud (alayhi salam) is every other day that is 180 days a year. The same hadith also mentions fasting every 2nd or 3rd day, so we have 120 and 90, factors of 360.
  • Fasting the first 15 days of Shaban, that is the 8th Islamic month is also significant where 15 x 8 = 120, a factor of 360. 

All these fasts are optional except Ramadhan. Now, if you total the actual days of optional fasting that comes to 2 days for Ashura, 6 for Shawwal, 12 for Ayam al-Bid, 10 for Dhul Hijjah. That is a total of 30 days of actual fasting, so really just an extra month of fasting which is 2/12 months or 1/6th of the year.  This doesn’t even include Shaban which is not as emphasized in Muslim communities as the other sunnah fasts. And the reward you would get for those extra 30 days? 360 days for Ashura, 360 days with Shawwal, 360 days with Ayam al-Bid, 720 days with Dhul Hijjah, which is a total of 1800 or 5 years worth of reward for fasting 30 extra days! So you only fast 30 extra days besides Ramadhan and get the reward of 5 years! SubhanaAllah, pretty mind boggling stuff!

“Which one of the Favours of your Lord will you deny?”

Why 360?

Why is there a mathematical pattern relating to 360 and its factors apparent in relation to fasting? Allah knows best. One explanation I did came across was that Ethiopian Orthodox Christians are required to fast 180 days a year! Apparently, this is because Maryam the mother of Isa (Jesus alayhi salam) fasted 6 months every year. We Muslims fast at least 1 month or 2 months. So the possible wisdom is Muslims fast much fewer days than the Christians, but are given double the rewards the Christians gets, that is up to 360. This is the generosity, blessing and favour Allah has shown to the Muslim ummah over the Christian ummah! I believe this is because of Allah’s love of Sayyidina Rasulullah (salallahu alayhi wasalam). Alhamdulillah, we have many easy options for fasting but are given great rewards for them

For those of you who are keen, you know there is also a sunnah fast on Mondays and Thursdays of each week. This is significant because the same Ethiopian Orthodox Christians also fast every Wednesday and Friday, so Muslims fasting Mondays and Thursdays is a way of making us distinct from that previous religious community. It is also worth noting fasting in Islam is in commemoration of blessed and joyous occasions, like completing Ramadhan or Abraham’s sacrifice but if you look at fasting in the Jewish communities, it is as marked by sadness and sorrow. Islam is therefore more spiritually optimistic than those nations of the past.

More Hijri Mathematical Patterns?

The mathematical patterns made me wonder if there are other patterns in the Islamic calendar. Here are some possible findings:

  • The 4 sacred months are also recommended for worship which is approximately 120 days.
  • Rabi al-Awwal is interesting too because it is the 3rd month and the Mawlid an-Nabi (salallahu alayhi wasalam) is on the 12th day, so 3 x 12 is 36.
  • The last 10 days of Ramadhan, the 9th month, is significant. The 9th month is the last 3rd of the year. The last 10 days of Ramadhan, from the 20th to the 30th, are the last 3rd of the 9th month. And during that time, in the last 3rd of the night we recite the Qur’an and by then our taraweeh has reach the last 3rd of the Qur’an. (Read that again if it didn’t make sense) There are 4 chronological levels of 3rds here, that is again 12, a factor of 360. Or we could say there is 4 dimensions to these last 10 days, like a kernel within a kernel aligning in this period, so the last 10 days are really like 40 days in magnitude.   

These are only a few things I found and I have looked mainly at months. One could similarly explore mathematical patterns in Islamic hours in the day (hour of jumuah, night before jumuah, hour before fajr, the Final Hour, etc) or even decades of Islamic history for patterns (the first years of Nubuwwah, the first 3 generations etc). Or similarly, exploring the effect of seasons and spiritual practices in Islam like fasting in winter when days are short and praying the night in summer when the nights are short, thereby making it easier for us.


I don’t believe in numerology or anything like that but I do believe Allah has a Sunnah (a pattern) in creation and its good to find that pattern as a sign of His Knowledge and Majesty. I have pointed out only a few of these patterns. In Muslim communities, we emphasis 40 and 786 as being spiritually significant. For the reasons mentioned above, I think 36 and its factors are also significant. Surah YaSin is described as the ‘heart of the Qur’an’ and is the 36th chapter of the Qur’an. The middle of the entire Qur’an is in the 18th chapter of the Qur’an (surah Kahf) and comes right after the 18th verse, again factors of 36. And when we consider the fasting hadith mentioned above, 36 or 360 becomes a symbol of Allah’s All-Encompassing Generosity to us Muslims. This exercise was interesting for me in an attempt to quantify how much Allah’s Mercy to Muslims is greater than Allah’s Mercy to the People of the Book.

For me it is important not to get bogged down in the details or this number or that number being special, but to see all numbers point to the One, al-Wahid, al-Ahad. If we can see all numbers as a sign of Allah, then just mentioning any number besides 1, will remind us of Allah.



*Its also interesting to note that mathematically the first Muslims were not always precise, the lunar Hijri calendar has about 354 days, or 11-12 days shorter than solar year, and Muslims like to approximate (ie 40 Hadith Nawawi is actually 42 hadith).  Our days are also reversed because the day for Muslims begins at sunset, not sunrise and there is no certainty with moonsighting. This is to say spirituality in Islam, is not supposed to be exact, it is approximate, and that is more in line with trusting in Allah.

*Post-script: This hadith is also interestingThe Messenger of Allah ṣallallāhu 'alayhi wa sallam (peace and blessings of Allāh be upon him) said: “Friday is twelve hours in which there is no Muslim slave who asks Allah subḥānahu wa ta'āla (glorified and exalted be He) for something but He will give it to him, so seek it in the last hour after ‘Asr.” [Sunan an-Nasa’i].

Subhana kallahumma wa bihamdika wa ash-haduana la illaha illa Ant wa astaghfiruka wa atubu ilayk, ameen.

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