Hari Raya dates (1923 - 2100)

Ramadan is the month in which the Quran was revealed as guidance to man and clear proof of guidance, and criterion (of falsehood and truth). So when you see the new moon you should fast the whole month.

Surah al-Baqarah, version 185. English translation by Ahmed Ali (1993) Al-Quran: A comtemporary translation, Princeton University Press, Priceton. The original text reads:
شَهْرُ رَمَضَانَ ٱلَّذِىٓ أُنزِلَ فِيهِ ٱلْقُرْءَانُ هُدًۭى لِّلنَّاسِ وَبَيِّنَـٰتٍۢ مِّنَ ٱلْهُدَىٰ وَٱلْفُرْقَانِ ۚ فَمَن شَهِدَ مِنكُمُ ٱلشَّهْرَ فَلْيَصُمْهُ ۖ وَمَن كَانَ مَرِيضًا أَوْ عَلَىٰ سَفَرٍۢ فَعِدَّةٌۭ مِّنْ أَيَّامٍ أُخَرَ ۗ يُرِيدُ ٱللَّهُ بِكُمُ ٱلْيُسْرَ وَلَا يُرِيدُ بِكُمُ ٱلْعُسْرَ وَلِتُكْمِلُوا۟ ٱلْعِدَّةَ وَلِتُكَبِّرُوا۟ ٱللَّهَ عَلَىٰ مَا هَدَىٰكُمْ وَلَعَلَّكُمْ تَشْكُرُونَ ١٨٥

The first day of the 10th month in Islamic lunar calendar, \(s\), is know as Eid al-Fitr عيد الفطر. Although the first day of all the months in a Islamic lunar calendar is supposed to be observational in Malaysia, the date of \(s\) is strictly observational and it is often accompanied by an announcement by the Keeper of the Rulers's Seal (KRS) on YouTube or TV.

The calculation of \(s\) to match the version to be announced by the KRS is rather simple. One has to only locate the position of the astronomical new moon, \(N\) when the adjusted lunation number is 10 in modulo 12, $${\rm BLN} + 5 = 10 \;{\rm mod}\;12$$ Depending on the position of the new moon, we introduce a suitable offset to the \(N\) to arrive at \(s\), that is $$ s = \begin{cases} N + 1 & \textrm{if $N$ is in the ante-meridian region}\\ N + 2 & \textrm{otherwise} \end{cases} $$ where the value of \(N\) must be adjusted to Malaysian timezone.

Approximately every 32 or 33 years, the position of \(s\) roughly aligns with the beginning of the lunisolar cycle in the Chinese system, giving rise to a co-celebration, \(\kappa\) or gongxi raya. For the range covered, \(\kappa\) typically appears in triplets (e.g. 1931-1933, 1964-1966, 1996-1998, 2029-2031, 2094-2096). The notable exception is the \(\kappa\)-twin in 2062 and 2063.

1. Brown Lunation Number (BLN) is a sequential number introduced in American Ephemeris used to track new moon. Number 1 is associated with 17 January 1923.
   
   
2. Other dates that are strictly observational in Malaysia are the first day of Ramadan, \(r\) and the day of Eid al-Adha, \(q\). The announcement of \(r\), \(s\), and \(q\) are usually done by the KRS.
   
   
3. It was always clear to my mother that \(s\) can never fall on the first day of a Chinese month. She told me this when I was young, and it sparked my curiosity, leading to the investigation of the pattern of \(\kappa\). Recently, a colleague remarked that the projected canonical date for Eid al-Fitr 2026 might be incorrect, with potential planning implications. I replied that I had once compiled a 100% accurate list of Eid al-Fitr dates spanning many years, and that I would recalculate them as I had promised her.
   
   
4. The Chinese dates are calculated using the formulas given in Reingold and Dershowitz (2018). See E. M. Reingold and N. Dershowitz (2018) Calendrical calculations: The ultimate edition (4th edition), Cambridge University Press, Cambridge.

The following dates for Eid al-Fitr, \(s\), are calculated from the values of the position of the astronomical new moon, \(N\), and they are independent of the canonical Islamic lunar calendar used in Malaysia. For example, the government listed the estimated \(s\)-value as 21 March 2026 (1 Syawal 1447). The \(s\)-value listed by the following table disagrees with the official estimation and listed 20 March 2026 as the solution for 1 Syawal 1447.