When is Deepavali (Diwali)?

Helmer Aslaksen and Olivier Beltrami

Introduction

Deepavali is a national public holiday in India, Sri Lanka, Nepal, Mauritius, Fiji, Malaysia and Singapore. The holiday in Sri Lanka, Malaysia and Singapore will about half the time fall one day earlier than the holiday in India and Mauritius. In Nepal both days are public holidays.

In Singapore, the Hindu Endowments Board only makes an estimate of the date of Deepavali, and waits for calendars from India to appear before the date of the public holiday is confirmed by the Ministry of Manpower. Unfortunately, those estimates are often wrong, and the date for the holiday has to be reviesed after the start of the year. This has happened four times since 2002.

In Singapore, the date of Deepavali in 2009 was on 21 February 2008 estimated to be 15 November 2009. However, it was easy to see that it should be 17 October 2009. We contacted both the Ministry of Manpower and the Hindu Endowment board in February 2008, and almost one year later, on 10 February 2009, they finally announced the change. For more info, please see the news update from Q++Studio. The updated list of public holidays is announced by the Ministry of Manpower.

The Sanskrit word Deepavali means an array of lights. As the knowledge of Sanskrit diminished, the name was popularly modified to Diwali, especially in northern India. There are various ways to spell it in English, using either "Dee" or "Di" and "v" or "w". I write Deepavali when I refer to the holiday in the south and Diwali when I refer to the holiday in the north.

In India there are both national and state public holidays. Naraka Chaturdasi (the day before the new Moon) is celebrated as a state holiday in Tamil Nadu, Kerala and Puducherry. The next day is Amavasya (the new Moon day) and Lakshmi Puja is celebrated as a national public holiday. The next day is Pratipat and Govardhan Puja is celebrated as a state holiday and New Year Day in Gujarat and Karnataka. The next day is Dvitiya and Bhai Duj (Bhai Dooj) is celebrated as a state holiday in Uttar Pradesh and Uttarakhand.

On an Indian government web site it says: "In certain States the practice is to celebrate the occasion a day in advance, i.e., on "Naraka Chaturdasi Day". In view of this there is no objection if holiday on account of Deepavali is observed on "Naraka Chaturdasi Day (in place of Deepavali Day) for the Central Government Offices in a State if in that State that day alone is declared as a compulsory holiday for Diwali for the offices of the State Government."

The goal of this web page is to explain some of the issues involved in computing the date of Deepavali. There are a number of regional variations, and it is often difficult to find out which conventions are being used in different calendars. However, after reading this page, I hope you will understand the issues involved, and be able to find out more for yourself about any regional calendars you might be interested in.

I will also discuss some of the computational issues, so that you will be able to do your own computations.

This page is still under construction. I will add more details as time permits.

I'm grateful to Olivier Beltrami and Akshay Regulagedda for help.

I hope some of you may find it useful. If you have any corrections or additional information, I would love to hear from you.

My main reference on Indian calendars is the book Indian Calendric System by Commodore S.K. Chatterjee (Retd.).

Months

Deepavali is determined using the Indian lunisolar calendar. I have put up web page on Months in the Indian Calendars, which is based on work by one of my students Akshay Regulagedda. If you are mostly interested in understanding which day Deepavali falls on, I will just state that it can be shown that Deepavali will fall between Oct 15 and Nov 15.

Tithis

In order to understand the Indian lunisolar calendar, we must understand tithi. Tithi is a lunar day, or the time it takes for the longitudinal angle between the moon and the sun to increase by 12°. There are 30 tithis in each lunar month, and the vary from approximately 19 to approximately 26 hours. The day gets its name from the name of the tithi at the time of sunrise.

Since a tithi can be more than 24 hours, there will sometimes be a tithi that contains two sunrises. In that case we will get a repeated day. Since a tithi can be less that 24 hours, there will sometimes be a tithi that contains no sunrise. In that case we will skip a day.

The second to last tithi before the new Moon is called Chaturdasi and the tithi ending at the new Moon is called Amavasya. Notice that the new Moon will occur during the Amavasya day, unless the Amavasya day is skipped.

Rules

  1. In South India the main Deepavali celebration is Naraka Chaturdasi in the morning of Chaturdasi day (29) in the lunar month of Asvina. (If there is an added Chaturdasi day it falls on the second Chaturdasi day, and if the Chaturdasi day is skipped it falls on the Amavasya day.)
  2. In northern India the main Diwali celebration is Lakshmi Puja on Amavasya. However, Lakshmi Puja is supposed to be done during a time period called Pradosha. It is the first 2/15 of the night, or about the first 1:36 hours after sunset. It is more important that it is done during the Amavasya tithi than during the Amavasya day, so as we will see below, it will sometimes fall on the Chaturdasi day.
  3. In Bengal the main holiday is Kali Puja, which is celebrated during the Amavasya tithi, but during nisitha, which is from around 24 minutes before midnight to around 24 minutes after midnight. It is more important that it is done during the Amavasya tithi than during the Amavasya day, so as we will see below, it will sometimes fall on the Chaturdasi day.

This gives four separate cases to consider for the northern Diwali.

Suppose the Amavasya tithi contains one Pradosha, which falls during the Amavasya day. In that case Diwali is celebrated during Pradosha 2, which will be both during the Amavasya day and the Amavasya tithi.

Suppose the Amavasya tithi contains one Pradosha, which falls during the day Chaturdasi day. (I leave it as an exercise to the reader to check that in this case there cannot be a skipped Chaturdasi.) It is more important that the tithi is Amavasya than that the day is Amavasya, so in that case Diwali is celebrated during Pradosha 1, which will coincide with the southern Naraka Chaturdasi on Chaturdasi.

If the Amavasya tithi contains two Pradoshas, there are different conventions according to Chatterjee, but my impression is that most Indians would pick Pradosha 2, since that would be both during the Amavasya tithi and the Amavasya day.

If the Amavasya tithi contains no Pradosha, I believe that most Indians would pick Pradosha 2, since that at least falls during the Amavasya day. (It cannot both be no Amavasya day and no Pradosha in the Amavasya tithi.)

The last two cases are rare, and the first two are about equally likely. So as a rough approximation Naraka Chaturdasi will fall on the same day as Lakshmi Puja and about half the time it will fall one day before.

Regarding Kali Puja, I leave it as an exercise to the reader to figure out that if the Amavasya starts between sunrise and 24 minutes after midnight on Chaturdasi day, then Kali Puja will be celebrated on the Chaturdasi day. If the Amavasya tithi contains two or no nisithas, I believe that most Indians would pick the nisitha on the Amavasya day.

Rule of thumb

The (amanta) lunar month takes its number from the solar month that starts in it, but its name from the solar month in which it starts. So the seventh lunar month Asvina will normally start in the sixth solar month Asvina (Tamil: Purattasi) and end in the seventh solar month Kartika (Tamil: Aipasi). If it ended before, there would most likely be a leap month, in which case the leap month would end in Kartika/Aipasi. So most of the time, Deepavali falls on the krishna Chaturdasi in Kartika/Aipasi. In fact, some people will tell you that that is the rule. However, I believe strongly that this is just a rule of thumb, and not the actual rule. I believe that even the Indian solar calendars use the lunisolar calendars for most of the festivals.

However, let us for a moment take this rule of thumb at face value. Can that ever lead to Deepavali and Diwali being one month apart?

The first question is then what to do if there are two Chaturdasis in Kartika/Aipasi. Because of the way the names of the lunar and solar are names, I am convinced that they would then chose the first, so this would not cause a late Deepavali.

If there is a leap month, Diwali will be late, so we want the samkranti to be before the new Moon. And we want the solar month to miss the Chaturdasi at the beginning, and start with Amavasya or Pratipat. In that case we would have to wait for the end of the month to get Deepavali. How could that happen? We need to be careful about how the Tamil calendar starts the solar month. The Tamil rule is that when the samkranti takes place before sunset, then the solar month starts on the same day, while if it takes place after sunset, then the solar month will start the following day. So suppose that the samkranti happens before the new Moon, and that the Chaturdasi ends before sunrise on the first day of the solar month. That is exactly what happens in 2009. The samkranti is at 09:10 on 18/10/2009, so that is the first day of the solar month, which is an Amavasya day. So in this case the lunisolar rules would give an early Deepavali, while a solar rule would give the Tamil holiday one month later that the lunisolar Diwali. In fact, as long as the samkranti is after sunset on the 17th, we will get the same problem.

Dates

Here is a table for the dates of Deepavali in Singapore since 1999.

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
7/11 26/10 14/11
4/11
(3/11)
24/10
(23/10)
11/11 1/11 21/10 8/11
27/10
(28/10)

The numbers in parenthesis are the initial estimates by the Hindu Endowments Board. The web page at MOM for public holidays in 2008 has not yet been updated.

Here is a table for the dates of Deepavali in Sri Lanka since 2003. They agree with the Singapore/Chennai dates.

2003 2004 2005 2006 2007 2008
24/10 11/11 1/11 21/10 8/11 27/10

Here is a table for the dates of Diwali in India since 1999.

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
7/11 26/10 14/11 4/11 25/10 12/11 1/11 21/10 9/11 28/10

As you can see, the dates are the same in 6 years and different in 4 years.

Computations for 2008 and 2009

I will now show how the computations can be done for 2008 and 2009. I will use data from www.tamil-calendar.com. I believe that the Tamil calendar is based on Chennai (13° 4' N, 80° 14' E), while the northern Indian calendar uses Ujjain (23° 9' N, 75° 46' E) and the Sri Lankan calendar uses Colombo (6° 55' N, 79° 52' E). Between 15/10 and 15/11, the sunrise and sunset times for Chennai will be between 05:59 and 06:07 and 17:39 and 17:49. For Ujjain we get from 06:23 to 06:40 and from 17:48 to 18:01, and for Colombo from 05:57 to 06:00 and from 17:49 to 17:55. If the tithis end near sunrise or sunset time, you will have to check more carefully on Sunrise Sunset Calculator Calendar at www.tamil-calendar.com. This was an issue in 2005. Using the latitude of Ujjain, I got Chaturdasi on 31/10, but using the latitude of Chennai, I got Chaturdasi on 1/11.

In Singapore, the date of Deepavali in 2009 was on 21 February 2008 estimated to be 15 November 2009. However, it was easy to see that it should be 17 October 2009. We contacted both the Ministry of Manpower and the Hindu Endowment board in February 2008, and almost one year later, on 10 February 2009, they finally announced the change. For more info, please see the news update from Q++Studio. The updated list of public holidays is announced by the Ministry of Manpower.

Let me explain how this works. Using www.tamil-calendar.com you get the following table. Since the Hindu days starts at sunrise, we use a value greater than 24 hours for the ending time of tithis that end between midnight and sunrise.

2008/10/26 Trayodasi until 26:46
27 Chaturdasi until 27:34 Naraka Chaturdasi
28 Amavasya until 28:45 Lakshmi Puja
2009/10/16 Trayodasi until 14:33
17 Chaturdasi until 12:39 Naraka Chaturdasi and Lakshmi Puja
18 Amavasya until 11:05

In 2008 the Chaturdasi tithi runs from 02:46 on 27/10 to 03:34 on 28/10. This means that 27/10 is Naraka Chaturdasi since the tithi at sunrise is Chaturdasi. The Amavasya tithi runs from 03:34 on 28/10 to 04:45 on 29/10, so the Amavasya tithi contains the Pradosha on 28/10.

In 2009 the Chaturdasi tithi runs from 14:33 on 16/10 to 12:39 on 17/10. This means that 17/10 is Naraka Chaturdasi. The Amavasya tithi runs from 12:39 on 17/10 to 11:05 on 18/10, so the Amavasya tithi ends before Pradosha on the Amavasya day, but contains the Pradosha on 17/10, so Naraka Chaturdasi and Lakshmi Puja will both be on 17/10.

It only remains to explain why there should not be a leap months starting on 19/10/2009. Different ways of computing the Kartika samkranti gives different values, but the latest I have seen is at 09:10 on 18/10/2009, so the new Moon at 11:05 on 18/10/2009 is inside Kartika. I do not understand how HEB came up with the estimate of 15/11/2008.

Exercise

Do you wan to test if you know how to confirm these dates? Here is a table of tithi times you can use. Let me give you some hints.

In 1999 Trayodasi lasted until 06:09 on 6/11. The sunrise in Chennai was at 06:04, so that was a Trayodasi day there, but in Ujjain there were two Chaturdasi days.

In 2002 there was no Chaturdasi day. In that case the daily calendar on www.tamil-calendar.com doesn't give the time for Chaturdasi, and you have to use their tithi calculator on www.chennaiiq.com manually.

In 2005 the names of the day depends on whether you use Chennai or Ujjain latitudes. So if you use Ujjain computations but Tamil rules, you will get Naraka Chaturdasi one day earlier.

In 2006 there was a leap Chaturdasi. On www.tamil-calendar.com that is listed as Chaturdasi lasting until 00:00.

1999/11/06 Trayodasi until 06:09
07 Chaturdasi until 07:36 Naraka Chaturdasi and Lakshmi Puja
08 Amavasya until 09:24
2000/10/25 Trayodasi until 15:29
26 Chaturdasi until 14:17 Naraka Chaturdasi and Lakshmi Puja
27 Amavasya until 13:30
2001/11/13 Trayodasi until 16:29
14 Chaturdasi until 14:10 Naraka Chaturdasi and Lakshmi Puja
15 Amavasya until 12:12
2002/11/03 Trayodasi until 09:25
Chaturdasi until 29:45
04 Amavasya until 26:06 Naraka Chaturdasi and Lakshmi Puja
05 Pratipat until 22:39
2003/10/23 Trayodasi until 24:49
24 Chaturdasi until 21:45 Naraka Chaturdasi
25 Amavasya until 18:22 Lakshmi Puja
2004/11/10 Trayodasi until 24:36
11 Chaturdasi until 22:32 Naraka Chaturdasi
12 Amavasya until 19:59 Lakshmi Puja
2005/10/31 Trayodasi until 06:16
01 Chaturdasi until 06:54 Naraka Chaturdasi and Lakshmi Puja
02 Amavasya until 06:56
2006/10/19 Trayodasi until 29:53
20 Chaturdasi whole Hindu day
21 Chaturdasi until 08:27 Naraka Chaturdasi and Lakshmi Puja
22 Amavasya until 10:45
2007/11/07 Trayodasi until 23:28
08 Chaturdasi until 26:01 Naraka Chaturdasi
09 Amavasya until 28:34 Lakshmi Puja

Questions

If you are an expert on Indian calendars, I would be very happy if you could help me with information about the following questions.

It is hard to reverse engineer calendars. We need to know the following.

I am not sure about the answer to these questions for either the Sri Lankan, Tamil or Indian calendars. I have tried different computations myself, but in the end I just settled on www.tamil-calendar.com. These issues will only make a difference in special cases, but I would be very grateful if anybody has any detailed information about the official Sri Lankan, Tamil and Indian calendars.

Online calendars

State holidays

Web pages by the Society for the Confluence of Festivals in India

Deepavali in South Africa

References

Back to Helmer Aslaksen's page on Indian Calendars.


Helmer Aslaksen
Department of Mathematics
National University of Singapore
helmer.aslaksen@gmail.com

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