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The Logic of the Hindu Calendar | Future IQ

40,095 views Wait, is this logic right? • Jan 02, 2026
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Slog Reference: Logic of the Indian Calendar

Description

Why did the Hindu calendar in 2025 have two different days for Diwali? Why do Hindu festivals keep shifting days every year? Hindu festivals in fact, have a mathematically accurate system and thus the argument of "shifting days" becomes redundant. In this episode, we delve into the logic of the Hindu calendar, also popularly known as the Indian calendar.

This calendar is not simply based on the lunar cycle, but it derives it's logic from precise mathematical calculations of the positions of the solar system. We breakdown every single concept in depth. What Tithi is in Astrology, how is a day in Hindu calendar different from a day in the Gregorian calendar, what is a Poornimanta system & what is a Amanta system within the Hindu calendar itself, how do the Zodiacs fit into this, and many more related concepts.

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Videos referenced in today’s episode:
Why Makar Sankranti Never Stays on One Date: https://youtu.be/ewtdZKayD24
Game Theory Schelling Point Explained: https://youtu.be/kWHiDVjZQ7I
Why Diwali Was Never About Religion: https://youtu.be/_AByBm35DgI
Origin & Evolution of Astrology: https://youtu.be/gatm0hDY-iE

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Source / References:
https://en.wikipedia.org/wiki/Hindu_calendar
https://en.wikipedia.org/wiki/Astronomical_basis_of_the_Hindu_calendar
https://en.wikipedia.org/wiki/Adhika-masa
https://timesofindia.indiatimes.com/life-style/events/when-is-diwali-on-october-20-or-21-kashi-vidwat-parishad-announces-the-correct-date/articleshow/124367342.cms

Chapters:
00:00 IS the Hindu Calendar Dumb or Genius?
03:15 What is Tithi?
08:23 Why is Diwali sometimes in Ashwin and sometimes in Kartik?
11:40 Pradosh vs Sunrise
13:25 The Problem of 11 extra days
16:00 The Solution of Adhik Maas

Related Slog Matches

Logic of the Indian Calendar

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Transcript

I always thought the Hindu calendar was dumb. the festivals keep shifting around and a random month gets added randomly without any logic and uh you know sometimes like the second of the month is followed by fourth of the month and third gets skipped and things like that right but then I studied it in more detail and I realized that there is a very nice elegant system to all of it which is different from the system followed by the western calendar the Gregorian calendar so I thought you know new year has just started and let me explain how the Indian calendar works.
So in today's episode I'm going to answer questions like why this year there was confusion about Diwali being on 20th or 21st and also there is always perpetually confusion about Diwali falling in the month of Ashwin or Kartik. Correct. something I've never understood and plus what is this titi thing right and why does it start at random times of the day yeah right and so on but let me ask this question why is it not dumb that the festivals keep shifting that's because of the difference in the lengths of the Indian and western calendars right so the western calendar is longer than the Indian calendar so the Indian calendar also makes adjustments adds days sometimes there is adikmas what no First
of all, Indian calendar does not add days. Okay. Okay. All months in the Indian calendar are exactly 30 days. Okay. Second of all, you say the dates are shifting. I say the dates are not shifting at all. Right? Diwali is always on the 15th day of the Krishna Paka of Kartik. Right? So the western calendar keeps shifting. What is up with that? Right? Plus western calendar sometimes has 30 days, sometimes has 31 days, sometimes 29. How dumb is that? Yeah, that's because all of those Roman emperors decided to steal dates from each other and add it to their own months and whatnot. So yeah, we know that history.
Isn't it much better that a month has a fixed number of days every time because the month which is one revolution of the moon is always the same duration, right? So why not just break it up into 30 days? It makes sense logically to break all of the months into exactly 30 days. In fact, there was this entire movement of uh 12 months of 30 days each and then 5 days of new year celebrations. I don't know what happened to that but that was actually not not a very bad idea sometimes I think.
So here is the thing right all over the world month which is which comes from the word moon is one revolution of the moon. Correct? Uh and that is 30 days roughly. Right? Because the moon going from one full moon to the next full moon is 29 and 1/2 days. Exactly. Right. So you had to round up or round down. Now why didn't we round down to 29? Can you guess? Uh mathematics I'm guessing 29 is a difficult number to divide by and 30 is an easier number to divide by. You have 15 days here, 15 days here.
Absolutely. Yeah. I mean if you want to do Krishna paksha and shukla pak you can't have 14 and three quarters and things like that right yeah makes it very difficult I know what you were going to ask and I'm going to ask you the same question what happens to that half a day which keeps get get which keeps getting added on because 29 and a half days is the cycle of the moon 30 days is the length of the month so you have a half day balance that you need to adjust somewhere right so that's why what the Indian calendar does is that it doesn't use a definition of day as sunrise to sunrise or whatever, right?
Okay. It uses a definition of day as 130th of a revolution of the moon and that is called a titi, right? Okay. So, titi is 130th of the 29.5 days it takes for the moon to complete one revolution. How will you calculate 2030th of 29.5 days? It's a very complicated number. How do you calculate it? Right? I mean you can do the calculation but the point is there were no watches, no hours and seconds and all that, right? Yeah. So how did they do that? So it has to do something with to do with the moon, right? You look at the moon I mean looking at the moon must be involved somehow, right?
Yes. So what they did was they saw okay one month is one full moon to next full moon. Correct. What you notice is that it goes from a full moon to a new moon where you can see that the phase is changing by 180°. Right? And then from that new moon to the next full moon is another 180°. So a total of the phase changes by 360°. Correct? Divide that by 30 and you get 12°. So one titi is the amount of time taken for the phase of the moon to shift by 12°.
So in that tiny little moon, they looked at 12° of phase change. How did they calculate 12° in that tiny little phase? Well, see their disadvantage was that they didn't have sophisticated instruments like we have now. Yes. Their advantage was that they were very smart people. Okay. You know what they did? Imagine this is the sun. Okay. And this is the moon. Well, this is Venus. But sure, moon. Moon. Okay. And here is the earth. Okay. Okay. So now from the earth, if you are looking into the sky, you see the sun here, you see the moon here. Correct. And if you calculate this angle which is pretty easy to do even if you are living in ancient times this
angle is always exactly the same as the angle of the face of the moon. Right? So when you start at new moon you'll see that the angle is 0° correct and as you shift 12° 12° 12° 12° here you're 90° after about 7 8 days. Correct? 15 days later you are at 180° and then another 15 days later you're back to zero. Right? Smart. So the precise definition of titi is that when you look in the sky you calculate the angle between the sun and the moon and when that goes from 0 to 12 that's the first titi 12 to 24 that's the second titi 24 to 36 third titi and so on and when it comes back to
360 month is over a this requires a heliocentric model of the solar system so kudos to that and b not not necessarily Okay, they did it by just looking at the angle. It doesn't matter whether the you think these are all revolving around the earth or not, right? You just look at how it is shifting. Okay, fair enough. Because at the end of the day, the moon would still complete a 360° uh whatever around the sky and therefore 12°. Sure, that makes sense. So the difference between the sun and the moon in the sky, whatever degrees gives you the titi of that particular phase of that particular month, yeah, so to speak. Plus, this also explains why
the titi starts at a random time during the day, right? Yeah. Because 29.5 divided by 30 is not exactly uh going to start at midnight and end at midnight. Basically, it comes out to around average of 23 hours and 37 minutes, right? Correct. Which means that every day the start of the next titi is going to be 23 minutes a little earlier. Right. And as a result, this Diwali 20th October, the titi started at 3:44, no 3:44 p.m. on 20th October and it ended at 5:54 p.m. the next day, 21st.
That's more than 24 hours. That's nearly 26 hours. Why is this city longer than 24 hours? Shouldn't it be shorter? Yes. So, now comes the second part of the explanation, the twist. Right? The moon goes around the earth. It doesn't go in a circle. It goes in an elliptical orbit. Oh. And as a result, when it is closer to the earth, it goes faster. And when it is farther from the earth, it goes slower. As a result, 12° the time taken for 12° isn't the same throughout the month, right? So sometimes it is just 19 hours, sometimes it is all the way up to, you know, 27 hours almost.
Okay? So that's why the duration of the titi keeps shifting. Yeah. But then why is Diwali sometimes in ashwin and why is it sometimes in Karthik? That is a question I still have. That is fairly simple. Okay. That north India says that one month is from full moon to full moon. So that is called the purimant system. Month ends pur month. Correct. Whereas middle India which is Gujarat, Maharashtra, Karnatak and a couple of other states here in the middle we use a amant system which goes month starts at Amawashia and ends at Amawasia. Right.
Okay. As a result uh the amawasia which comes in Diwali. Diwali is at the same day in both places. Yeah. It is Krishna 15. Yeah. Except that in the purimant system it is in the middle of the month. Correct. And for the uh system it is the beginning of the month. It is no it is the last day of the previous month. Right. So for them it is the last day of Ashwin and then Karthik starts on the day after Diwali. Whereas for North India this is middle of Karthik right?
Okay. Okay. Now now that makes sense. I've been wondering that. But yeah. Okay. But now here comes the other question. If my titi starts in the middle of 20th and ends in the middle of 21st, what date should I associate the titi with or more importantly uh let's say Ganesh chhaturi, right? Should I celebrate on the previous day or the next day? How do you decide? Well, the beginning of the titi is how you decide the no pretty much all our systems what you do is you take the titi you look at which sunrise is included in the titi and then that whole day is used as the day for celebrating festivals right so whichever
day contains the sunrise so basically if a titi goes across two days you will always celebrate uh the festivals on the next day because that is the day containing the sunrise. Okay? Except except when a titi has two sunrises. Oh, well now that's a problem. Okay. Because you can have a situation where a titi starts just before sunrise and then it's a 26-hour titi. So it is the next sunrise as well. Next sunrise. So now two days are included in that titi. Yeah. and you just deal with it, right?
How do you deal with it? I mean I mean that say that titi basically now uh spans two days and usually you'll celebrate things on the first of those two days. You can have the reverse problem also a titi starts just after sunrise and ends before next day's sunrise in which case that ti is skipped. So this date could be the second and the next one can be the fourth and third is skipped entirely. Right? That also happens. Okay. Okay. and he thinks this is not complicated but the Gregorian calendar is complicated. Both are complicated in their own ways. Gregorian you think is not complicated because they taught you this in first standard and second standard and third standard
where they didn't just teach me they taught the whole world that and the whole world agreed to accept that as fact. That's a shelling point which we should cover in a different episode. But one interesting twist right see if sunrise is when the date of the titi is there should be no confusion about whether Diwali is on 20th or 21st right? Yeah. So here is the problem. Okay. What happens is that Diwali I mean we did an episode on Diwali and we said it is the celebration of lighting up during the amosa. Right. Correct. So the whole point is that Amosia on the day of Amamasia when things get dark that's when you have to put up the lights. It
doesn't make sense to do it connected to sunrise. Okay. So the time just before and after uh sunrise is called praosh. All right. So uh for Diwali the roughly 2 and a half hours after sunset is called praosh. Okay. And the titi which contains the praosh of the amawasia that is used as the date of Diwali by many communities. Okay. Whereas some communities still stick to the stand. No no no we want a standard system. We stick to the sunrise method. And so those people ended up with 21st whereas the Pradesh people ended up with 20th. Right? That explains why sometimes different communities have Diwali on different days. So in essence, all of this confusion with the calendar is
essentially people looking at different calendars and adopting different calendars within the same lunar concept is what is happening right now. Why does adhikmas come into the picture? How does adhikmas an extra month come into the picture? So I mean see basically the fundamental problem with the universe has to do with a couple of things right. One is that the time taken for earth to complete one rotation which we define as one day. The time taken for the moon to complete one revolution which we define as a month and the time taken for the earth to complete one revolution around the sun which we define as a year.
These durations are not multiples of each other. So any system you use is going to have a drift and you have to come up with a system for the drift. Okay. Now the Gregorian calendar, the calendar we all use, you are all very familiar with the fact that it has 365 days but the actual year is 365 and a quarter. Correct? So every year you lose half a day and then every fourth year you have to insert a leap day. Correct. Correct. Now in the Indian system we said that a year consists of 12 months where a month is exactly 29 and a half days in revolution right?
What you end up with is roughly about you know 3 uh 54 days and now you have 11 days extra. Correct. So because of that what happens is that from year to year the whole thing is shifting by 11 days. M but you are thinking it is shifting by 11 days with respect to 1st January. Remember that Gregorian calendar doesn't exist. They are making this 2,000 years ago. So it's shifting with respect to what? Uh it's not shifting at all. Right. Ah it is shifting with respect to position of the sun with respect to the rest of the universe.
Okay. Right. And it is shifting with respect to the shortest day of the year, longest day of the year, the seasons. Right. Right. So if you don't do anything, what will happen is that rainy season, the Indian calendar calculates months by the moon and the year according to the sun. But there is a gap of 11 days through the calculations. You have to account for this 11 days somewhere because if you don't then over a period of 5 10 15 20 years you go from 11 55 110 and so on so forth until you'll probably end up a year short right so um Gregorian system has the same problem on a smaller scale but the drift is much smaller
but they have to still fix it right and they do it using leap days right leap days yeah what we do instead is okay remember what is the problem the problem is that the moon's revolutions are out of sync with the movement of the sun in the sky across the Yeah. In reality, it is not movement of the sun. It is movement of the earth around the sun. But to us, it looks like sun is shifting in the sky. Correct. The sun appears at different points every to make this much more systematic, you know what they did like maybe 2,000 years ago took the entire sky and they divided it up into 12 slices of 30°
each. Okay. Do you know what these slices are called? I am guessing they are the zodiac. They are the signs of the zodiac. I mean the zodiac is named after a constellation but it's not just random constellations, right? The zodiac is really a slice 30° slice of the sky and the name given is based on a bunch of stars found in that slice. Correct? Now exactly 112th of the real year the sun shifts from one zodiac from one slice to the other. Correct. Okay. Do you know what that point is called? Shifting from one slice to the other.
Uh no I genuinely don't. I am that is called a scranti. Sranti means movement transition of the sun from one zodiac to the other that's a sranti and because our moon months are roughly one month each and sranti also happens roughly one month uh apart that's why every month see has correct but because of our shift what happens is that every once in a while you end up with a moon month which starts just after a sranti and ends just before the next sranti right because there is an 11 point something day gap small gap right h what we do is that whenever we get a month like this with zero srantis we call it an adikmas
okay we give it the same name as the next month which is going to come so if the next one is karthartik then this will be called adik karthartik and that is normal kartik or you know sudha karthartik Nijakartik. Oh, and that's it. That's all you need to do. Every time you get a month with zero srantis, you insert it as an adikmas and that's it. This system will work for millions of years and always manage the drift without a problem. By contrast, the Gregorian calendar where everything is preddecided, their shifts get more and more complicated, right? So you insert one leap day every four years. Correct? But then it drifts so that every 100 years
is not a leap year. So the Gregorian calendar the way it handles this is by having preddecided uh corrections for the drift. And so there is always going to be a drift right. So what happens is every four years you insert one day leap day but now you have overorrected. So what happens is every 100 years you have an extra day. So every 100th year is not a leap year. So 1900 was not a leap year. Correct? But now you have undercorrected. So every 400th year is a leap year. So 2,000 was a leap year even though every 100 and so on. Right? And it's just I mean they going to keep having to do
this kind of correction. Whereas we because it is based on actual position of sun that's it that system will work ever. Yeah. We just basically say oh this month had no sranti this month did not have the sun moving from one sign of the zodiac to another so it's an adikmas this month as in the moon month as in the Indian lunar month right makes sense so because it is so dynamic uh it will correct itself over a period of I guess 2 years 3 years there will be one nadik mass or something two every two and a half years roughly there is a nadik mass correct it was 11 11 + 5 so something like yeah
wow so but You know this is the system used in most of India. Like I said, North India has a purimant calendar, new full moon to full moon. Middle India has an amant calendar. Actually, Kerala and Tamil Nadu have a solar calendar. They are not based on the moon like us. And West Bengal, Orisa, Assam have a combination of solar and uh lunar calendar. So you know it gets very interesting but that we will cover in a different episode on scrantis. I was just trying to wrap my head around this concept of scrantis and how it meshes with the lunar new year and the solar new year and now he's telling me there is a hybrid version
that is followed in the eastern parts of India and the southern parts of India follow a solar calendar. Okay. Wow. At least I now understand the Indian lunar calendar better. So thank you for that. Yeah. So I think the point I wanted to make was just because the western calendar is accepted all over the world and we just teach that again and again we sort of accept it as if it's the most natural thing it is not right the Indian calendar is equally if not more natural especially for the things that we really uh care about right but also this explains why ties are like this they start at random times and sometimes they are skipped and you know I think the
adikma system is also So quite interesting. So yeah, what I realized is that the Indian calendar was based on a system of very precise mathematics and very specific observations that you could do without involving acceptance from multiple people from a community as in you didn't have to make axium saying okay January has 31 days, August has 31 days but February has 28 days and 29 every four years. So the Indian calendar I think was designed as a system where anybody anywhere in the world could just look up at the sky figure out what the moon looks like figure out where the sun is and say oh this is XYZ day of XYZ year.
Yeah. And XYZ month rather. And there is a certain amount of elegance to it. But then in terms of learning curves, it has a very steep learning curve. And I hope we managed to make that steepness a little softer for you because he definitely did for me. And if you have any thoughts on these, we have a WhatsApp community where we discuss stuff like this. And sometimes the discussions get really fun, sometimes really spicy as well. Come join us there. QR code on your screen link in the description. Shri Kant here, Navin here, Future IQ.
And if you like this episode, you will like our episode on astrology which is based on very similar concepts. Yeah, you will. And we should do an episode on Sranti as well. Yes. Coming up next.