Tithi — The Lunar Day

We are now ready for the first of the five limbs of panchang. It is the most important one, the one most often used in everyday life — the one your grandmother was checking when she said “today is Ekadashi” or “Purnima is on Tuesday this month.” It is called tithi (तिथि), and it is the lunar day.

Tithi is not the same as a regular day. A regular day, as we saw, is about Earth’s rotation. A tithi is about the Moon — specifically, about the angle between the Sun and the Moon as seen from Earth. That sounds technical, but the idea is very simple, and once you see it, you cannot un-see it. By the end of this chapter we will have computed an actual tithi by hand, walked through the Jain six-ghati rule on a real date, and understood why a single tithi can be 20 hours long one week and 26 hours long the next.

The 12° rule

Imagine you are standing on Earth, looking up. The Sun and the Moon are both somewhere in the sky. The Moon is moving around the Earth. That means, from our point of view, the Moon is gradually moving away from the Sun’s position in the sky each day, getting further ahead, then catching up again on the other side, in a 29.53-day cycle. (This is the synodic month we met in the previous chapter.)

The Indian calendar takes this cycle and divides it into 30 equal parts. The full circle around the sky is 360°. Divide that by 30 and you get 12°. Each 12° gap between the Moon’s position and the Sun’s position is one tithi.

More formally, if we denote the Moon’s ecliptic longitude as λ_M and the Sun’s as λ_S, the tithi index at any moment is:

Tithi number = floor((λ_M − λ_S) mod 360 ÷ 12) + 1

That single formula, with the 12° spacing, is the entire astronomical definition. Everything else — naming, paksha, festival timings — is interpretation.

The 30 tithis: Shukla and Krishna paksha

Those 30 tithis are split into two halves of 15 each.

• Shukla Paksha (शुक्ल पक्ष) — the bright fortnight. From new moon to full moon. The Moon is waxing, getting fuller every night.
• Krishna Paksha (कृष्ण पक्ष) — the dark fortnight. From full moon to next new moon. The Moon is waning, getting thinner every night.

Within each paksha, the 15 tithis have names. The first 14 share the same names in both halves — they are simply numbered. The 15th has a special name in each half: Purnima for the full moon at the end of Shukla, Amavasya for the new moon at the end of Krishna.

So if someone says “Krishna Ashtami”, they mean the 8th tithi of the dark fortnight — that is the day we call Janmashtami, the birth of Krishna. “Shukla Chaturthi” means the 4th tithi of the bright fortnight. The naming is regular and predictable once you have the pattern. A festival date in the Indian calendar is always “month + paksha + tithi”: Vaishakh Shukla Tritiyameans “the third tithi of the bright fortnight in the month of Vaishakh.” That is Akshaya Tritiya.

The Jain Tirthankara connection

For Jain readers, tithi has a particular weight. The five kalyanakas — chyavan (descent), janma (birth), diksha (renunciation), kevalajnana (omniscience), and nirvana (liberation) — of each Tirthankara are recorded as month + paksha + tithi. The Pramanik Panchang Events Master maintains these for all 24 Tirthankaras. When you see “Mahavir Janma Kalyanak” on a date, it is because Chaitra Shukla Trayodashi falls on that civil day. Festivals are not attached to fixed calendar dates; they are attached to lunar coordinates that recur each year as the Sun and Moon revisit the relevant configuration.

Why tithis are not equal in clock-time

Here is the subtle part. A tithi is defined by a 12° angular gap between Sun and Moon — not by a fixed amount of time. The Moon does not move at a constant speed across the sky. Sometimes it is a bit faster, sometimes a bit slower. So one tithi might take about 20 hours to complete, and the next might take about 26 hours.

Why does the Moon’s apparent speed change? Two reasons, both stated cleanly by Kepler in 1609 and known qualitatively to Indian astronomers many centuries earlier under the names manda and shighra.

1. The Moon’s orbit is an ellipse, not a circle. When it is closer to Earth (at perigee, near a point called the lunar apsis) it moves faster across the sky; when farther (at apogee) it moves slower. This effect alone produces a variation of about ±13% from the mean speed.
2. The Sun is also moving in apparent longitude (because Earth is moving around the Sun). The Sun’s motion is also slightly non-uniform, by Kepler’s second law applied to Earth’s orbit, but this is a much smaller effect — about 1° variation across the year.

On average, a tithi is about 23 hours and 37 minutes long — slightly less than a regular solar day (the synodic month is 29.53 days ÷ 30 tithis = 23.62 hours). This is why a tithi can begin and end at any time of day or night. Two tithis can occur within a single 24-hour day, or one tithi can span across two days.

And that creates a question. If a tithi can change in the middle of the day, which tithi does the day “belong to”?

How different traditions answer the question

This is the central question that splits panchang traditions, and understanding it is what allows you to compare two panchangs intelligently when they disagree on a festival date.

The basic puzzle: imagine the morning of 15th of some month. Sunrise is at 6:30 AM. Tithi 5 (Panchami) is in effect at 6:30 AM but ends at 8:00 AM, after which Tithi 6 (Shashthi) takes over and remains until tomorrow morning. Is today Panchami, or Shashthi?

Different traditions give different answers, and each answer is defensible.

• Sunrise rule (general Smarta tradition). Whichever tithi is current at the moment of sunrise is the tithi for the day, regardless of how briefly. By this rule, today would be Panchami, even though it ends 90 minutes after sunrise.
• Daytime majority rule (some Vaishnava traditions for fast days). Whichever tithi covers more than half the time between sunrise and sunset is the tithi for the day.
• Sunset rule (some southern regional panchangs for specific observances). Whichever tithi is current at sunset.
• Six-ghati rule (Jain udaya tithi, used by this panchang). The tithi must be in effect for at least the first six ghatis (~2h 24m) after sunrise to count as the udaya tithi. If it ends sooner, the next tithi takes over the day.

None of these are “wrong.” They are different conventions for handling the same astronomical fact (a tithi change near sunrise). The Jain six-ghati rule has a particular logic to it that we explain next.

The Jain rule — Udaya tithi with six ghatis

The Jain tradition specifies: the tithi that is active during the first 6 ghatis (about 2 hours and 24 minutes) after sunrise is the tithi for the entire day. This is called udaya tithi (उदय तिथि)— the “rising tithi” — because it is the tithi that prevails as the day rises.

Why specifically six ghatis? A ghati is (घटी) 24 minutes; six of them is 144 minutes, or 2 hours 24 minutes. In the classical Jain scheme, this corresponds to the first muhurta after sunrise plus the morning twilight period, traditionally considered the most ritually significant window of the day — the time of navakar mantra and morning observances. Tying tithi-determination to this window aligns the calendar with ritual life: the tithi that holds during morning observances should be the tithi attributed to the day. The rule is also clean, deterministic, and fully computable — properties that matter when you are running a calendar for an entire community across many locations and times.

Worked example A — tithi survives the window

Suppose Tithi 5 (Panchami) began yesterday at 10:00 PM and ends today at 10:00 AM. Sunrise today is at 6:30 AM. The first six ghatis run from 6:30 AM to 8:54 AM. Is Panchami in effect for that entire window?

Yes — Panchami is active from 6:30 AM all the way until 10:00 AM, which is well after 8:54 AM. So Panchami is the udaya tithi. Today, from midnight to midnight, is recorded as Panchami in the Jain panchang. Even though Panchami ends at 10:00 AM and the rest of the day is technically Shashthi, that does not change the label. The day is Panchami.

Worked example B — tithi fails the window

Suppose Tithi 5 began yesterday at 4:00 AM and ends today at 7:00 AM. Sunrise is again at 6:30 AM. The first six ghatis run from 6:30 AM to 8:54 AM. Is Panchami in effect throughout that window?

No — Panchami is active from 6:30 AM to 7:00 AM (only 30 minutes), and then Shashthi takes over from 7:00 AM through 8:54 AM and beyond. Panchami did not hold the window. Therefore the udaya tithi for today is Shashthi. Today is Shashthi from midnight to midnight, even though it “started” technically as Panchami.

Worked example C — boundary case

What if Panchami ends at exactly 8:54 AM, on the boundary? Different acharyas have given slightly different rulings on the boundary case. The conservative Jain reading, and the one this panchang follows, is that the tithi must be present throughout the six-ghati window — strictly. If the change happens at the boundary or before, the next tithi wins. This means a tithi must be active at the start of the seventh ghati to be the udaya tithi.

Tithi vriddhi and tithi kshaya

Two more terms you will eventually run into.

Because tithis are uneven in length, sometimes a single tithi is long enough to stretch across two consecutive sunrises. In that case, two consecutive days both get labelled with the same tithi. This is called tithi vriddhi (तिथि वृद्धि)— “tithi growth.” A tithi that takes two days to be observed.

The opposite also happens. Sometimes a tithi is so short, and positioned so unfortunately, that it begins and ends entirely between two sunrises — meaning it never “rises” on its own day. The calendar simply skips it. This is called tithi kshaya (तिथि क्षय)— “tithi loss.” A tithi that gets dropped from the calendar.

On average these mostly cancel out and a lunar month still has 30 tithis spread across roughly 29–30 civil days. But it is why two people in different traditions can sometimes disagree by one day on when a festival falls — and now you understand why. When a tithi like Mahashivaratri (Phalgun Krishna Chaturdashi) is either vriddhi (lasts two days) or near-vriddhi, different rules about “which day to observe it on” produce divergent festival dates. The disagreement is real; the astronomy is unambiguous.

The mean tithi vs the true tithi

One last technical point that you may encounter in older texts. Classical Indian astronomy distinguishes between the mean tithi (मध्यम तिथि) — computed assuming the Sun and Moon move at constant average speeds — and the true tithi (स्पष्ट तिथि) — computed using their actual non-uniform motion. The siddhanta texts contain elaborate corrections to convert mean to true. Modern panchangs always use the true tithi, computed from current astronomical ephemerides. We mention this only so that if you read a nineteenth-century almanac and see the term, you know what the author meant.

What you should be able to do now

After this chapter, you should be able to:

• State the 12° rule in one sentence.
• Compute, given Sun and Moon longitudes, which tithi is in effect.
• Name the two pakshas and what is happening to the Moon in each.
• Explain why tithi length varies by 20–26 hours, and connect it to the Moon’s elliptical orbit.
• List the four major rules different traditions use to assign a tithi to a civil day.
• State the Jain udaya-tithi six-ghati rule and apply it to a sample day.
• Define tithi vriddhi and tithi kshaya, and explain why they cause inter-tradition festival-date disagreement.

Open the daily panchang on this site. Find today’s tithi at the top, along with the time at which it ends. Notice that the tithi is named for the entire day, even if it ends in the morning — that is the udaya rule in action. Now go to a date a few months ahead, find a day with a long tithi-end time (say, late evening), and check what the tithi is. Predict, using the rule, what tomorrow’s tithi will be. Then verify.

In the next chapter we look at the simplest of the five limbs — vara, the weekday — and find that even Monday-Tuesday-Wednesday has a deeper structure than we usually notice. The order of the days of the week is not arbitrary; it is the answer to a specific astronomical question, and the seven-fold cycle is older than any of the modern calendars that use it.