How Tithi (Lunar Day) Is Calculated from Moon–Sun Positions — A Worked Example

Every panchang lists a tithi for the day — Trayodashi, Chaturdashi, Purnima — and most people treat it like a calendar date you look up. It is not. A tithi is computed from just two numbers: the ecliptic longitudes of the Moon and the Sun at the moment you care about. One subtraction, one division, and you have the tithi. This guide states the exact rule, lists all thirty tithis, explains why tithis are not 24 hours long, and then works a complete example — real longitudes for Lahore on 24 October 2026 — showing every step.

The single rule: 12 degrees of elongation

Take the Moon’s geocentric ecliptic longitude and subtract the Sun’s geocentric ecliptic longitude. The result, normalized to 0°–360°, is called the elongation — how far ahead of the Sun the Moon has travelled around the zodiac since the last new moon.

One tithi = exactly 12° of elongation.

That is the entire definition. The Moon gains on the Sun at an average rate of about 12.19° per day (the Moon moves ~13.18°/day eastward, the Sun ~0.98°/day, and 13.18 − 0.98 ≈ 12.2), so 360° of elongation takes roughly 29.53 days — one synodic lunar month — and 360 / 12 = 30 tithis per lunar month.

The tithi number at any moment is:

tithi = floor(elongation ÷ 12) + 1

And the paksha (fortnight) falls out of the same number:

• Elongation 0°–180° (tithis 1–15): Shukla Paksha, the waxing fortnight. At 0° the Moon and Sun are conjunct (Amavasya, new moon); at 180° they are opposite (Purnima, full moon).
• Elongation 180°–360° (tithis 16–30): Krishna Paksha, the waning fortnight. At 360°/0° the cycle closes back at Amavasya.

A useful corollary: the ayanamsa correction (the ~24° difference between tropical and sidereal zodiacs) cancels out completely, because the tithi depends only on the difference of the two longitudes. Whether you compute in tropical or sidereal coordinates, the elongation — and therefore the tithi — is identical.

The thirty tithis

Each 12° slice has a name. Tithi 1 covers elongation 0°–12°, tithi 2 covers 12°–24°, and so on:

Shukla Paksha (waxing):

1. Pratipada (Prathama) · 2. Dwitiya · 3. Tritiya · 4. Chaturthi · 5. Panchami · 6. Shashthi · 7. Saptami · 8. Ashtami · 9. Navami · 10. Dashami · 11. Ekadashi · 12. Dwadashi · 13. Trayodashi · 14. Chaturdashi · 15. Purnima

Krishna Paksha (waning):

16. Pratipada · 17. Dwitiya · 18. Tritiya · 19. Chaturthi · 20. Panchami · 21. Shashthi · 22. Saptami · 23. Ashtami · 24. Navami · 25. Dashami · 26. Ekadashi · 27. Dwadashi · 28. Trayodashi · 29. Chaturdashi · 30. Amavasya

So “tithi 13 of the month” with elongation below 180° is Shukla Trayodashi; the same number 13 with elongation above 180° (tithi 28) is Krishna Trayodashi. The name repeats across pakshas — the paksha is what disambiguates.

Why tithis are not 24 hours long

If elongation grew at exactly 12°/day, every tithi would last exactly 24 hours. It does not, for two physical reasons:

1. The Moon’s orbit is elliptical. Near perigee the Moon races (over 15°/day of orbital motion); near apogee it crawls. The elongation rate swings roughly between 11° and 15° per day.

2. The Earth’s orbit is elliptical too, so the Sun’s apparent speed varies slightly through the year.

The result: a tithi lasts anywhere from about 19 to 27 hours, averaging ~23.6 hours. Two knock-on effects appear in real panchangs:

• Kshaya tithi (lost tithi): if a tithi begins after one sunrise and ends before the next, no sunrise falls inside it — that tithi never becomes “the tithi of the day” and is skipped in day-counting.
• Vriddhi / adhika tithi (extra tithi): if a tithi spans two sunrises, it is counted on both days and the calendar effectively gains a day.

The tithi boundaries themselves — the exact moments elongation crosses each multiple of 12° — are what panchang software actually computes, usually quoted to the minute.

Worked example: Saturday, 24 October 2026, Lahore, 12:00 noon PKT

Inputs — geocentric ecliptic longitudes for 24 October 2026, 07:00 UTC (12:00 noon PKT), computed from standard low-precision solar/lunar theory:

• Sun’s longitude: 210.887°
• Moon’s longitude: 6.306°

Step 1 — Elongation. Moon − Sun = 6.306 − 210.887 = −204.581°. Normalize by adding 360°: 155.419°.

Step 2 — Tithi number. 155.419 ÷ 12 = 12.95. Floor = 12, plus 1 → tithi 13.

Step 3 — Paksha. 155.419° < 180° → Shukla Paksha (waxing).

Step 4 — Name. Tithi 13 of Shukla Paksha = Shukla Trayodashi.

Answer: at noon in Lahore on 24 October 2026, the running tithi is Shukla Paksha Trayodashi.

Now the boundaries. Scanning the elongation hour by hour around this date gives the exact moments it crosses multiples of 12° (times in PKT):

Check the lengths: Dwadashi lasted 23 h 50 m, Trayodashi 23 h 04 m, Chaturdashi 22 h 24 m, Purnima 21 h 51 m — visibly shrinking as the Moon accelerates toward perigee. None is 24 hours, which is exactly the point.

Two cross-checks against published panchangs for 24 October 2026: they list Trayodashi (Shukla) ending early afternoon, followed by Chaturdashi — matching our computed 1:20 PM PKT boundary to within minutes — and they name the day’s tithi Trayodashi, because Trayodashi was already running at Lahore’s sunrise (~6:11 AM PKT; elongation then ≈ 152°, still inside tithi 13). The convention is that the tithi running at sunrise is the tithi of the day, even though a new tithi begins mid-afternoon.

Also note the full moon is one step away: elongation reaches 180° on the morning of 26 October, which is Purnima — consistent with the published festival calendar placing Sharad Purnima around that date.

Five mistakes that break real tithi calculations

1. Reading the tithi from the Moon’s sign or nakshatra alone. The tithi is a function of the Moon–Sun difference. The Moon’s lone position tells you nothing about it — you need both longitudes.

2. Assuming every tithi is 24 hours. Real tithis run ~19–27 hours. Spacing events “one tithi apart” by calendar days will drift; use the elongation boundaries.

3. Applying the ayanamsa twice or worrying about it at all. The elongation is ayanamsa-independent. Any consistent zodiac (tropical or sidereal) gives the same tithi.

4. Confusing the moment’s tithi with the day’s tithi. At 2:00 PM PKT on 24 October the running tithi is already Chaturdashi, but the day’s tithi (sunrise rule) is Trayodashi. Panchangs print the sunrise tithi; muhurat software uses the running one.

5. Forgetting the wrap at 0°/360°. When the Moon’s longitude is numerically smaller than the Sun’s (as in this example: 6.306° vs 210.887°), the raw subtraction is negative — add 360° before dividing, or you will land in the wrong paksha entirely.

Compute it for your own date

You need only the two longitudes for your moment — any ephemeris or astronomy library gives them; the elongation arithmetic above does the rest. The nakshatra calculator and rashi calculator cover the Moon-based side of the panchang, and the kundali matching calculator handles compatibility — then apply the 12° rule here to pin down the tithi underneath any of them.

FAQ

What is a tithi, in one sentence?

The time during which the Moon–Sun elongation increases by exactly 12° — one-thirtieth of a lunar month, lasting roughly 19–27 hours.

How is tithi different from a lunar day in the Western sense?

A Western “lunar day” usually means 1/29.53 of a synodic month counted from a new moon. A tithi is finer-grained and phase-anchored: thirty equal 12° slices of elongation, each with its own name, so the tithi directly encodes the Moon’s phase.

Why do two panchang apps sometimes disagree on today’s tithi?

They disagree on the boundary times, not the rule. A few arcminutes of difference in the computed Moon position (different ephemeris, parallax or refraction corrections, topocentric vs geocentric) shifts a boundary by minutes — enough to flip which tithi is “running” near the crossover, while both apps use the same 12° definition.

Does the tithi depend on my location?

Barely. Elongation is essentially geocentric; topocentric parallax shifts the Moon’s apparent longitude by up to ~1°, which can move a boundary by up to an hour or so. That is why panchangs are computed per city, but the tithi sequence is the same worldwide.

What are Shukla and Krishna Paksha?

The waxing and waning fortnights. Shukla Paksha runs from Amavasya (elongation 0°) to Purnima (180°); Krishna Paksha runs from Purnima back to Amavasya (180°–360°). The tithi names repeat, so “Trayodashi” alone is ambiguous — the paksha completes it.

What is a kshaya tithi?

A tithi so short (near perigee, when elongation races) that it starts after one sunrise and ends before the next. With no sunrise inside it, it never becomes any day’s tithi and is skipped in the calendar count — roughly a few times a year.

Can a tithi really last two calendar days?

Yes — that is a vriddhi (adhika) tithi. Near apogee the Moon dawdles, a tithi stretches past 24 hours and contains two sunrises, so it is counted as the tithi of both days.

How do I find the exact start and end of the current tithi?

Compute elongation now, find the surrounding multiples of 12°, and solve for when elongation equals each — either by scanning forward/backward in small time steps (as in the worked example) or with a root-finder on the elongation function. Panchang software does exactly this, quoting the result to the minute.