Here is a simple way to understand and calculate tithi (lunar day) in traditional Indian astronomy, which is also used in many calendars and religious observances.

What a tithi is

• A tithi is a 12-degree step in the angular difference between the Moon and the Sun.
• There are 30 tithis in a lunar month (usually), but the exact times can shift with the Moon’s motion and local time definitions.

How to calculate it (practical method) 1) Find the longitudes

• Determine the ecliptic longitude of the Moon (MoonLong) and the Sun (SunLong) for the date and exact time you care about.
• Use an astronomy Ephemeris or online calculator that gives celestial longitudes. The important part is the angular positions along the ecliptic.

2) Compute the difference

• Compute delta = (MoonLong − SunLong) modulo 360 degrees, so delta is in the range 0 to 360.

- If MoonLong is behind SunLong, add 360 to keep delta positive.

3) Determine the tithi number

• Divide delta by 12: q = delta / 12.
• The tithi number is floor(q) + 1.

- For example: - delta in [0, 12) → tithi 1 (Prathama) - delta in [12, 24) → tithi 2 - … - delta in [288, 300) → tithi 25 - delta in [300, 312) → tithi 26 - ... up to delta in [348, 360) → tithi 30

• If delta is exactly a multiple of 12 (e.g., 12, 24, 36, …), that moment is the end of one tithi and the precise start of the next. Observers may note the exact instant when delta equals k×12 degrees.

4) Local time and calendar specifics

• The exact tithi used in a calendar can depend on local rules:

- Which moments are used to mark the start of a tithi (local mean solar time, sunrise-based definitions, or a standard civil time). - Ayanamsa (the precession-corrected alignment between zodiacal signs used in some calendars) can shift longitudes and thus tithi boundaries.

• To assign a date in a specific calendar, you typically compute the tithi across the chosen local time standard and map the boundary instants to calendar dates in that system.

Notes and caveats

• Small differences in ephemeris data or time standard (UTC vs local solar time) can shift the exact start/end times of a tithi by minutes.
• Some months can appear to have 29 or 30 tithis depending on the Moon–Sun relative positions; the cycle is continuous, and calendar labeling handles this with the chosen rule set.

If you want, tell me the date, time, and location (time zone) you’re using, and I can illustrate the calculation step by step for that specific case.