One synodic cycle, thirty tithis
For a given instant, subtract the Sun’s apparent geocentric ecliptic longitude from the Moon’s and wrap the difference into 0°–360°. Divide that elongation by 12° and take the whole-number segment. The result is one of thirty numbered tithis. Segments 0–14 belong to Shukla, the waxing paksha; segments 15–29 to Krishna, the waning paksha. The fifteenth waxing tithi is Purnima and the fifteenth waning tithi is Amavasya. The Positional Astronomy Centre’s national panchang explanation defines a tithi by the Moon gaining 12° of longitude on the Sun; its name table lists the traditional English transliterations.
Unlike a fixed 24-hour civil date, a tithi’s duration varies because the Moon’s speed relative to the Sun changes. A tithi can begin during a local day, last into the next, or pass entirely between two sunrises. The calendar therefore presents both the daily sunrise label and the complete series of ending instants. The next-tithi column in that series tells you which segment begins at the ending instant. A row at local midnight belongs to the new civil month only; adjacent month tables do not duplicate that event.
Why local sunrise matters
A daily panchanga commonly names the tithi prevailing at sunrise. Sunrise is local: its UTC time depends on latitude, longitude, date, and a rise convention. This calculator asks for coordinates and finds each sunrise with the bundled astronomical library’s solar rise search. It then computes the Moon–Sun separation at that instant. The tithi changeover itself is a geocentric angular event and has one UTC instant everywhere. A sunrise in Delhi and a sunrise in London can therefore sample different tithis on dates with the same civil number.
The daily row states when its sunrise tithi ends, even if that ending lies on the following civil date. “Same tithi at next sunrise” means no ending occurred between those two sunrises, so the sunrise label repeats. “Two tithi endings” means the intermediate tithi may never be named at sunrise: it is still visible in the lower event table. These counts are diagnostic, not judgments about a festival or observance.
Sidereal setting and the clock
The tool calculates both Sun and Moon as apparent geocentric longitudes on the true ecliptic of date using bundled Astronomy Engine 2.1.19. The site’s other Vedic calculators may subtract an approximate Lahiri ayanamsa to find sidereal rashi or nakshatra. A tithi uses Moon minus Sun; subtracting the same ayanamsa from both cancels it exactly. No Lahiri correction is therefore applied to the tithi result. That distinction prevents a sidereal zodiac setting from appearing to change the lunar phase angle.
The chosen month is a local civil interval at one user-entered fixed UTC offset. The tool converts its two midnight edges to UTC, finds changeovers, then prints both local clock and UTC labels. If an area changes clocks within the month, a single offset will mislabel some local rows. Use the UTC column and the actual zone rule for those instants. The calculator does not infer a city, legal time zone, or historical daylight-saving rule.
Precision and comparison
The calculation samples the Moon–Sun angle every two hours and brackets each detected 12° crossing. Bisection narrows a crossing to 15 seconds; rows print only minutes. Exact agreement with an almanac is not promised: ephemerides, apparent-position conventions, solar-rise models, and rounding can differ. Latitude matters for the sunrise table, not for the geocentric tithi ending instant. Near a sunrise boundary, a small numerical difference can change which tithi is assigned to a day.
The daily panchanga calculator adds nakshatra, yoga, karana, and weekday for a chosen date and instant. This monthly page concentrates on tithi through the whole selected month. Neither page supplies regional festival assignment or an auspicious-time rule. Compare an external almanac only after matching the location, rise convention, clock offset, and whether the quoted time is a tithi’s beginning or ending.
Frequently asked questions
Is a tithi the same as a Moon phase?
Both depend on Sun–Moon angular separation. A broad phase name such as waxing crescent spans several tithis; this calendar divides the full cycle into thirty 12° intervals.
Why do some sunrise tithi names repeat?
A tithi can last longer than the gap between two local sunrises. The same tithi is then present at both sunrises.
Why can a tithi be absent from the sunrise list?
A shorter tithi can start and finish between consecutive sunrises. It is still listed by ending time in the event table.