Find the correct Shraddha tithi for ancestor rituals from the date of death, with annual Pitru Paksha dates.
Give a date of death and this page finds the tithi for the annual (pratyabdika) shraddha and the day in the year's Pitru Paksha on which that tithi falls, for a target year and a place. The anchor is not sunrise: it is aparahna-vyapini, the day whose aparahna the death tithi pervades.
Manu III.278 puts the rite of the gods in the forenoon and the rite of the pitrs in the aparahna, so the afternoon is the prescribed time and the afternoon is what a candidate day has to be tested against. Matching at sunrise instead puts the rite a whole day late whenever the tithi's boundary falls in the morning, which happens on roughly a quarter of cases, silently, on a fortnight that is otherwise correct.
Aparahna is taken in the five-fold reading, the stretch of daylight from three fifths to four fifths of the arc, which is this codebase's named default; the Kalanirnaya calls the five-fold division the one resorted to in the sastric passages. On an ordinary day that is roughly two and a quarter to two and three quarter hours, and it moves with the season and the latitude because it is a proportion of the real daylight.
The window in which the rite may be performed is wider than the anchor and is reported separately, so the two are never confused. The rite is begun in kutapa, the eighth diurnal muhurta, whose midpoint is apparent noon, and must close by the Rauhina, the twelfth: diurnal muhurtas eight to twelve, which is the tail of madhyahna plus the whole of aparahna (Prajapati-smrti 158-159; Matsya Purana 22).
The five-fold division itself is Satapatha Brahmana II.2.3.9 with Prajapati-smrti 156-157, reported by Kane in History of Dharmasastra Vol. II Part I.
The sources do not agree on what the pitrs attend. Manu III.278 gives aparahna, which is the anchor this page uses for the date and names as such. Kane, History of Dharmasastra V.i p.74, quotes the Grhya-parisista for the other: the pitrs attend on that tithi which exists at the time when the sun sets.
Both are computed for every candidate day and both are shown, because showing one and hiding the other would be this app settling a question the sources leave open.
When the question spans two days - the tithi touches the aparahna of both, or of neither - the Dharmasindhu (p.216, the Nirnaya Sindhu pp.354-355 the same) settles it for the annual, monthly and Mahalaya shraddha: the whole aparahna on one day only, that day; on both days, on neither, or in equal part, the earlier; in unequal part, the greater. The page names that day and shows both days with their coverage, beside Madhava's rival reading - the earlier day only if the next tithi is in ksaya - and the sunset reading.
The yugmavakya is the pairing rule that, for ordinary vratas, joins a tithi to its neighbour and can move an observance by a day. Kane records that pitr rites are expressly not governed by it, so no pairing, no plus or minus one day, and no second-day-of-the-pair adjustment is applied anywhere in this calculation.
That statement is carried in the response itself rather than left as a comment in the engine, so that no later screen can quietly reintroduce it. The day returned is the day on which the death tithi actually pervades aparahna, and nothing shifts it afterwards.
Pitru Paksha is the dark fortnight of Bhadrapada, and this page selects it from the almanac's own masa rather than from a hard-coded September to October range, because the fortnight drifts across an August to November window from year to year and a fixed range would be wrong in the years it drifts out of.
The fortnight is listed day by day with the tithi on each, and the days on which the death tithi is present at aparahna are marked, so a family that remembers the tithi but not the Gregorian date can still find the day. Because aparahna is a proportional division of the local daylight, supplying a place changes which day is marked in the borderline cases.