Going from a Gregorian date to a Hindu one is a lookup. You take the date, find the tithi running at sunrise, name the month, and you are done.
Going the other way is not a lookup, and it is not a function. Some Hindu dates have no Gregorian date at all. Others have two.
Every converter I could find returns exactly one date regardless of which case it is in. That is the thing this page does differently.
Why the reverse direction breaks
A tithi is one thirtieth of the Moon's circuit relative to the Sun: twelve degrees of elongation. It is an arc, not a duration.
The Moon does not cross that arc at a constant rate. Near perigee it takes under twenty hours. Near apogee, over twenty-six. Meanwhile sunrises stay stubbornly twenty-four hours apart, and it is the tithi at sunrise that names the day.
So two things happen, both regularly.
A short tithi can begin after one sunrise and end before the next. No day carries it. If you ask for that date, the honest answer is that it does not exist in the Gregorian calendar, not that it is approximately some nearby day.
A long tithi can span two sunrises. Two days carry the same name. Asking for that date has two answers.
How often, exactly
This is measurable, so it is worth measuring rather than describing.
Over five Vikram years at Varanasi there are 1800 tithi names. Of those, 82 have no Gregorian date at all and 53 have two. That is 4.6% and 2.9%, or 7.5% between them, better than one name in every fourteen.
The two figures are not independent, and the relationship is a good check on whether a converter is working.
There are thirty tithis to a lunation of about 29.53 days, so tithi names outnumber days by 30 ÷ 29.53, about 1.6%. That surplus has to appear somewhere, and it appears as skips exceeding doubles. Measured across those five years: 82 against 53, a net 1.6%.
A converter whose repeats outnumbered its skips would be broken in a way that no single lookup could ever reveal. That identity is asserted in this site's tests.
The third ambiguity: which month you meant
In a year with an intercalary month, a month name belongs to two months.
Ask for Shravana Shukla Panchami in Vikram Samvat 2080 and there are two answers a lunation apart: 23 July 2023 in Adhika Shravana, or 21 August 2023 in Nija Shravana. The page asks which you mean rather than choosing.
An observance kept annually normally follows the Nija month, since an adhika masa is an insertion rather than a return of the same month. Some families keep both.
The month has two names, and both are right
A lunar month can run new moon to new moon (amanta, across the south and west) or full moon to full moon (purnimanta, across the north).
During the waxing fortnight the two agree completely. During the waning fortnight the purnimanta month has already moved on, so it carries the following month's name.
The page prints both for every date. A date in Shravana Krishna paksha by amanta reckoning is Bhadrapada Krishna by purnimanta reckoning, and someone looking for it under either name should find it. The day is identical; only the label moves.
Three eras, and why they disagree with each other
The page reports three year-counts, and they do not turn over on the same day.
Vikram Samvat, Chaitra-based, is the usual northern reckoning and runs about 57 years ahead of the Common Era. Shaka Samvat, the Indian national calendar's era, runs 78 behind and also turns at Chaitra, so it is always exactly 135 less than the Chaitra-based Vikram year.
Vikram Samvat, Kartika-based is the Gujarati reckoning, and it turns at Diwali instead. So for the stretch between Chaitra and Kartika it trails the northern year by one, and for the stretch from Kartika to Phalguna the two agree.
That is why a Gujarati almanac and a north Indian one can print different samvat numbers for the same day without either being wrong. The page shows both and names which is which.
The arithmetic here has a trap that is easy to fall into. The samvat turns at Chaitra, in March or April, so a date in January belongs to the samvat that began the previous spring. A converter that keys off the Gregorian year alone reports January dates a full year early, and it does so silently.
Why the two calendars cannot line up in the first place
The mismatch is not a defect in either system. It is what happens when you build one calendar on the Moon and another on the Sun.
A lunation (new moon to new moon) averages 29.53 days. Twelve of them come to about 354. A solar year is 365.24. Neither number divides the other, and neither is a whole number of days, so no arrangement of months can make the two agree permanently.
The Gregorian calendar solves this by abandoning the Moon entirely. Its months have nothing to do with lunar phases; a "month" is a bookkeeping unit of 28 to 31 days, chosen so that twelve of them fill a solar year.
The Hindu calendar refuses that trade. Its months are real lunations, so the Moon's phase on a given date is not an accident, and a full moon really does fall on Purnima everywhere and always. The price is that twelve of those months fall eleven days short of the solar year, and the calendar has to make the shortfall up.
It makes it up by inserting a thirteenth month roughly seven years in nineteen. That keeps the festivals in their seasons while keeping the months tied to the Moon, and it is why the two calendars drift against each other by about eleven days a year and then lurch back by nineteen.
Conversion between them is therefore not a formula. It is a lookup against where two bodies actually were.
Reading the tithi times
The forward direction gives you a span, not an instant, and the span is worth reading rather than skipping.
A tithi that begins at 06:53 and ends at 04:52 the following morning is telling you something: it started just after sunrise and ended just before the next one, and it is therefore a tithi that names no day. A tithi running from 04:44 to 06:25 the next day spans two sunrises and names both.
The start and end times also explain why an observance can be on a day the tithi is barely present for. Festivals are decided by the tithi occupying a particular window, and that window is not always sunrise. The festival calendar applies those rules; this page gives you the raw spans they are applied to.
What the sunrise reckoning means in practice
One consequence catches people out. Because the day is named by the tithi at sunrise, the Hindu day effectively runs sunrise to sunrise rather than midnight to midnight.
So an event at 2 a.m. belongs to the previous Hindu day, not the one the wall clock shows. A birth just after midnight on the 15th may carry the tithi and weekday of the 14th, which is why a birth chart and a birth certificate can disagree about the day without either being wrong.
The page uses the same convention throughout, and reports the sunrise it reckoned from so the boundary is visible rather than implied.
Why the city changes the answer
The tithi boundary is a single instant worldwide. Sunrise is not.
A tithi ending twenty minutes after sunrise in one city ends twenty minutes before it in another, and the day it names changes accordingly. That is not a rounding difference; it moves the date.
So a conversion is only meaningful with a place attached, and a table of Hindu dates published nationally is really a table for one city. The selector here is doing work.
What the page shows you
In the forward direction: the tithi with its start and end times, the paksha, the month under both reckonings, all three eras, and the sunrise the day was reckoned from.
In the reverse direction: the date, or two dates, or a clear statement that there is none, and in that last case, the exact span the tithi occupied, so you can see for yourself that it fell between two sunrises rather than being missing from the data.
That last part matters. "No date" from a calculator usually means a bug. Here it is an answer, and the page shows its working so you can tell the difference.