If your family keeps a birthday by tithi rather than by date, you already know the date moves. What is less obvious is that it moves in a strict pattern, and that the pattern is the calendar doing its job rather than failing at it.
The sequence
Take a birth on 15 August 1990, which was Shravana Krishna Navami. Here is where that tithi falls over the following years, with how far it moved each time:
| Year | Falls on | Moved |
|---|---|---|
| 1991 | 3 September | +19 |
| 1992 | 22 August | −11 |
| 1993 | 12 August | −11 |
| 1994 | 30 August | +18 |
| 1995 | 19 August | −11 |
| 1996 | 6 September | +19 |
| 1997 | 26 August | −12 |
| 1998 | 16 August | −10 |
Every step is either about eleven days earlier or about nineteen days later. There is no third case.
Why those two numbers
Twelve lunar months come to about 354 days. A solar year is 365. So a tithi anniversary falls about eleven days earlier each Gregorian year, and that is the ordinary case.
Left alone, that drift would carry every observance through all four seasons in roughly thirty-three years. A monsoon festival would become a winter one. Since the festivals and observances are tied to seasons, the calendar does not leave it alone.
Roughly seven years in nineteen, a thirteenth month is inserted. That year runs about 384 days, and instead of sliding eleven days back the anniversary jumps about nineteen days forward.
The two rates hold each other in place. Seven jumps of nineteen against twelve slides of eleven comes to +133 against −132: near enough zero across nineteen years.
Which is why the date comes back
Look at the last line of that table again, and then at 2009.
Nineteen years after 15 August 1990, the tithi falls on 15 August 2009. The same date.
That is the Metonic cycle, and it is not a coincidence of this particular birthday. 235 lunar months agree with 19 solar years to within a couple of hours, which is the same near-commensurability that fixes the intercalation rate at seven in nineteen. Seen from one end it is a rule about inserting months; seen from the other it is your tithi birthday returning to the date you were born on, once every nineteen years.
The years it does not happen
Some years the anniversary has no Gregorian date at all.
A tithi is twelve degrees of the Moon's elongation, not a length of time. Near perigee the Moon crosses it in under twenty hours, and such a tithi can begin after one sunrise and end before the next. No day carries it.
Across six sample birthdates over thirty years each (180 anniversary-years) fifteen had no date and three had two. So it is not a curiosity; it is roughly one year in twelve.
The page reports those years as having no date rather than substituting a nearby day, because which day an observance moves to is a decision for the tradition rather than for arithmetic. Some families keep it on the day the tithi begins; some on the following day.
Shraddha
The annual shraddha is kept on the tithi of death, during Pitru Paksha, the Krishna paksha of amanta Bhadrapada, which a purnimanta household calls Ashwin Krishna. Same fortnight, two names.
The fortnight closes at Sarvapitri Amavasya, on which shraddha is performed for anyone whose tithi is not known. The page gives that date alongside every year, and it does so for a practical reason: in a year when the death tithi is skipped, Sarvapitri is the answer the tradition already provides.
That case is not hypothetical. In Vikram Samvat 2081, Bhadrapada Krishna Pratipada (the first tithi of the fortnight) had no Gregorian date at all.
The intercalary month, and which one an anniversary follows
In a year carrying an adhika masa of the same name, the month name belongs to two months a lunation apart.
An anniversary follows the Nija month, the true one, since an adhika masa is an insertion rather than a return of the same month. The page resolves it that way and marks the year, so you can see when the choice arose. Some families observe in both months, which is a decision the page does not make for you.
What moves the answer
The month is taken from the amanta reckoning. A purnimanta household names a Krishna-paksha anniversary with the following month, but lands on the same day, since it is the same tithi in the same lunation and only the label differs.
The city matters more than it looks. A tithi boundary is one instant worldwide, but sunrise is not, so a tithi ending shortly after sunrise in one city ends shortly before it in another, and the anniversary moves by a day. A date computed for Delhi is not automatically the date for Chennai.
Why the drift is not a flaw
It is worth saying plainly, because a date that moves invites the assumption that something is broken.
The Hindu calendar keeps its months tied to real lunations. A full moon falls on Purnima, always, everywhere, because Purnima is defined as the full moon. That is a property the Gregorian calendar gave up entirely: its months are bookkeeping units of 28 to 31 days with no relation to the Moon at all.
Keeping the months lunar has a price, and the price is that twelve of them fall eleven days short of a solar year. The calendar pays it by inserting a thirteenth month periodically, and the eleven-day drift you see in your own birthday is that payment being made in instalments.
So the anniversary moving is the same mechanism that guarantees the Moon is where the calendar says it is. You cannot have one without the other.
Reading the table
Each row gives the Gregorian date, how far it moved from the previous year, and the length of the lunar year that produced the move.
A move of about eleven days back comes with a lunar year of roughly 354 days. A jump of about nineteen days forward comes with one of roughly 384. The two columns are the same fact stated twice, and having both makes it obvious which years carried an intercalary month without needing to be told.
Where a year offered a choice between an Adhika and a Nija month of the same name, the row says which one the anniversary was placed in.
Two households, two month names, one day
A Krishna-paksha anniversary carries different month names in different parts of India, and it is worth knowing before you compare notes with relatives.
A lunar month runs new moon to new moon across the south and west, and full moon to full moon across the north. During the waxing fortnight the two agree entirely. During the waning fortnight the northern reckoning has already started the next month, so it uses the following name.
A death or birth in Shravana Krishna paksha is therefore Shravana in Pune and Bhadrapada in Lucknow. The tithi is the same tithi, the day is the same day, and the observance falls on the same date. Only the label moves.
The page prints the amanta name because that is what the underlying month engine is built on, and it computes the anniversary from the tithi rather than from the name, so the answer is unaffected by which convention your family uses.
Why an anniversary can be a day out from a relative's
Two people can compute the same tithi anniversary and get dates one day apart without either having made a mistake.
The tithi boundary is a single instant everywhere on earth. Sunrise is not. If a tithi ends at 06:20 and sunrise is 06:10 in one city and 06:30 in another, the first city has that tithi at sunrise and the second does not, and the day the anniversary falls on differs accordingly.
This is not a rounding artefact and it cannot be averaged away. It is the direct consequence of naming days by a solar event and observances by a lunar one. A family spread across Chennai, Delhi and London should expect the occasional split, and the honest thing for a calculator to do is compute for the place you name rather than for a notional national location.