About 358 AD, Hillel II established a fixed Jewish calendar based on mathematical and astronomical calculations. It replaced previous systems which had been based on observation of the moon, when the first sliver of light following a new moon determined the first day of the month. Click here to access his actual dates for 563 AD and view approximate dates for 31 AD that are based on Pope Gregory's western calendar established in 1582.
Ten days were added to the calendar by Pope Gregory in 1582 when October 5th became October 15th. So to convert back to a previous Julian date, if it is just prior to that day in 1582 we subtract 10 days from the Gregorian date, if before 1500 9 days, 1400 8 days, 1300 7 days, 1100 6 days, 1000 5 days, 900 4 days, 700 3 days, and before 600 was 2 days.
Accordingly that Passover Sunday in 563 AD is in fact March 25th in the Julian calendar that the Romans used.
Continuing with the above rules, if before 500 subtract 1 day from the date.
Before 300 AD, the 10 days are finally accounted for.
Then, if before March 1st in 200 AD, it appears we subtract 1 day from the day of the week instead, to account for the leap day that was used in the Julian calendar on Feb 29th,
and if before 100 AD, subtract 2 days from the day of the week.
Thus that Passover "Tuesday" in 31 AD lines up again as Sunday March 25th.
Now, as mentioned above, the actual time when it was chosen (as recorded in Scripture) was back then based on a priestly declaration regarding the new moon and the start of the month.
The early church records - according to Dionysius in 525 AD - indicated that Easter came on Sunday March 25th in 31 AD. Accordingly, the first day of the Passover occurred at the crucifixion on Friday March 23rd. While this may suggest a two day discrepancy, the later change of approach from observation to "technical" Passovers means that there is minimal / no historical contradiction with Hillel's calendar.
In fact, one explanation may be that from early on, the Friday crucifixion was associated by many religious scholars with the 14th day of the Jewish month, as that was the day a Passover lamb was sacrificed before the evening meal. This meant the 15th day of the month, the first day of the Feast, when the whole world was delivered because of the death of Christ, this day found itself recorded as occurring on Saturday, March 24th. In 525 AD, the situation further complicated itself in Dionysius's 532 year calculations, when in 563 AD, March 24th reverted back to being itself seen as the 14th day of that Jewish month. Accordingly the "15th" day found itself as coming that next day i.e. Sunday, March 25th.