Because Jesus was crucified on a Friday, we need to find a Friday Passover in the Spring of AD 31.

Passover was always on the 14th day of the first month of the Jewish religious calendar. The months began with the first sighting of a crescent moon, which appeared a few days after the new moon. (The new moon is identified here as a solid black circle; the full moon as a solid white circle.) Depending on when the crescent was first observed, the fourteenth day of the month that began in mid-March of AD 31 would probably have landed on March 28 or 29. But Passover was never observed in March, because it was too early for the barley harvest. They needed a fresh sheaf of ripe barley for the wave sheaf offering two days after the passover.

So in AD 31 they needed to wait until the next month to begin their new year. (This extra month had to be inserted every few years because their calendar was not a full 365 days.) The next new moon fell on April 10 that year. If the new crescent was first observed on the evening of what we call April 13, then Day #1 of the new year would have been counted from sundown on April 13 until sundown on April 14. So the fourteenth day of their month, Passover, would have been celebrated from sundown on Thursday, April 26, until sundown on Friday, April 27. That makes Friday, April 27, AD 31, the most likely date for Jesus' crucifixion.

And Sunday, April 29 would have been the date of His resurrection. Incidentally, Jesus could not have been resurrected on Easter Sunday, because Easter is always the first Sunday after the first full moon after the Spring equinox. So Easter, a pagan holiday pre-dating the time of Christ, was probably on April 1 that year, four full weeks before Jesus' resurrection.