History only allows for a limited time frame for when Jesus could possibly have died on the cross. The Bible says that Jesus died while Pontius Pilate was governor over Judaea, Herod Antipas over Galilee, and Caiaphas was High Priest. Herod reigned from 4 BC to 39 AD. Pilate reigned from AD 26 to 36, and Caiaphas was High Priest from AD 18 to 36. So the possible time range of Jesus' death would be from AD 26 to 36.
Also of interest, the Samaritan historian named Thallus, in his work Histories, says that the moon of April 3rd of 33 AD was a Paschal full moon. A Paschal full moon corresponds to 14th day of a lunar month (the 14th day of Nisan of 33 AD is April 3rd). Paschal means Passover, and it was named so because it is the full moon of the Passover. This affirms that the crucifixion occurred on a Passover.
Eusebius, writing about the 18th year of Tiberius Caesar, wrote that Christ died that year. Using Wikipedia's dates, this would be 33 AD. According to Wikipedia, Tiberius began his reign on the 18th of September in 14 AD. Counting September as his first month, the crucifixion occurring in his 18th year would be 33 AD, since he would have reigned 18 years 7 months.
The angel Gabriel came to Daniel and told him that the Jews would have 70 7s to finish the transgression against God, to be done with sin, for reconciliation to be made, to bring in everlasting righteousness, to complete God’s revelation, and to consecrate the Holy of Holies. Then the angel said that after the decree to rebuild Jerusalem until the Anointed One would die there would be 7 7s and 62 7s. It was Artaxerxes who made the decree in 444 BC in his 21st year. The "7s" are said to mean weeks of years, according to biblical scholars. After doing the math, there would be 49 years and 434 years, which adds up to 483 years. Now this is lunar years, since the all dates in the Old Testament follow the lunar calendar. To convert any Old Testament date to a Gregorian date (our calendar is called the Gregorian calendar), follow the following equation:
(x=biblical date, y=Gregorian date)
After applying this method to the Daniel prophecy, from the decree to the Crucifixion, there were 476 years, 3 weeks, 3 days, 15 hours, 9 minutes, 54 seconds, and 43.2 milliseconds (once an exact total of lunar days is found, a more correct exact total can be calculated). Add 476 years to 444 BC and the sum is 33 AD. If you consider that there was a lunar eclipse (that lasted 2 hours and 50 minutes) on April 3rd of 33 AD, and that April 3rd was right before the passover (meaning this was the day Jesus died on the cross), then we can work backwards to find out exactly when Artaxerxes gave the decree. This date would be Friday, March 13th, 444 BC. This date is Artaxerxes' 21st year.
Year of the King
However the Book of Nehemiah says that it was his 20th year. Nehemiah was using a Jewish calendar that rendered the month of Tishri as the first month, which is in the fall. The decree was given in Nisan, in the spring. To Nehemiah, it was still Artaxerxes' 20th year. According to our form of reckoning time, it would have been the 21st year.
The accounts of Jesus' crucifixion mention the events in nature surrounding Jesus' death. The Gospel of John says that it was cold the night of Jesus' trial, so likely it took place during the winter or spring.
The sun appeared to have stopped shining and caused darkness over the land at noon until 3 o'clock PM. This was not caused by a solar eclipse, since one did not happen on April 3rd, 33 AD nor do solar eclipses last that long.
Following Jesus' death, there was an earthquake. Geologists have discovered that a minor earthquake did happen within the ten year timespan of AD 26-36. It is said to have been "sufficiently energetic to deform the sediments of Ein Gedi but not energetic enough to produce a still extant and extra-biblical historical record." (NBC News) Another source says that there was one on April 3rd of 33 AD that was energetic enough to have caused the temple curtain to have torn. It says there was another on Sunday, as the Gospel of Matthew records.
In Acts, Peter says that there was a blood moon on the day Jesus was crucified. A blood moon happens when the moon is in a lunar eclipse. Indeed there was a lunar eclipse on April 3rd of 33 AD according to NASA.