The probable date of the Birth of Jesus is in June of 2 BC and of the crucifixion, April 3, 33 AD fits best.
The study on the Star of Bethlehem is perhaps the most convincing, compelling evidence for both dates. In September of 3 BC, the planet Jupiter was seen to be in conjunction with the star Regulus, and entered retrograde motion, and returned, and then reversed again, for a triple conjunction. If one assumes a conception at the first conjunction, that would place the birth of Jesus somewhere in June of the following year, at which time there was a conjunction between Jupiter and Venus, that clearly would have been the brightest star in the sky.
At the crucifixion, we have the scientific evidence of the Lunar eclipse on that date, along with the historical record of a great darkness which could not have been an eclipse, both pointing to April 3rd.
For more detailed analysis of these dates for the birth and death of Jesus, visit the Star of Bethlehem website.