Why is Jesus' crucifixion dated to AD 30–33?

Jesus is said to have died during that range because a bible verse says he was "about 30" at a certain event before his death.

1 Ad plus 30 is 31 ad. Add 2 years to account for undated and unrecorded adventures and you get 33 ad.

the previous answer which got down voted is generally correct. Almost everything we know about Jesus comes to us from the New Testament. Jesus's crucifixion date is calculated based on a literal interpretation of the bible. The date chosen seeks to find a year which proves not one Gospel, but all four Gospels (Mark, Luke, Matthew and John) and the Narratives of Paul; correct. All of which (but Luke and Matthew) differ subtly on Jesus's Crucifixion.

Chronology of Jesus
In the crucifixion narrative, the synoptic gospels stress that Jesus celebrated a Passover meal (Mark 14:12ff, Luke 22:15) before his crucifixion, which contrasts sharply with the independent gospel of John who is explicit that the official "Jewish" Passover (John 11:55) started at nightfall after Jesus' death. In his 2011 book, Colin Humphreys proposes a resolution to this apparent discrepancy by positing that Jesus' "synoptic" Passover meal in fact took place two days before John's "Jewish" Passover because the former is calculated by the putative original Jewish lunar calendar (itself based on the Egyptian liturgical lunar calendar putatively introduced to the Israelites by Moses in the 13th century BC, and still used today by the Samaritans). The official "Jewish" Passover in contrast was determined by a Jewish calendar reckoning which had been modified during the Babylonian exile in the 6th century BC. This modified Jewish calendar is in use among most Jews today. One basic difference lies in the determination of the first day of the new month: while the Samaritans use the calculated (because by definition invisible) new moon, mainstream Jews use the first observation of the thin crescent of the waxing moon which is on average 30 hours later. The other basic difference lies in the fact that the Samaritan calendar uses a sunrise-to-sunrise day, while the official Jewish calendar uses a sunset-to-sunset day. Due to these differences, the Samaritan Passover is normally one day earlier than the Jewish Passover (and in some years two or more days earlier). The crucifixion year of Jesus can then be calculated by asking the question in which of the two astronomically possible years of AD 30 and AD 33 is there a time gap between the last supper and the crucifixion which is compatible with the gospel timeline of Jesus' last 6 days. The astronomical calculations show that a hypothetical AD 30 date would require an incompatible Monday Last Supper, while AD 33 offers a compatible Last Supper on Wednesday, 1 April AD 33, followed by a compatible crucifixion on Friday, 3 April AD 33.[150]

Given these assumptions he argues that the calculated date of Wednesday 1 April AD 33 for the Last Supper allows all four gospel accounts to be astronomically correct, with Jesus celebrating Passover two days before his death according to the original Mosaic calendar, and the Jewish authorities celebrating Passover just after the crucifixion, using the modified Babylonian calendar. In contrast, the Christian church tradition of celebrating the Last Supper on Maundy Thursday would be an anachronism.[151][152] The calculated chronology incidentally supports John's and Paul's narratives that Jesus died at the same hour (Friday 3pm) on 3 April AD 33 that the Passover lambs were slaughtered.[153]

In a review of Humphreys' book, theologian William R Telford counters that the separate day schema of the Gospel's Holy Week "is an artificial as well as an inconsistent construction". As Telford had pointed out in his own book in 1980,[154] "the initial three-day structure found in [Mark 11] is occasioned by the purely redactional linkage of the extraneous fig-tree story with the triumphal entry and cleansing of the temple traditions, and is not a chronology upon which one can base any historical reconstructions."

The version of the Nicene creed as modified by the Council of Constantinople in AD 381 includes:

he was crucified for us under Pontius Pilate, and suffered, and was buried, and the third day he rose again, according to the Scriptures, and ascended into heaven, and sitteth on the right hand of the Father;

https://en.wikipedia.org/wiki/Nicene_Creed1

So a large proportion of all the Christians who ever lived have been taught that Jesus was crucified under Pontius Pilate.

Pontius Pilate[b] was the fifth governor of the Roman province of Judaea, serving under Emperor Tiberius from 26/27 to 36/37 CE. He is best known today for being the official who presided over the trial of Jesus and ordered his crucifixion. Pilate's importance in modern Christianity is underscored by his prominent place in both the Apostles and Nicene Creeds. Due to the Gospels' portrayal of Pilate as reluctant to execute Jesus, the Coptic and Ethiopian Churches believe that Pilate became a Christian and venerate him as a martyr and saint.[7]

https://en.wikipedia.org/wiki/Pontius_Pilate#Trial_and_execution_of_Jesus2

All four canonical gospels state that Jesus was crucified during the prefecture of Pontius Pilate, the Roman governor of Roman Judaea.[92][93]

In the Antiquities of the Jews (written about AD 93), Josephus states (Ant 18.3) that Jesus was crucified on the orders of Pilate.[94] Most scholars agree that while this reference includes some later Christian interpolations, it originally included a reference to the execution of Jesus under Pilate.[95][96][97][98][99]

In the second century the Roman historian Tacitus[100][101] in The Annals (c. AD 116), described the persecution of Christians by Nero and stated (Annals 15.44) that Jesus had been executed on the orders of Pilate[94][102][102] during the reign of Tiberius (Emperor from 18 September AD 14–16 March AD 37).

According to Flavius Josephus,[103] Pontius Pilate was governor of Judea from AD 26 until he was replaced by Marcellus, either in AD 36 or AD 37, establishing the date of the death of Jesus between AD 26 and AD 37.[104][105][106]

https://en.wikipedia.org/wiki/Chronology_of_Jesus3

So if Pilate's governorship is dated correctly, Jesus should have been crucified sometime between AD 26 and 37.

And the date range has been narrowed down by other factors.

There is no consensus regarding the exact date of the crucifixion of Jesus, although it is generally agreed by biblical scholars that it was on a Friday on or near Passover (Nisan 14), during the governorship of Pontius Pilate (who ruled AD 26–36).[85] Scholars have provided estimates for the year of crucifixion in the range 30–33 AD,[86][87][88] with Rainer Riesner stating that "the fourteenth of Nisan (7 April) of the year A.D. 30 is, apparently in the opinion of the majority of contemporary scholars as well, far and away the most likely date of the crucifixion of Jesus."[89] Another preferred date among scholars is Friday, April 3, 33 AD.[90][91]

https://en.wikipedia.org/wiki/Crucifixion_of_Jesus#Chronology4

And the Wikipedia articles and many other sources discuss the various arguments for when the Passover would have been celebrated during various years when Pontius Pilate was governor, and when the Crucifixion happened relative to the Passover, and which year thus best fits the Gospel narratives.

For example, was the "darkness" at the crucifixion an eclipse? If so, there would be only a very few possibilities when PIlate was governor. So the date of 3 April AD 33 has been suggested for the Crucifixion.

https://en.wikipedia.org/wiki/Chronology_of_Jesus#Eclipse_method5

So if you read the chronological sections of the Wikipedia articles mentioned, or other discussions of the chronology of Jesus, you will see the various clues that scholars use to try to find the date of the Crucifixion, and thus you can form an opinion about how accurate the dating of the crucifixion to the period of AD 30 to 33 is.