When did Saul rule Israel? How long was his reign?
While the information given in the Bible has been repeatedly proven accurate, dates have been a particular challenge because earlier cultures did not use fixed calendars as we do. Instead, time was measured based as elapsed from certain major events or significant person. Since major events rarely took place at the start of a year, we can be off by up to a year, depending on how we round the date given.
For example, the reigns of Israel's kings are generally measured from the time a particular rule ascended to the throne. It is not bad when you are off by a year for a single king, but when you have ten kings in a row, you can be off by up to ten years before or after depending on when the change in kingships occurred.
Every once in a while, a significant event is measured, not by the immediate event, but by a more distant event. These points in time help us to reduce the margin of error that creeps into our estimates of the dates. For example, we are told that Solomon's temple was started 480 years after the Israelite's exodus from Egypt (I Kings 6:1). This point in time corresponds to the fourth year of Solomon's reign. Solomon's father, David, reigned 40 years over Israel (I Kings 2:11). The king prior to David, Saul, reigned 40 years (Acts 13:21). The biggest difficulty is that David named Solomon as his successor prior to his death (I Chronicles 23:1). We don't know how many years that Solomon reigned while his father David lived, nor do we know if the years given for David and Solomon's reigns include or exclude this overlap. We do know that David died before the temple was started in the fourth year of Solomon's reign, so the overlap was probably between 1 and 3 years.
An additional difficulty comes in that Paul states that Saul reigned 40 years in Acts 13:21. "And afterward they asked for a king; so God gave them Saul the son of Kish, a man of the tribe of Benjamin, for forty years." Yet, I Samuel 13:1 in the NASB says, "Saul was forty years old when he began to reign, and he reigned thirty two years over Israel." The NIV renders it, "Saul was thirty years old when he became king, and he reigned over Israel forty-two years." And the NKJV says, "Saul reigned one year; and when he had reigned two years over Israel." The NKJV is the most literal of translations. The literal translation is "A son of a year, Saul, in his reigning and two years he reigned over Israel." It assumes that the events prior to I Samuel 13:1 took place during the first year of Saul's reign and the following events took place during the second and third year of his reign. The NASB and NIV assume that a digit was dropped in the description of Saul's reign due to copying errors. Based on some Septuagint translations, the NIV assume the first number was meant to be 30 and based on Paul's assertion that Saul reigned forty years, they assume the second number is 42 (with Paul rounding the date in Acts). Personally, I find these assumptions to be too much. There is no reason to assume I Samuel 13:1 is the standard summary of a king's reign, since it is given in middle of Saul's reign and not at the beginning or end. Interestingly, while not inspired, Josephus, an ancient Jewish historian, also states that Saul reigned 40 years. Hence, any apparent conflict between I Samuel 13:1 and Acts 13:21 is due to mistranslations and not due to the actual text.
The start of Solomon's reign is generally measured to about 971 B.C. This means that David's reigned started around 1011 B.C. and Saul's reign would have started around 1051 B.C.
Using another point in time, "It happened in the fifth year of King Rehoboam that Shishak king of Egypt came up against Jerusalem" (I Kings 14:25). Rehoboam is Solomon's son and successor. Scholars are fairly certain that Shishak's campaign took place in 924 B.C. Using this as a base date and knowing that Solomon reigned 40 years (II Chronicles 9:30), we come to 969 B.C. as the start of Solomon's reign; 1009 B.C. as the start of David's reign; and 1049 B.C. as the start of Saul's reign.