Edwin R. Thiele in The Mysterious Numbers of the Hebrew Kings (1951) concluded that two different methods for counting the years of a king's reign were used at different times and places. In the accession method, the year in which a king ascended to the throne was called his accession year, and the following year was the first year of that king's reign. In the non-accession method, the year of a king's accession is simply counted as the first year of his reign. According to Thiele, the Kingdom of Israel appears to have used the non-accession year method for counting years, while the Kingdom of Judah used the accession method until Athaliah seized power in Judah, when Israel's non-accession method appears to have been adopted in Judah. In addition, Thiele also concluded that Israel counted years using the ecclesiastical new year starting in the spring month of Nisan, while Judah counted years using the civil year starting in the autumn month of Tishrei.
a * indicates that that king is listed in matthew as an ancestor of Jesus Ish-bosheth ruled Israel 2 yrs while David ruled in Judah
↑Edwin Thiele, The Mysterious Numbers of the Hebrew Kings, (1st ed.; New York: Macmillan, 1951; 2d ed.; Grand Rapids: Eerdmans, 1965; 3rd ed.; Grand Rapids: Zondervan/Kregel, 1983). ISBN 082543825X, 9780825438257
↑1 Sam 4
18And it came to pass, when he made mention of the ark of God, that he fell from off the seat backward by the side of the gate, and his neck brake, and he died: for he was an old man, and heavy. And he had judged Israel forty years.
↑1 Sam 7
13So the Philistines were subdued, and they came no more into the coast of Israel: and the hand of the LORD was against the Philistines all the days of Samuel.
14And the cities which the Philistines had taken from Israel were restored to Israel, from Ekron even unto Gath; and the coasts thereof did Israel deliver out of the hands of the Philistines. And there was peace between Israel and the Amorites.
15And Samuel judged Israel all the days of his life.
16And he went from year to year in circuit to Bethel, and Gilgal, and Mizpeh, and judged Israel in all those places.
17And his return was to Ramah; for there was his house; and there he judged Israel; and there he built an altar unto the LORD.
1And it came to pass, when Samuel was old, that he made his sons judges over Israel.
2Now the name of his firstborn was Joel; and the name of his second, Abiah: they were judges in Beersheba.
3And his sons walked not in his ways, but turned aside after lucre, and took bribes, and perverted judgment.
4Then all the elders of Israel gathered themselves together, and came to Samuel unto Ramah,
5And said unto him, Behold, thou art old, and thy sons walk not in thy ways: now make us a king to judge us like all the nations.
21and thereafter they asked for a king, and God did give to them Saul, son of Kish, a man of the tribe of Benjamin, for forty years;
↑1 Sam 13
1Saul reigned one year; and when he had reigned two years over Israel,
2Saul chose him three thousand men of Israel;
↑1 Sam 25
1And Samuel died; and all the Israelites were gathered together, and lamented him, and buried him in his house at Ramah. And David arose, and went down to the wilderness of Paran.
↑2 Sam 5
4David was thirty years old when he began to reign, and he reigned forty years.
5In Hebron he reigned over Judah seven years and six months: and in Jerusalem he reigned thirty and three years over all Israel and Judah.
↑1kings 2 11And the days that David reigned over Israel were forty years: seven years reigned he in Hebron, and thirty and three years reigned he in Jerusalem.
↑1 Kings 11
42And the time that Solomon reigned in Jerusalem over all Israel was forty years.
↑1 King 14 21And Rehoboam the son of Solomon reigned in Judah. Rehoboam was forty and one years old when he began to reign, and he reigned seventeen years in Jerusalem, the city which the LORD did choose out of all the tribes of Israel, to put his name there. And his mother's name was Naamah an Ammonitess.
↑1 King 15
1Now in the eighteenth year of king Jeroboam the son of Nebat reigned Abijam over Judah.
2Three years reigned he in Jerusalem. and his mother's name was Maachah, the daughter of Abishalom.
↑1 King 15
9And in the twentieth year of Jeroboam king of Israel reigned Asa over Judah.
10And forty and one years reigned he in Jerusalem. And his mother's name was Maachah, the daughter of Abishalom.
↑1 King 22
41And Jehoshaphat the son of Asa began to reign over Judah in the fourth year of Ahab king of Israel.
42Jehoshaphat was thirty and five years old when he began to reign; and he reigned twenty and five years in Jerusalem. And his mother's name was Azubah the daughter of Shilhi.
↑2 King 8
16And in the fifth year of Joram the son of Ahab king of Israel, Jehoshaphat being then king of Judah, Jehoram the son of Je hoshaphat king of Judah began to reign.
17Thirty and two years old was he when he began to reign; and he reigned eight years in Jerusalem.
↑2 Chron 21
12And there came a writing to him from Elijah the prophet, saying, Thus saith the LORD God of David thy father, Because thou hast not walked in the ways of Jehoshaphat thy father, nor in the ways of Asa king of Judah,
13But hast walked in the way of the kings of Israel, and hast made Judah and the inhabitants of Jerusalem to go a whoring, like to the whoredoms of the house of Ahab, and also hast slain thy brethren of thy father's house, which were better than thyself:
14Behold, with a great plague will the LORD smite thy people, and thy children, and thy wives, and all thy goods:
15And thou shalt have great sickness by disease of thy bowels, until thy bowels fall out by reason of the sickness day by day.
↑2 King 8
25In the twelfth year of Joram the son of Ahab king of Israel did Ahaziah the son of Jehoram king of Judah begin to reign.
26Two and twenty years old was Ahaziah when he began to reign; and he reigned one year in Jerusalem. And his mother's name was Athaliah, the daughter of Omri king of Israel.
↑2 King 11
1And when Athaliah the mother of Ahaziah saw that her son was dead, she arose and destroyed all the seed royal.
2But Jehosheba, the daughter of king Joram, sister of Ahaziah, took Joash the son of Ahaziah, and stole him from among the king's sons which were slain; and they hid him, even him and his nurse, in the bedchamber from Athaliah, so that he was not slain.
3And he was with her hid in the house of the LORD six years. And Athaliah did reign over the land.
↑2 King 12 21Seven years old was Jehoash when he began to reign.
1In the seventh year of Jehu Jehoash began to reign; and forty years reigned he in Jerusalem. And his mother's name was Zibiah of Beersheba.
↑2 King 14
1In the second year of Joash son of Jehoahaz king of Israel reigned Amaziah the son of Joash king of Judah.
2He was twenty and five years old when he began to reign, and reigned twenty and nine years in Jerusalem. And his mother's name was Jehoaddan of Jerusalem.
↑2 King 15
1In the twenty and seventh year of Jeroboam king of Israel began Azariah son of Amaziah king of Judah to reign.
2Sixteen years old was he when he began to reign, and he reigned two and fifty years in Jerusalem. And his mother's name was Jecholiah of Jerusalem.
↑2 King 15
32In the second year of Pekah the son of Remaliah king of Israel began Jotham the son of Uzziah king of Judah to reign.
33Five and twenty years old was he when he began to reign, and he reigned sixteen years in Jerusalem. And his mother's name was Jerusha, the daughter of Zadok.
↑2 King 16
1In the seventeenth year of Pekah the son of Remaliah Ahaz the son of Jotham king of Judah began to reign.
2Twenty years old was Ahaz when he began to reign, and reigned sixteen years in Jerusalem, and did not that which was right in the sight of the LORD his God, like David his father.
↑2 King 18
1Now it came to pass in the third year of Hoshea son of Elah king of Israel, that Hezekiah the son of Ahaz king of Judah began to reign.
2Twenty and five years old was he when he began to reign; and he reigned twenty and nine years in Jerusalem. His mother's name also was Abi, the daughter of Zachariah.
↑2 King 21
1Manasseh was twelve years old when he began to reign, and reigned fifty and five years in Jerusalem. And his mother's name was Hephzibah.
↑2 King 21 19Amon was twenty and two years old when he began to reign, and he reigned two years in Jerusalem. And his mother's name was Meshullemeth, the daughter of Haruz of Jotbah.
↑2 King 22
1Josiah was eight years old when he began to reign, and he reigned thirty and one years in Jerusalem. And his mother's name was Jedidah, the daughter of Adaiah of Boscath.
↑2 King 23
31Jehoahaz was twenty and three years old when he began to reign; and he reigned three months in Jerusalem. And his mother's name was Hamutal, the daughter of Jeremiah of Libnah.
↑2 King 23
34And Pharaoh nechoh made Eliakim the son of Josiah king in the room of Josiah his father, and turned his name to Jehoiakim, and took Jehoahaz away: and he came to Egypt, and died there.
35And Jehoiakim gave the silver and the gold to Pharaoh; but he taxed the land to give the money according to the commandment of Pharaoh: he exacted the silver and the gold of the people of the land, of every one according to his taxation, to give it unto Pharaohnechoh.
36Jehoiakim was twenty and five years old when he began to reign; and he reigned eleven years in Jerusalem. And his mother's name was Zebudah, the daughter of Pedaiah of Rumah.
↑2 King 24 8Jehoiachin was eighteen years old when he began to reign, and he reigned in Jerusalem three months. And his mother's name was Nehushta, the daughter of Elnathan of Jerusalem.
↑2 King 24
17And the king of Babylon made Mattaniah his father's brother king in his stead, and changed his name to Zedekiah.
18Zedekiah was twenty and one years old when he began to reign, and he reigned eleven years in Jerusalem. And his mother's name was Hamutal, the daughter of Jeremiah of Libnah.
↑2 King 25 22And as for the people that remained in the land of Judah, whom Nebuchadnezzar king of Babylon had left, even over them he made Gedaliah the son of Ahikam, the son of Shaphan, ruler.
↑2 Sam 2
8But Abner the son of Ner, captain of Saul's host, took Ishbosheth the son of Saul, and brought him over to Mahanaim;
9And made him king over Gilead, and over the Ashurites, and over Jezreel, and over Ephraim, and over Benjamin, and over all Israel.
10Ishbosheth Saul's son was forty years old when he began to reign over Israel, and reigned two years. But the house of Judah followed David.