The Arithmetic of the Sumerian King List

The Flood Clock

The Sumerian King List does not only name the kings before the flood. It adds them up.

"In 5 cities 8 kings; they ruled for 241200 years. Then the flood swept over."

That total is the starting point for everything on this page. Every figure below comes from the reign lengths in the Electronic Text Corpus of Sumerian Literature translation, and every sum and percentage has been checked.

The Unit: The Sar

Sumerian scribes counted in base 60. The large units were the geš (60), the ner (600) and the sar (3,600).

Divide the pre-flood total by 3,600 and the result is exactly 67 sar. In ner it is exactly 402.

The Five Cities

The cities are not in order of size. Bad-tibira, the second city, is the largest by far. Eridu and Bad-tibira together hold 172,800 years, or 48 sar, which is 71.6% of the whole pre-flood span. The other three cities share the remaining 68,400 years, exactly 19 sar.

The two largest cities also form a clean ratio: Bad-tibira’s 30 sar to Eridu’s 18 is 5 to 3.

The Eight Kings

• Average reign: 241,200 ÷ 8 = 30,150 years.
• Most common reign: 28,800 years, shared by three kings (Alulim, En-men-gal-ana and En-sipad-zid-ana). That is 8 sar each.
• Median reign: also 28,800 years.
• Longest reign: En-men-lu-ana of Bad-tibira, 43,200 years (12 sar), or 17.9% of the total.
• Shortest reign: Ubara-Tutu of Shuruppak, 18,600 years. The longest reign is about 2.3 times the shortest.

The Break After Six Kings

Here is the most striking pattern. The first six kings rule for whole numbers of sar: 8, 10, 12, 8, 10 and 8. Together that is exactly 56 sar, or 201,600 years.

The last two do not. En-men-dur-ana rules 5 sar and 5 ner, and Ubara-Tutu rules 5 sar and 1 ner. Together they give 39,600 years, exactly 11 sar.

So the clock can be cut two ways: by city (18, 30, 8, 5 5/6 and 5 1/6 sar) or by king (56 sar, then 11). Every reign is also a whole number of ner: 48, 60, 72, 48, 60, 48, 35 and 31.

A Different Total: Berossus

Not every ancient account gives the same figure. Berossus, the Babylonian priest who wrote in Greek in the third century BC, records ten kings before the flood who together reign 120 saroi, or 432,000 years.

That is about 1.8 times the King List total, with two more kings and the flood hero counted among the ten. Berossus counts in saroi, which are generally understood as the Greek form of the Babylonian unit, and he arrives at a different sum.

What the Arithmetic Shows

In the ETCSL version used here, the totals are tidy. The five cities add up to exactly 67 sar, and the first six kings add up to exactly 56.

What the text does not tell us is why. Writing numbers in base 60 makes round totals more likely, so some of this tidiness may follow from the counting system. Some of it may have been planned by whoever composed the list. The sources do not decide between those, and we will not claim more than the numbers themselves show.

What can be said is simple. In the ETCSL version used here, the pre-flood section of the King List is built from reign lengths that are all multiples of 600.