Babylonian numerals

Published juin 4, 2026 · By NumberWiki

The base-60 cuneiform numeral system used in Mesopotamia from roughly 2000 BCE to the start of the Common Era — the world's earliest known positional number system, and the direct ancestor of the way we still measure time and angles today.

The two wedges

Babylonian numerals are built from exactly two cuneiform signs: a vertical wedge 𒁹 (Unicode U+12079) for one, and a corner wedge or winkelhaken 𒌋 (U+1230B) for ten. Both were impressed into wet clay tablets with a single triangular reed stylus — the vertical sign held upright, the corner sign rotated. Everything in the system is built by repeating and arranging these two marks.

To write the digits 1 through 59, scribes stacked up to five winkelhakens for the tens and up to nine vertical wedges for the units, grouped neatly into rows so a literate reader could count them at a glance. For example:

1 — 𒁹
5 — 𒐊 (five vertical wedges arranged in a row)
10 — 𒌋
23 — 𒌋𒌋𒁹𒁹𒁹 (two tens, three ones)
59 — five winkelhakens followed by nine wedges, the largest single digit the system represents

Base 60, positional

The Babylonian system is positional — the same digit means different amounts depending on where it sits. But the base is 60, not 10. A two-place number like 𒁹 𒌋𒌋𒁹𒁹𒁹 means "1 sixty plus 23 ones," or 83. Three places means hundreds of sixties — 60 × 60 = 3,600 — and so on.

Sixty is a remarkable base to settle on. It divides evenly by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 — more divisors than any smaller number, and more than the next several larger numbers too. That makes fractional arithmetic dramatically easier: a third of 60 is 20 with no remainder; a quarter is 15; a fifth is 12. The same calculations in base 10 give repeating decimals. For scribes doing astronomy, surveying, and grain accounting on clay tablets — without our notion of "decimal point" — the divisibility of 60 was practical genius.

Why 60 specifically? The classical guess, going back to Theon of Alexandria, was its rich divisibility. Otto Neugebauer in the twentieth century argued it emerged from the merger of two earlier counting traditions — a base-6 mercantile system and a base-10 system — when the Sumerian and Akkadian populations fused. Neither explanation is settled. What is settled is that the system worked: Babylonian astronomers used it to compute lunar and planetary positions with accuracies that astonished the Greeks who inherited their tables.

The missing zero (and the eventual placeholder)

Early Babylonian numerals had no zero. An empty middle place was simply left blank — and the reader had to figure out from context whether 𒁹 𒁹 meant 1 × 60 + 1 = 61, or 1 × 3600 + 0 × 60 + 1 = 3601, or something larger. This was workable for everyday accounting but a real obstacle in precise astronomy.

By the Seleucid period (around 300 BCE), Babylonian scribes introduced a placeholder sign — typically two small slanted wedges — to mark an empty middle place. This is not a zero in the modern sense: it was never used as a final digit (no scribe wrote "30 0" for thirty), and it had no arithmetic meaning on its own. But it solved the ambiguity problem, and it is the earliest known use of a positional placeholder in any civilisation. The full algebraic zero — a number you can add to and multiply with — would not arrive for another thousand years, in India.

Why we still use base 60

The Babylonian system is unique among ancient numerations because it never quite went away. When the Greeks adopted Babylonian astronomical tables, they kept the sexagesimal subdivisions for angle and time measurement even as they computed integer counts in their own alphabetic system. The Romans kept the convention. Islamic astronomers preserved and refined it during the medieval period. By the time the European scientific revolution rebuilt astronomy and trigonometry, the Babylonian sexagesimal subdivisions were so embedded in the working tools that nobody seriously proposed replacing them.

That heritage is the reason that, four thousand years later, you still:

Read time as 60 seconds in a minute and 60 minutes in an hour.
Measure angles as 360 degrees in a circle (6 × 60), with each degree subdivided into 60 arcminutes and each arcminute into 60 arcseconds.
Express geographic coordinates in degrees, minutes, and seconds of arc.
Hear "half past" and "quarter to" — phrases that exist because 60 has clean halves and quarters that 100 doesn't.

Every clock face is a Babylonian artifact. The decimal-time experiments of the French Revolution — 10 hours per day, 100 minutes per hour, 100 seconds per minute — lasted about two years before being abandoned. Base 60 had won, and it won partly because the math is easier.

Reading a Babylonian number on this site

NumberWiki renders Babylonian numerals on every number page from 1 up to 12,960,000 (60⁴ − 1). The most-significant sexagesimal place is on the left, separated from lower places by a narrow space. Where a middle place is empty, we render a middle dot (·) for legibility — this is a modern editorial convention; classical tablets simply left a gap.

Some examples to read:

60 — 𒁹 · (one sixty, zero ones)
144 — 𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹 (two sixties, twenty-four ones)
3600 — 𒁹 · · (one × 60² with two empty places)
86400 — the seconds in a day, displayed in its native base

The historical bracket

Cuneiform writing first appeared in southern Mesopotamia around 3200 BCE as a system of pictograms impressed on clay. The mature positional sexagesimal numeration emerged with the Old Babylonian period (approximately 2000–1600 BCE), under the dynasty of Hammurabi. From there it was the standard for mathematics and astronomy across the Mesopotamian world — used by the Assyrians, the Neo-Babylonians, and the Persian and Seleucid administrations that followed — well into the Common Era. The last datable cuneiform astronomical tablets are from about 75 CE, and the last cuneiform tablet of any kind is dated 79 CE, the same year Vesuvius destroyed Pompeii. By then the system was over two thousand years old.

The Unicode standard added cuneiform in version 5.0 (July 2006), which finally made it possible to render Babylonian numerals as live text on web pages — what you see throughout this site. The relevant codepoints live in the Cuneiform block U+12000–U+123FF; the two numeral signs we use are U+12079 (𒁹, single wedge) and U+1230B (𒌋, winkelhaken). To see them on your own device you need a font with cuneiform coverage (Noto Sans Cuneiform is the standard free option, and ships with most modern operating systems).