Science · Numbers

Why 60 Became the Number of Time

How an ancient counting system still runs our clocks and compasses.

The question

Why does an hour have 60 minutes, and a circle 360 degrees?

The short answer

We inherited base-60 counting from ancient Mesopotamia. Sixty divides so many ways that astronomers kept it for time and angles, long after decimal counting won elsewhere.

10 1 2 5 10 4 divisors 12 1 2 3 4 6 12 6 divisors 60 1 2 3 4 5 6 10 12 15 20 30 60 12 divisors 100 1 2 4 5 10 20 25 50 100 9 divisors
60 has twelve divisors: it splits cleanly into halves, thirds, quarters, fifths, sixths, tenths and twelfths.

What science knows

Historical Fact

Sumerian and later Babylonian scribes counted in base 60 (sexagesimal) from the third millennium BCE. Greek astronomers such as Hipparchus and Ptolemy adopted it for angles and fractions, and it passed into medieval astronomy and clocks.

The words record the history: a “minute” is from the Latin pars minuta prima, the first small part, and a “second” is pars minuta secunda, the second.

The pattern

Established Mathematics

60 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. It is the smallest number divisible by every number from 1 to 6, which makes fractions like thirds exact rather than repeating decimals.

What is still uncertain

Mixed Evidence

Why the Sumerians chose 60 is debated: its divisibility, a merger of counting systems, or finger-counting methods. The 360-degree circle may echo the approximate number of days in a year, but that link is uncertain.

Why humans find it interesting

Cultural Tradition

The Chinese calendar also counts a 60-year cycle, pairing 10 Heavenly Stems with 12 Earthly Branches.

CUE perspective

CUE Perspective

Every glance at a clock is a small piece of Babylonian mathematics. Numbers that were chosen because they work can outlast empires.

CUE’s Chinese astrology draws on the same 60-year cycle of stems and branches, a tradition CUE reads symbolically rather than scientifically.

Explore next

Sources

  • Robson, Mathematics in Ancient Iraq: A Social History (Princeton University Press, 2008)
  • Neugebauer, The Exact Sciences in Antiquity (Brown University Press, 1957)
  • Ifrah, The Universal History of Numbers (Wiley, 2000)

Written by CUE from the sources above. Some topics were suggested by Polymath; its claims are not reproduced.