Why a circle has 360 degrees

Published julio 5, 2026 · By NumberWiki

We measure a full turn as 360 degrees, an hour as 60 minutes, a minute as 60 seconds, a day as 24 hours, and a year as 12 months. None of these numbers is metric, and none is an accident. They are the living legacy of a counting system invented in Mesopotamia thousands of years ago — and they survive for one very practical reason: these numbers divide beautifully.

The Babylonian base 60

The Babylonians counted not in tens but in base 60 (sexagesimal). Sixty seems an odd choice until you look at its divisors: 60 can be split evenly into halves, thirds, quarters, fifths, sixths, tenths, twelfths, fifteenths, twentieths, and thirtieths. It has twelve divisors in all — far more than ten. For a culture doing astronomy and trade without decimals or fractions in the modern sense, a number you can divide cleanly so many ways is enormously convenient. That single practical advantage is why base 60 outlived the empire that invented it.

Why 360 degrees

Split a circle into 360 parts and, like 60, it divides with astonishing ease — into 2, 3, 4, 5, 6, 8, 9, 10, 12, and more, so most common fractions of a turn land on a whole number of degrees. There's also an astronomical reason: a year is roughly 360 days (the Babylonians used a 360-day administrative calendar), and the Sun appears to move about one degree against the stars each day, so 360 degrees maps neatly onto the Sun's yearly journey around the sky. Combine "close to the number of days in a year" with "divides more cleanly than almost any nearby number" and 360 is the obvious winner. It stuck for over two thousand years.

60 minutes, 60 seconds

The same base-60 logic slices the degree — and the hour — into smaller parts. When medieval astronomers needed finer measurements, they divided each degree into 60 partes minutae primae, "first small parts" — our minutes — and each of those into 60 partes minutae secundae, "second small parts" — our seconds. That Latin is literally where the words come from. The clock inherited the same scheme: 60 minutes to the hour, 60 seconds to the minute, which is why a day contains 86,400 seconds and an hour contains 3,600.

12 and 24: hours, months, and the dozen

12 is the other great "divides-nicely" number of antiquity — splittable into halves, thirds, quarters, and sixths — and it shows up everywhere alongside 60. There are roughly twelve lunar cycles in a year, which gives us twelve months. The Egyptians divided the day and the night into twelve hours each, giving the 24-hour day. Even finger-counting may have helped: using the thumb to count the three joints of the other four fingers gets you to twelve on one hand — a plausible reason twelve and sixty (twelve times five) felt natural. The same instinct survives in the dozen and the gross (a dozen dozen, 144).

7 days of the week

The 7-day week is the odd one out — seven is prime and divides nothing cleanly. Its origin is astronomical and cultural rather than arithmetical: the ancients tracked seven "wandering stars" visible to the naked eye — the Sun, the Moon, and the five classical planets — and named a day for each. That planetary week, reinforced by the seven-day rhythm of the biblical creation story, spread across the ancient world and never went away, even though seven fits none of the tidy divisibility that shapes the rest of our timekeeping.

Why the old numbers survived the metric age

The metric system swept away old units for length and weight, but the clock and the compass held firm. There were serious attempts to "decimalise" time — the French Revolution briefly introduced a 10-hour day with 100-minute hours — and they failed. The reason is the same one that made 60 and 360 attractive in the first place: a highly divisible base lets you split a turn or an hour into thirds and quarters without ugly remainders, something base 10 simply can't do (ten divides only by 2 and 5). Four thousand years later, we still tell the time and steer by the numbers the Babylonians chose.

On NumberWiki

Numbers that are famous time or angle measures — 60, 360, 3,600, 86,400, 90 — carry "Time & calendar" and "Angle" notes on their pages, and highly divisible numbers like 12, 24, and 60 are flagged for their unusual number of divisors.