Nobody knows for sure why a full circle has 360 degrees
We split every circle into 360 parts without a second thought, yet the reason is lost. Perhaps ancient skywatchers matched it to the Sun's roughly daily step across the sky, perhaps Babylonian base-60 arithmetic chose it, perhaps it was simply easy to divide. Quite possibly all three nudged the number into place.
The calendar theory notes that a year has close to 360 days and that the Sun drifts about one degree along its yearly path each day; some ancient calendars, including Babylonian and Persian ones, used 360-day years. A second idea starts with geometry. Early trigonometry, used by Babylonian astronomers and their Greek heirs, worked with chords, and a chord equal to the radius spans a sixth of a circle. Divide that into 60, following base-60 counting, and you get a degree.
The third argument is sheer convenience. 360 has 24 divisors and splits evenly by every whole number from 1 to 10 except 7. That is why the world's 24 time zones each span a nominal 15 degrees of longitude. Among the Greeks, Hipparchus, Aristarchus and a few contemporaries were the first known to use 360 degrees of 60 arc minutes each, though Eratosthenes preferred cutting the circle into just 60 parts.
The base-60 habit survives in the minute and second of arc, whose names descend from an older chain of sixtieths that ran on to thirds and fourths, used by the astronomer al-Kashi among others. The subdivisions pay off at sea: one minute of latitude equals one nautical mile, which is why charts are marked in degrees and decimal minutes.
Not everyone liked it. The metric reformers of France tried a decimal system with 100 grades in a right angle and 400 in a circle, a unit now called the gon. Napoleon abandoned the scheme, but grades lingered, and French artillery sights used fractions of them in the First World War. Mathematicians, meanwhile, prefer radians, which make trigonometry cleaner; 180 degrees equals exactly pi radians.
Source: Degree (angle)
