Degree (°)
One 360th of a full turn. The everyday unit of angle, inherited from the ancient Babylonians' base-60 counting.
1 degree = 0.002777777778 turns (approximately).
About the degree
Dividing the circle into 360 parts traces back to the astronomers of ancient Babylon, who counted in base 60. Why 360 in particular is still debated. One explanation points to Persian and Babylonian calendars, which used a year of about 360 days, so the Sun seemed to advance roughly one degree each day. Another says the Babylonians started from the angle of an equilateral triangle and split it into 60 pieces, and a third credits early chord-based trigonometry, where a chord equal to the radius made a natural base. Greek astronomers such as Aristarchus and Hipparchus were among the first to use Babylonian astronomical knowledge systematically.
The number also divides well. 360 has 24 divisors and splits evenly by every whole number from 1 to 10 except 7, which suits a world cut into 24 time zones of 15 degrees of longitude each. Each degree breaks into 60 arcminutes, and each of those into 60 arcseconds. The SI Brochure lists the degree among the widely used non-SI units, equal to π/180 radian, about 0.01745. For scale, the Moon and the Sun each look about half a degree wide, and a little finger held at arm's length covers roughly one degree of sky.
Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Degree (angle); Wikipedia: Angular diameter
Degree conversion chart
1 degree expressed in every other angle unit:
| Unit | 1 degree |
|---|---|
| Radians | 0.01745329252 |
| Gradians | 1.111111111 |
| Turns | 0.002777777778 |
| Arcminutes | 60 |
| Arcseconds | 3,600 |
| Milliarcseconds | 3,600,000 |
| Milliradians | 17.45329252 |
| Right Angles | 0.01111111111 |
| Octants | 0.02222222222 |
| Sextants | 0.01666666667 |
| Hour Angles | 0.06666666667 |
| Mils (NATO) | 17.77777778 |
| Zodiac Signs | 0.03333333333 |
| Compass Points | 0.08888888889 |
| Mils (Soviet) | 16.66666667 |
| Streck | 17.5 |
| Binary Degrees | 0.7111111111 |
More General & non-SI units
- gradian (angle)
- turn (angle)
- arcminute (angle)
- arcsecond (angle)
- right angle (angle)
- octant (angle)
- sextant (angle)
- piece (counting & quantity)
- pair (counting & quantity)
- score (counting & quantity)
- hundred (counting & quantity)
- thousand (counting & quantity)
- million (counting & quantity)
- billion (short scale) (counting & quantity)
- trillion (short scale) (counting & quantity)
- billion (long scale) (counting & quantity)
Browse all angle units.