Turns to Degrees (turn to °)

1 turn equals 360 degrees exactly.

How to convert turns to degrees

To convert turns to degrees, multiply the number of turns by 360. This factor is exact. To go the other way, multiply degrees by 0.002777777778 (rounded).

degrees = turns × 360

Example: 10 turns = 3,600 degrees.

About these units

Turn (turn)

General & non-SICurrent unit

One full revolution, 360 degrees or 2π radians.

A turn is the simplest angle to define: the whole way around, back to the starting direction. It also goes by cycle and revolution, and it equals 2π radians, 360 degrees, or 400 gradians. In the International System of Quantities, rotation is a plain count of revolutions, the angle divided by 2π radians, and it can be negative or exceed one.

Measuring in turns is older than it might seem. Percentage protractors marked in hundredths of a turn have existed since 1922, and in 1962 the astronomer Fred Hoyle proposed the terms centiturn, milliturn, and microturn. A 1974 German standard, DIN 1315, suggested the symbol pla, from the Latin for full angle. Some HP calculators, such as the HP Prime of 2013, accept tr as an angle unit. In CSS, 1turn equals 360deg, so a rule can rotate an element by 1.75turn. Binary angular measurement in computing also treats a full turn as the value 1, which lets integer overflow wrap an angle around for free.

The turn is the reference unit for angle on this site.

Sources: Wikipedia: Turn (angle); MDN Web Docs: CSS <angle>; NIST Guide to the SI, Appendix B.8 (angle conversion factors)

Degree (°)

General & non-SICurrent unit

One 360th of a full turn. The everyday unit of angle, inherited from the ancient Babylonians' base-60 counting.

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.

1 degree = 0.002777777778 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Degree (angle); Wikipedia: Angular diameter

Related conversions

See all angle units.