Degree (angle)

Unit system Non-SI accepted unit
Unit of Angle
Symbol ° [1] [2] or deg [3]
Unit conversions
1 ° [1] [2] in ... ... is equal to ...
    turns    1/360 turn
    radians    π/180 rad
    gons    10/9g
One degree (shown in red) and
eighty nine degrees (shown in blue)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

It is not an SI unit, as the SI unit of angular measure is the radian, but it is mentioned in the SI brochure as an accepted unit. [4] Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians.


A circle with an equilateral chord (red). One sixtieth of this arc is a degree. Six such chords complete the circle.

The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. [5] Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The use of a calendar with 360 days may be related to the use of sexagesimal numbers.

Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system. [6] [7] The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.

Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. [8] [9] Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes. [10] Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.

The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda: [11]

Twelve spokes, one wheel, navels three.

Who can comprehend this?
On it are placed together
three hundred and sixty like pegs.
They shake not in the least.

—  Dirghatamas, Rigveda 1.164.48

Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors, [note 1] making it one of only 7 numbers such that no number less than twice as much has more divisors (sequence A072938 in the OEIS). [12] [13] Furthermore, it is divisible by every number from 1 to 10 except 7. [note 2] This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.

Finally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above.

Other Languages
العربية: درجة (زاوية)
asturianu: Grau sexaxesimal
беларуская: Вуглавы градус
भोजपुरी: डिग्री (कोण)
български: Градус (ъгъл)
bosanski: Stepen (ugao)
čeština: Stupeň (úhel)
Deutsch: Grad (Winkel)
Esperanto: Grado
français: Degré (angle)
贛語: 度 (角度)
한국어: 도 (각도)
hrvatski: Stupanj (kut)
Bahasa Indonesia: Derajat (satuan sudut)
interlingua: Grado (angulo)
íslenska: Gráða (horn)
italiano: Grado d'arco
Kiswahili: Nyuzi
Lëtzebuergesch: Grad (Wénkel)
magyar: Fok (szög)
македонски: Степен (агол)
Bahasa Melayu: Darjah (sudut)
Nederlands: Booggraad
日本語: 度 (角度)
Nordfriisk: Winkelgraad
norsk nynorsk: Vinkeleininga grad
ਪੰਜਾਬੀ: ਡਿਗਰੀ (ਕੋਣ)
Patois: Digrii
Plattdüütsch: Grad (Winkel)
português: Grau (geometria)
Simple English: Degree (angle)
slovenčina: Stupeň (uhol)
slovenščina: Kotna stopinja
کوردی: پلە (گۆشە)
српски / srpski: Лучни степен
srpskohrvatski / српскохрватски: Stepen (ugao)
suomi: Aste
Türkçe: Derece (birim)
українська: Градус (геометрія)
Tiếng Việt: Độ (góc)
ייִדיש: גראד
粵語: 角度
中文: 度 (角)