Degree (angle)

°degreesdegreedegrees of arcdegree turn180°degree of arc180360°90-degree
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.wikipedia
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Degree symbol

°degree signdegree
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.
The degree symbol is a typographical symbol that is used, among other things, to represent degrees of arc (e.g. in geographic coordinate systems), hours (in the medical field), degrees of temperature, alcohol proof, or diminished quality in musical harmony.

Angle

acute angleobtuse angleoblique
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.
The measure of the angle in another angular unit is then obtained by multiplying its measure in radians by the scaling factor k⁄2, where k is the measure of a complete turn in the chosen unit (for example 360 for degrees or 400 for gradians):

Radian

radiansradmicroradian
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.
The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees (expansion at ).

Non-SI units mentioned in the SI

accepted for use with SIAccepted for use with the SIaccepted unit
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.

International System of Units

SISI unitsSI unit
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.

Longitude

WestlongitudinalE
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. When this is not the case, as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be written using decimal degrees, with the degree symbol behind the decimals; for example, 40.1875°.
It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda .

Hipparchus

HipparchosHipparchus of NicaeaHipparchus of Nicea
Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically.
Except for Timocharis and Aristillus, he was the first Greek known to divide the circle in 360 degrees of 60 arc minutes (Eratosthenes before him used a simpler sexagesimal system dividing a circle into 60 parts); he also adopted the Babylonian astronomical cubit unit (Akkadian ammatu, Greek πῆχυς pēchys) which was equivalent to 2° or 2.5° ('large cubit').

Chord (geometry)

chordchords chord
The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle.
The first known trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7.5 degrees.

Sexagesimal

sexagesimal systembase 60base-60
The use of a calendar with 360 days may be related to the use of sexagesimal numbers. Alternatively, the traditional sexagesimal unit subdivisions can be used.
Similarly, the practical unit of angular measure is the degree, of which there are 360 (six sixties) in a circle.

Minute and second of arc

masarcsecondarc second
Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes. These subdivisions, also called the arcminute and arcsecond, are respectively represented by a single and double prime.
A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to 1⁄60 of one degree.

Latitude

latitudesSouthlatitudinal
When this is not the case, as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be written using decimal degrees, with the degree symbol behind the decimals; for example, 40.1875°.
It is measured in degrees, minutes and seconds or decimal degrees, north or south of the equator.

Prime (symbol)

prime symbolprimeDouble prime
These subdivisions, also called the arcminute and arcsecond, are respectively represented by a single and double prime.
As an angular measurement, 3° 5′ 30″ means 3 degrees, 5 arcminutes and 30 arcseconds.

Trigonometric functions

cosinetrigonometric functiontangent
This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians.
For this purpose, any angular unit is convenient, and angles are most commonly measured in degrees.

Babylonian astronomy

Babylonian astronomersBabylonianastronomer
The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle.

Metric system

metricmetric unitsmetric unit
With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal "degrees" called grad or gon, where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = 10⁄9 gon).

Nautical mile

nautical milesnmnmi.
Maritime charts are marked in degrees and decimal minutes to facilitate measurement; 1 minute of latitude is 1 nautical mile.
In the early 1600s English mathematician Edmund Gunter proposed that lines of latitude could be used as the basis for a unit of measurement for distance and proposed the nautical mile as one minute or one-sixtieth (1⁄60) of one degree of latitude.

Turn (angle)

turnturnsrevolution
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.
A turn is a unit of plane angle measurement equal to 2degrees or 400 gradians.

Square degree

deg 2 square degreesdeg2
Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere.

Gradian

gradgongrads
With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal "degrees" called grad or gon, where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = 10⁄9 gon).
It is equivalent to 1⁄400 of a turn, 9⁄10 of a degree, or undefined⁄200 of a radian.

Unit of measurement

unitunits of measurementweights and measures
Alternatively, the traditional sexagesimal unit subdivisions can be used.
When planning his journey across the Atlantic Ocean in the 1480s, Columbus mistakenly assumed that the mile referred to in the Arabic estimate of 56⅔ miles for the size of a degree was the same as the actually much shorter Italian mile of 1,480 meters.

Milliradian

milmradangular mil
An angular mil, which is most used in military applications, has at least three specific variants, ranging from 1⁄6,400 to 1⁄6,000.

Plane (geometry)

planeplanarplanes
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.

Astronomer

astronomersastrophysicistprofessional astronomers
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.

Ecliptic

ecliptical orbitsecliptic planeplane of the ecliptic
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.

Calendar

calendarscalendricalcalendar system
Some ancient calendars, such as the Persian calendar, used 360 days for a year.