Degree (angle)

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.

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


Equilateral chord with length equal to radius
A circle with an equilateral chord (red). One sixtieth of this arc is a degree. Six such chords complete the circle.[5]

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.[6] 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.[7][8] 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.[9][10] Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes.[11] 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:[12]

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).[13][14] 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.


For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. 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°.

Alternatively, the traditional sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes (of arc), and one minute into 60 seconds (of arc). Use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are respectively represented by a single and double prime. For example, 40.1875° = 40° 11′ 15″, or, using quotation mark characters, 40° 11' 15". Additional precision can be provided using decimals for the arcseconds component.

Maritime charts are marked in degrees and decimal minutes to facilitate measurement; 1 minute of latitude is 1 nautical mile. The example above would be given as 40° 11.25′ (commonly written as 11′25 or 11′.25).[15]

The older system of thirds, fourths, etc., which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today. These subdivisions were denoted by writing the Roman numeral for the number of sixtieths in superscript: 1I for a "prime" (minute of arc), 1II for a second, 1III for a third, 1IV for a fourth, etc. Hence the modern symbols for the minute and second of arc, and the word "second" also refer to this system.

Alternative units

Degree-Radian Conversion
A chart to convert between degrees and radians

In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. 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. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2π radians, so 180° is equal to π radians, or equivalently, the degree is a mathematical constant: 1° = ​π180.

The turn (or revolution, full circle, full rotation, cycle) is used in technology and science. One turn is equal to 360°.

With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal "degrees"[note 3] called grad or gon, where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = ​109 gon). Although that idea was abandoned by Napoleon, grades continued to be used in several fields and many scientific calculators support them. Decigrades (​14,000) were used with French artillery sights in World War I.

An angular mil, which is most used in military applications, has at least three specific variants, ranging from ​16,400 to ​16,000. It is approximately equal to one milliradian (c.16,283). A mil measuring ​16,000 of a revolution originated in the imperial Russian army, where an equilateral chord was divided into tenths to give a circle of 600 units. This may be seen on a lining plane (an early device for aiming indirect fire artillery) dating from about 1900 in the St. Petersburg Museum of Artillery.

Conversion of common angles
Turns Radians Degrees Gradians (Gons)
0 0 0g
1/24 π/12 15° 16 2/3g
1/12 π/6 30° 33 1/3g
1/10 π/5 36° 40g
1/8 π/4 45° 50g
1/2π 1 c. 57.3° c. 63.7g
1/6 π/3 60° 66 2/3g
1/5 2π/5 72° 80g
1/4 π/2 90° 100g
1/3 2π/3 120° 133 1/3g
2/5 4π/5 144° 160g
1/2 π 180° 200g
3/4 3π/2 270° 300g
1 2π 360° 400g

See also


  1. ^ The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
  2. ^ Contrast this with the relatively unwieldy 2520, which is the least common multiple for every number from 1 to 10.
  3. ^ These new and decimal "degrees" must not be confused with decimal degrees.


  1. ^ HP 48G Series – User's Guide (UG) (8 ed.). Hewlett-Packard. December 1994 [1993]. HP 00048-90126, (00048-90104). Retrieved 6 September 2015.
  2. ^ HP 50g graphing calculator user's guide (UG) (1 ed.). Hewlett-Packard. 1 April 2006. HP F2229AA-90006. Retrieved 10 October 2015.
  3. ^ HP Prime Graphing Calculator User Guide (UG) (PDF) (1 ed.). Hewlett-Packard Development Company, L.P. October 2014. HP 788996-001. Retrieved 13 October 2015.
  4. ^ Bureau International des Poid et Mesures (2006). "The International System of Units (SI)" (8 ed.). Archived from the original on 1 October 2009.
  5. ^ Euclid (2008). Eements. Translated by Heiberg, Johan Ludvig; Fitzpatrick, Richard (2nd ed.). online: Princeton UP. p. bookIV. ISBN 978-0-6151-7984-1.
  6. ^ "Degree". MathWorld.
  7. ^ Jeans, James Hopwood (1947). The Growth of Physical Science. p. 7.
  8. ^ Murnaghan, Francis Dominic (1946). Analytic Geometry. p. 2.
  9. ^ Rawlins, Dennis. "On Aristarchus". DIO - The International Journal of Scientific History.
  10. ^ Toomer, Gerald J. Hipparchus and Babylonian astronomy.
  11. ^ "2 (Footnote 24)". Aristarchos Unbound: Ancient Vision / The Hellenistic Heliocentrists' Colossal Universe-Scale / Historians' Colossal Inversion of Great & Phony Ancients / History-of-Astronomy and the Moon in Retrograde! (PDF). DIO - The International Journal of Scientific History. 14. March 2008. p. 19. ISSN 1041-5440. Retrieved 16 October 2015.
  12. ^ Dirghatamas. Rigveda. pp. 1.164.48.
  13. ^ Brefeld, Werner. "Divisibility highly composite numbers".
  14. ^ Brefeld, Werner (2015). (not defined). Rowohlt Verlag. pp. Not yet published.
  15. ^ Hopkinson, Sara (2012). RYA day skipper handbook - sail. Hamble: The Royal Yachting Association. p. 76. ISBN 9781-9051-04949.

External links

A. H. Bulbulian Residence

The A. H. Bulbulian Residence is a house located at 1229 Skyline Drive, Rochester, Minnesota, United States. It was designed by noted architect Frank Lloyd Wright for Arthur H. Bulbulian, a pioneer in the field of facial prosthetics. It is down the street from the Thomas Keys House and not far from the James McBean Residence, all three examples of Wright's Usonian genre of architecture. The Bulbulian Residence is a one-story house built with one 120-degree angle, and is constructed of cement brick and cypress. The house has recently been restored to near-original condition.


Bo-taoshi (Japanese: 棒倒し, Hepburn: bōtaoshi, "pole toppling"), is a capture-the-flag-like game, played on sports days at schools in Japan. The game, traditionally played by cadets at the National Defense Academy (NDA) of Japan on its anniversary, is famous for its size, wherein two teams of 150 individuals each vie for control of a single large pole. Each team is split into two groups of 75 attackers and 75 defenders. The defenders begin in a defensive orientation respective to their own pole, while the attackers assume position some measure away from the other team's pole. A team is victorious if it is able to lower the pole of the opposing team (which begins perpendicular to the ground) to a thirty-degree angle (respective to the ground), before the other team reaches this goal. Until a rule-change in 1973, the angle of victory was only forty-five degrees.

Corner (route)

A corner route is a pattern run by a receiver in American football, where the receiver runs up the field and then turns at approximately a 45-degree angle, heading away from the quarterback towards the sideline. Usually, the pass is used when the defensive back is playing towards the inside shoulder of the receiver, thus creating a one on one vertical matchup. The corner route is less likely to be intercepted when compared to the slant route, because it is thrown away from the middle of the field. The pass is used frequently in the West Coast offensive scheme, where quick, accurate throwing is key. The pass may also be used closer to the goal line in what is called a "fade". The quarterback will lob the ball over a beaten defender to a wide receiver at the back corner of the end zone.

Ellipsoidal reflector spotlight

Ellipsoidal reflector light (abbreviated to ERS, or colloquially ellipsoidal or ellipse) is the name for a type of stage lighting instrument, named for the ellipsoidal reflector used to collect and direct the light through a barrel that contains a lens or lens train. The optics of an ERS instrument are roughly similar to those of a 35 mm slide projector. There are many types of ERS that are designed for the myriad applications found in the entertainment industry. ERS instruments come in all shapes and sizes. Each particular model of ERS has its own set of characteristics. Generally, ERS instruments are the most varied and utilized type of stage lighting instrument. ERS may also be referred to as Profile Spotlights (especially in Europe) because the beam can be shaped to the profile of an object. Ellipsoidal reflectors are used for their strong, well-defined light and their versatility. Leko and Source Four are brand names which are often, but inaccurately, used to refer to any sort of ellipsoidal.

Characteristics of a typical ellipsoidal lighting unit include:

An ellipsoidal reflector

An adjustable lens tube containing the lens or lens train. Adjusting the tube by pushing it further in or pulling it further out of the unit allows changes to the focus (softness or hardness) of the beam of light projected by the unit. This results from changing the distance between the reflector and the lens train. "Zoom" ERS instruments can vary the size of beam as well as the focus

One or two Plano-Convex (PC for short) lenses within the lens tube to create the lens train. The Plano-Convex lenses, named for having one flat side and one convex (bowed out) side, have their convex sides facing each other within the tube. The distance between these lenses and the distance between them and the reflector determines how wide the output beam of light is

A set of brackets on the end of the lens tube for the insertion of gel frames, a color changing unit or any variety of accessories. Most modern units include two slots that allow for combining different accessories

A series of four shutters mounted at the internal focal point (the place where the varying angles of light coming off the reflector meet) of the unit. These allow for precise shaping and sizing of the unit's beam as lines. Additionally, an iris may be present to size the beam circularly.

A slot in the body of the unit for the insertion of metal gobos to change the pattern of the light in most cases is present, this slot can also hold a glass gobo, dichroic colour roundel or an effects unit such as a gobo rotator or irisThe lamps are loaded from the rear (in most cases), and either mounted axially, or radially with the base either up or down (the orientation is important when mounting the instrument as using the light upside down will shorten lamp life) at a 45-degree angle or sometimes at a 90-degree angle. The filament of the lamp is at one focal point of the ellipsoidal reflector and the gate with the shutters and gobo are at the other focal point.


Episiotomy, also known as perineotomy, is a surgical incision of the perineum and the posterior vaginal wall generally done by a midwife or obstetrician. Episiotomy is usually performed during second stage of labor to quickly enlarge the opening for the baby to pass through. The incision, which can be done at a 90 degree angle from the vulva towards the anus or at an angle from the posterior end of the vulva (medio-lateral episiotomy), is performed under local anesthetic (pudendal anesthesia), and is sutured after delivery.

Its routine use is no longer recommended. Despite this, it is one of the most common medical procedures performed on women. In the United States, as of 2012, it was performed in 12% of vaginal births. It is still widely practiced in many parts of the world, including Japan, Taiwan, China, and Spain.


A Fleaker is a brand of container for liquids used in the laboratory. It can be described as a cross between the Griffin beaker and the Erlenmeyer flask.Like a beaker, the bottom is flat, with the sides meeting the bottom at a 90 degree angle. The sides are vertical for most of the height; near the top, the sides curve in to form a neck with a widely flared rim. The wide rim makes it easier to pour from or filter into; the narrow neck reduces loss of the contents due to splashing and serves as a grip for handling and pouring.

Fleaker containers have a plastic lid with a built in rubber stopper. When on the Fleaker, the lid covers the narrow neck. Fleaker containers work as well as other glassware for liquids and solutions, but are inappropriate for slurries, precipitates, and recrystallizations (since the narrow neck makes it difficult to remove solids completely from a Fleaker).

The Fleaker was invented by Roy Eddleman, founder of Spectrum Medical Industries (now Spectrum Laboratories). Fleaker is a registered trademark of Spectrum Laboratories, licensed to Corning.

ISSF 25 meter standard pistol

25 metre standard pistol is one of the ISSF shooting events, introduced at the ISSF World Shooting Championships in 1970. It has its roots in the NRA conventional pistol competitions.

The standard pistol match is shot with a regular sport pistol (also called a standard pistol) in caliber .22 LR. As with all ISSF pistol disciplines, all firing must be done with one hand, unsupported.

The 60-shot match is divided into 5-shot strings with different timings:

4 strings within 150 seconds each - competitor can begin the series in any fashion he/she chooses.

4 strings within 20 seconds each - competitor must begin each strings with pistol in one outstretched arm from the 45-degree angle starting position.

4 strings within 10 seconds each - competitor must begin each string with pistol in one outstretched arm from the 45-degree angle starting position.Just like 25 metre center-fire pistol, standard pistol is a non-Olympic event and so gains little attention. It is one of the few events where targets did not change in 1989, so no resetting of records has been made. As a result, many records are rather old.

Iliotibial band syndrome

Iliotibial band syndrome (ITBS) is a common injury to the knee, generally associated with running, cycling, hiking or weight-lifting (especially squats).

Inverted vee antenna

An inverted vee antenna is a type of antenna similar to a horizontal dipole, but with the two sides bent down towards the ground, typically creating a 120 or 90 degree angle between the dipole legs. It is typically used in areas of limited space as it can significantly reduce the ground foot print of the antenna without significantly impacting performance. Viewed from the side, it looks like the English letter "V" turned upside down, hence the name. Inverted vee antennas are commonly used by amateur radio stations, and aboard sailing vessels requiring better HF performance than available with a short whip antenna. Inverted vee antennas are horizontally polarized and have a similar pattern compared to a traditional horizontal dipole.


The kyoketsu-shoge (距跋渉毛), which means "to run about in the fields and mountains", is a double edged blade, with another curved blade attached near the hilt at a 45–60 degree angle. This is attached to 12 to 18 feet of rope, chain, or hair which then ends in a large metal ring. It is thought to have developed before the more widely known kusarigama (sickle and chain). Ninja were usually of the peasant class and the blade of the kyoketsu-shoge was originally a farming tool.Almost exclusively used by the ninja, the kyoketsu-shoge had a multitude of useful applications. The blade could be used for pulling slashes as well as thrusting stabs. The chain or cord, sometimes made from human hair or horsehair for strength and resiliency, could be used for climbing, ensnaring an enemy, binding an enemy and many such other uses. The long range of the weapon combined a cutting tool along with the capability to strike or entangle an enemy at what the user perceived to be a 'safe' distance out of the way. When skilled with this weapon it could be used to entangle a sword and rip it from the opponents hands rendering him harmless. The kyoketsu-shoge cord and ring was sometimes used to wrap around an enemy's legs and trip them.

Typically the round ring was flat rather than round in cross section to provide a firmer grip and a more sturdy frame, as the ring was also used for strikes and deflective blows in use. This tool was also used as a climbing aid, and it could be thrown and lodged in corners. Kyotetsu shoge was the weapon used by Nobu of The Hand in Daredevil season 1 on Netflix.

Mark 36 SRBOC

The BAE Systems Mark 36 Super Rapid Bloom Offboard Countermeasures Chaff and Decoy Launching System (abbreviated as SRBOC or "Super-arboc") is a short-range mortar that launches chaff or infrared decoys from naval vessels to foil anti-ship missiles. Each launcher has three tubes set at a 45-degree angle, and three tubes set at a 60 degree angle, providing an effective spread of decoys and countermeasures to defeat radio frequency emitting missiles. The SRBOC can also be fitted with the TORCH infrared "flare" decoy system. A typical ship's load is 20 to 35 rounds per launcher.

As of 2010, the Mark 36 SRBOC is used by 19 navies around the world. It is similar to the NATO Sea Gnat system.

The Flyrt radar-decoy drone was designed to be launched from the Mark 36 launcher.

Meehambee Dolmen

The Meehambee Dolmen is a megalithic portal tomb dating from about 3500 BC located in County Roscommon, Ireland.

It has been discovered by two local children in the 1960s who have unearthed two stone axes.Originally supported on 6 upright portals, 2.3 metres high. The capstone is estimated to weigh twenty-four tonnes. The portal stone supporting the back of the capstone has collapsed, allowing the capstone to slide backwards out of position, causing the doorstone to collapse also. The capstone now rests at a 45-degree angleIt is thought that these tombs, of which over 1,200 have been identified in Ireland were either the burial place of a single important king or chieftain or perhaps the tombs of several members of a tribe who inhabited the area in the Neolithic era.


The Panzerwurfmine (abbreviated to PWM) was a shaped charge hand-thrown anti-tank grenade used by Luftwaffe ground troops in World War II.


In heraldry, purpure () is a tincture, equivalent to the colour "purple", and is one of the five main or most usually used colours (as opposed to metals). It may be portrayed in engravings by a series of parallel lines at a 45-degree angle running from upper right to lower left from the point of view of an observer, or else indicated by the abbreviation purp.

Purpure has existed since the earliest periods, for example in the purpure lion of the arms of León; at that time, it was painted in a greyer shade. However, it has never been as common as the other colours, and this has led to some controversy as to whether it should be counted among the common colours. In French heraldry, the colour is usually excluded from the common colours as well as considered "ambiguous" (could be either colour or metal), and Finnish heraldry restricts its use to certain additaments.There is at least one instance of it being blazoned as "Imperial Purple". One of the most expensive colors to acquire in ancient times, Tyrian purple was used in the war banner of Byzantine Emperor Komnenos: Purpur (porphyr red) a double-headed eagle displayed Or.

Sometimes, the different tinctures are said to be connected with special meanings or virtues, and represent certain elements and precious stones. Even if this is an idea mostly disregarded by serious heraldists throughout the centuries, it may be of anecdotal interest to see what they are, since the information is so often sought after. Many sources give different meanings, but purpure is often said to represent the following:

Of jewels, the amethyst

Of heavenly bodies, Mercury (this is disputable. Western Alchemy associates the amethyst with Jupiter; viz. 777.)

The planet Mercury is further associated with the element mercury or "quicksilver" in traditional alchemical/occultistic lore


The RPG-43 (for ruchnaya protivotankovaya granata obraztca 1943 goda meaning "hand-held anti-tank grenade") was a high explosive anti-tank (HEAT) hand grenade used by the Soviet Union during the Second World War. It entered service in 1943, replacing the earlier models RPG-40 and RPG-41. The RPG-43 used a shaped charge HEAT warhead, whereas the RPG-40 used the simpler HE (high explosive) warhead. The RPG-43 had a penetration of around 75 mm of rolled homogeneous armour at a 90 degree angle. Later in the war, it was improved and became the RPG-6.

Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line.

Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry.

Slant (route)

A slant route is a pattern run by a receiver in American football, where the receiver runs up the field at approximately a 45-degree angle, heading to the gap between the linebackers and the linemen. Usually, the pass is used when the corner or nickelback are playing farther away from the receiver, so a quick pass is able to be completed before the defender has time to try to break up the pass. The pass is used frequently in the West Coast system, where quick, accurate throwing is key. This route is most commonly used to exploit the cover 2 defense. Usually throwing in the seam between the safety and the cornerback is the key to getting a completion using this route.

Tent stitch

Tent stitch is a small, diagonal needlepoint stitch that crosses over the intersection of one horizontal (weft) and one vertical (warp) thread of needlepoint canvas forming a slanted stitch at a 45-degree angle. It is also known as needlepoint stitch and is one of the most basic and versatile stitches used in needlepoint and other canvas work embroidery. When worked on fine weave canvas over a single warp and weft thread it is known as petit point in contrast to stitches, such as Gobelin, worked over multiple warp and/or weft threads.

"Petit point" comes from the French language, meaning "small point" or "dot".

Wing chord (biology)

Wing chord is an anatomical measurement of a bird's wing. The measurement is taken with the wing bent at a 90-degree angle, from the most prominent point of the wrist joint to the most prominent point of the longest primary feather. It is often taken as a standard measurement of the proportions of a bird and used to differentiate between species and subspecies.

Base units
Derived units
with special names
Other accepted units
See also

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