Degree (angle)
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A degree (symbol °) is a unit used to measure plane angles. One degree equals 1/360 of a full rotation. Therefore, a complete rotation measures 360°, a half rotation 180°, and a quarter rotation 90°.
The degree is not the standard unit of the SI system—that is the radian—but it is accepted for use with SI. It is commonly used in geometry, surveying, navigation, and engineering.
Subdivisions
A degree is subdivided on a sexagesimal basis: one degree contains 60 arcminutes (symbol ′), and one arcminute contains 60 arcseconds (symbol ″). This system is still used in measuring latitude and longitude and in astronomy. Decimal notation also exists, for example 23.45°.
Relation to the radian
A full rotation equals 2π radians. Therefore, 180° = π radians, and one degree equals π/180 radians, approximately 0.01745 radians. Higher mathematics and calculus commonly use the radian, because the derivative formulas of trigonometric functions are simpler when the radian is used.
Historical origin
The division of a rotation into 360 parts derives from the sexagesimal system of Babylon and ancient astronomy, and the number 360 has many divisors, which facilitates the subdivision of a rotation. Other units exist, such as the gradian (gon), which divides a rotation into 400 parts, but its use is limited to some fields of surveying.