Degree angle)

Physical unit
Unit name	Degree
Unit symbol	${\displaystyle \mathrm {^{\circ }} }$
Physical quantity (s)	Flat angle
Formula symbol	The preferred angle designations are lowercase Greek letters ${\displaystyle (\alpha ,\beta ,\gamma ,\dots )}$
dimension	${\displaystyle {\mathsf {{\frac {L}{L}}=1}}}$
system	Approved for use with the SI
In SI units	${\displaystyle \mathrm {1^{\circ }={\frac {\pi }{180}}\;rad\approx 0{,}017\,5\;rad} }$
Derived from	Full angle

The degree ( lat. Gradus , step, also degree of arc ) is a measure of angles . A small superscript circle (°) is used as the unit symbol for the degree, which is attached to the last digit of the numerical value without a space (see degree symbol ). 1 degree is defined as the 360th part of the full angle , i.e. H. 1 full angle = 360 °. One degree corresponds to the 360th part of a circle . The historical division is sexagesimal , in angular or arc minutes and seconds , see angle measure.

The specification of the angular width in degrees is referred to as a degree to differentiate from the radian measure in radians , for the conversion see there. When the gon was still called grad , the term old degree was also used for the degree.

Although the degree does not belong to the International System of Units (SI), it is approved for use with the SI. This makes it a legal unit of measurement .

separations

Fractions of degrees can be given in several variants:

• decimal : ggg, g… °
• sexagesimal :
  • Degrees and minutes: ggg ° mm ′
  • Degrees, minutes and seconds: ggg ° mm ′ ss ″
  • Degrees, minutes, seconds and tertiary : ggg ° mm ′ ss ″ tt ‴ (rare today)
• sexagesimal and decimal combined:
  • Minutes decimal: ggg ° mm, m ... ′
  • Seconds decimal: ggg ° mm ′ ss, s ... ″
  • Tertien decimal: ggg ° mm ′ ss ″ tt, t ... ‴

Conversion from sexagesimal to decimal representation:

${\displaystyle {\text{Winkel in Grad (dezimal)}}={\frac {{\tfrac {{\tfrac {tt}{60}}+ss}{60}}+mm}{60}}+ggg}$

Special features of the 360 ​​° division

The number 360 is one of the highly composite numbers . The division of the full angle into 360 degrees enables a scale to be subdivided into a corresponding number of equal, whole-number sections due to the many divisors. The 24 divisors of 360 are: 1; 2; 3; 4; 5; 6; 8th; 9; 10; 12; 15; 18; 20; 24; 30; 36; 40; 45; 60; 72; 90; 120; 180; 360

See also

• Line (angle unit)
• Degree measurement (geodesy)
• Arc minute
• Arc second

Individual evidence

1. ↑ The International System of Units (SI) . German translation of the BIPM brochure "Le Système international d'unités / The International System of Units (8e édition, 2006)". In: PTB-Mitteilungen . tape 117 , no. 2 , 2007 ( Online [PDF; 1.4 MB ]).
2. ↑ on the basis of EU Directive 80/181 / EEC in the states of the EU or the Federal Law on Metrology in Switzerland