Degree (angle)

Subdivisions[edit]

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 (DD notation); 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 represented by a single prime (′) and double prime (″) respectively. For example, 40.1875° = 40° 11′ 15″. Additional precision can be provided using decimal fractions of an arcsecond.


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).^[12]


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: 1^I for a "prime" (minute of arc), 1^II for a second, 1^III for a third, 1^IV for a fourth, etc.^[13] Hence, the modern symbols for the minute and second of arc, and the word "second" also refer to this system.^[14]


SI prefixes can also be applied as in, e.g., millidegree, microdegree, etc.