Let us say that I would like to store latitudes and longitudes like this:

lat 35 degree

long 80 degree

Which system of units does the unit 'degree' belong to? It is not really a SI unit nor a Imperial unit ...

  • 1
    en.wikipedia.org/wiki/Angle#Units suggests degrees are derived from the SI derived unit Radians – Ian Turton Apr 24 '15 at 10:59
  • First i removed, then added back the 'vector' tag back since a unit vector is an alternate means of storing angles. – Martin F Apr 24 '15 at 15:46

Degrees are part of a modified Sexagesimal (base 60) number system. Even though there are 360 degrees in a circle, 360 is 6 x 60. The origin of degrees as angular units is unclear (see wiki/Degree_(angle)#History.)

See Coordinate Conversion: Decimal Degree to Deg-Min-Sec of lat/long Coordinates for subdivisions of a degree.

In terms of fundamental physical units, mass, length and time, angles are actually unitless because they are derived from ratios of lengths:

For a sector: arc angle = arc length / radius

For a right triangle: angle
= arcsine (opposite / hypotenuse)
= arctan (opposite / adjacent)
= arccosine (adjacent / hypotenuse)

We still give a name to those natural unitless angles: radians.

2 π radians = 360 °

And, according to wiki/International_System_of_Units and convertunits.com/type/angle, the radian is derived from SI base units.

For data storage, you can use any units, so long as you have proper conversions to/from those used in the interfaces. Radians are most readily suitable for trigonometric functions, but then, if you use direction cosines, you can avoid some (costly) trigonometric functions.


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