The reason for there being 360° in a circle isn't completely understood. It may have something to do with being close to the number of days in a year (between 365 and 366). Mathematically, however, it appears to be an arbitrarily chosen value.
Alternative units of angular measure include:
- The grad, one 400th part of a circle — which makes the arithmetic easier to do without a computational aid.
- The radian, defined in terms of the radius of a circle and thus mathematically justified, as there are exactly radians in a circle (see also Circumference).
Degree measurement, although not mathematically justified, has a long historical tradition and are far more familiar to the layman than either the radian or the grad.
Non-integer numbers of degrees may be written in decimal or fractional form.
Fractional portions of degrees may also be written in minutes and seconds:
- There are 60 minutes (') in a degree.
- There are 60 seconds (") in a minute.
For example, 15.245° can be equivalently written 15° 14' 42".