Math Wiki

A degree, denoted by a small circle superscript (°), is a unit of angular measure constituting one 360th part of a complete revolution (or circle).

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".