Angle Measure in Degrees

Degrees vs Radians

Most readers will be familiar with angles expressed in degrees.  As there are  radians in a circle, there are 360 degrees. We denote 360 degrees with the shorthand . If an angle is expressed without the degree symbol (), then the angle is in radians. For example,  means angle theta is equal to 20 degrees, but means angle alpha is equal to 20 radians. Note that the angle for half of the unit circle is and also rad, so we use the fractions  to convert between the different units of angle measure.  The technique is known as unit analysis and is useful in all sciences.  EX:     Convert  to radians.


EX:     Convert  rad to degrees.

Sub Units: Degrees, Minutes, Seconds

Fractions of a degree are usually expressed as minutes and seconds.  Just as with time units, there are 60 seconds in a minute and 60 minutes in a degree.   You should be able to convert sub units to degrees with decimals and vice versa using similar unit analysis techniques as above.  EX:  Convert to degrees, minutes, and seconds.

Note that this is rounded to the nearest second.   For more precision, just add decimal places to the seconds unit.  EX:  Convert  to degrees with decimals.