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Thus 2 radians equals 360 degrees. This means that 1 radian = 180/ degrees, and 1 degree = /180 radians. The reason for this is that so many formulas become much easier to write and to understand when radians are used to measure angles. A very good example is provided by the formula for the length of a circular arc.
Radians, Degrees, and Converting Between. Purplemath. Radians and degrees are two types of units for measuring angles. There are very many such units (such as gradians and MRADs), but degrees and radians are the ones you are most likely to encounter in high school and college. Degrees are used to express both directionality and angle size.