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# Degree and Radian Measure Formula with Problem Solution

In mathematics, the radian is defined as the standard unit for measurement of angles. The measurement in angles is usually equal to the total length of a corresponding arc in a unit circle. The relationship between arch length and radius of a circle is generally defined with the help of radian of a circle. Degree and radian measure formula in mathematics is generally needed to convert degrees to radian and radians to degrees.

### Degree and Radian Measure Formula

$\LARGE Radian=\frac{Arc\;Length}{Radius\;Length}$

$\LARGE Radian=\frac{Degree\times \pi}{180}$

Further, degrees can be used to define the directionality and the size of an angle. If you are standing straight directly to north then it is defined as the zero degree if you end up again in North after a complete turn then the full revolution is marked as the 360°.

Next is radian but the question is why do we need to learn radian when we have the degrees. Actually, we need number to perform calculations in mathematics. There is nothing to do with degrees until they are converted to some equivalent form. If we right it as 2π then it is more significant than the previous ones.  Here, are how degrees can be converted to radians in mathematics.