Radian measure is the proportionate Ratio between the length of an arc and its radius. Some of the applications of Radian Measure are Arc Length, area of sector of a Circle, and angular velocity.

Arc length is the length of arc intercepted on circle measuring the radius 'r' with central angle of 'θ' radians which is given by products of radius and it is the measure of length.

S = r θ

With help of this formula we can easily calculate the Arc Length of Circle.

The formula here for the arc length of θ (theta) which is in the degrees of s = (θ / 360) * 2∏r. It is part of circumference. Always remember that 'θ' must be in radians. With help of an illustration we can understand this concept in a more precise manner.

Find the length of an arc of circle having radius 2 inch and central angle 5.1 radians.

Area = θr^{2} / 2,

If 'r' is in inch then the area will be in inch2.

Radians can easily be defined with help of trigonometric Functions. Use of Trigonometric Functions is much more convenient than radians. This can be explained as in form of sine and cosine functions. We can put sine functions whose unit measures are in degree to get appropriate answer, whereas if we put put sine functions which are measured in degrees for radians then answer we obtain will comparatively better than previous one. However both are arbitrary methods to measure angles but one is more convenient than other.

This is all about applications of radian measure.