Arc Length Formula in Radians
Before starting with the arc length formula in radians, let us first recall what is arc and arc length. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the endpoints of the arc. The arc length is defined as the interspace between the two points along a section of a curve. Learn about the arc length formula in radians, i.e., when the central angle is given in terms of radians, using solved examples.
What Is the Arc Length Formula in Radians?
Arc length of a circle can be calculated using different formulas, based on the unit of the center angle of the arc. The arc length formula in radians can be expressed as,
Arc Length = θ × r
where,
 L = Arc Length
 θ = Center angle of the arc in radians
 r = Radius of the circle
Let us see the applications of the arc length formula in radians in the following section,
Solved Examples Using Arc Length Formula in Radians

Example 1: Using the arc length formula in radians, Find the length of the arc cut off by a central angle of 4 radians in a circle with radius of 7 inches.
Solution:
To find: Length of the arc
Given:
Central angle of arc, θ = 4 radians
Radius, r = 7 inches
Using arc length formula,
L = θ × r
= 4 × 7
= 28 inches
Answer: Length of the arc = 28 inches.

Example 2: Find the radius of a circle, with an arc of length 8 inches subtending an angle equal to 6 radians at the center.
Solution:
To find: Radius of a circle
Given:
Central angle of arc, θ = 6 radians
Radius, r = 8 inches
Using arc length formula in radians,
L = θ × r
8 = 6 × r
r = 1.33 inches
Answer: Radius of the circle = 1.33 inches.