Formula For Arc Length
Before learning the formula for arc length, let us recall what is arclength. Arc length is better defined as the distance along the part of the circumference of any circle or any curve (arc). Any distance along the curved line that makes up the arc is known as the arc length. The length of an arc is longer than any straight line distance between its endpoints (a chord). The formula for Arc Length is the quickest way to find the length of the arc. The formula for Arc Length is explained below with solved examples.
What Is the Formula for Arc Length?
As we learned in the previous section, an arc is the portion of a circle's circumference. Thus, the formula for arc length can be expressed as a fraction of the circumference using the angle made by it at the center of the circle.
Arc = 2πr (θ/360)
Where,
 r = radius of the arc
 θ = angle made by the arc at the center (degree)
Let us apply the formula for arc length in the solved examples below.
Solved Examples Using Formula for Arc Length

Example 1: The angle subtended by an arc of radius 12 inches at the center is 45 degrees. Find its length.
Solution
To find: Length of the Arc
Given:r = 12 inches
θ = 45 degreeUsing formula for arc length,
Arc=2πr (θ/360)
Arc Length = 2π × (12) × (45/360)
Arc Length = 24π × 1/8
Arc Length = 3π
Arc Length = 3(22/7)
Arc Length = 66/7
Arc Length = 9.43Answer: The length of the Arc is 9.43 inches.

Example 2: Find the angle subtended by an arc of radius 14 cm and length is 8 cm. Find its length.
Solution
To find: Length of the Arc
Given: r = 14 cm
Arc = 8 cmUsing formula for arc length,
Arc = 2πr (θ/360)
8 = 2π × (14) ×(θ/360)
8 = 2 × (22/7) × (14) × (θ/360)
8 = 88 × (θ/360)
θ = 360 × 8/88
θ = 360/11
θ = 32.73
Answer: The angle subtended by an arc is 32.73 degrees.