Arc Length

Arc Length of a Circle

For a circle, an arc is simply a continuous portion of its circumference. The length of an arc depends on the circle’s radius and the central angle that the arc subtends (forms) at the center of the circle.

Formula for Arc Length of a Circle

The following diagram gives the formulas to calculate the arc length of a circle when the central angle is given in degrees and in radians. Scroll down the page for more examples and solutions.

 

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There are two main formulas, depending on whether the central angle is in degrees or radians:

1. When the Central Angle (θ) is in Degrees:
   Since there are 360° in a full circle, the formula is:
   \( s= \frac{θ}{360^{circ}}×2πr\)
   

Where:
s = arc length
r = radius of the circle
θ = central angle in degrees

2. When the Central Angle (θ) is in Radians:
   The formula is:
   s = rθ
   

Where:
s = arc length
r = radius of the circle
θ = central angle in radians

How to Find Arc Length: Degrees
Angle measured in Degrees
How to use the formula for calculating arc length?
How to find the perimeter of a sector?

• Show Step-by-step Solutions

Arc Length: Radians
How to use the formula for calculating arc length when the angle is given in radians?

• Show Video Solutions

Arc Length Theorem
How to Find the Length of an Arc
This video lesson discusses how to find the length of an arc. First, the arc length theorem is reviewed and explained. An example of find the length of a major arc is modeled. The given information is the measure of the related minor arc and the radius of the circle.

• Show Step-by-step Solutions

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