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Arc Length: Definition & Equation

Instructor: Ellen Manchester
Arc length is an important aspect to understanding portions of curved lengths. As you will learn in this lesson, combining our knowledge of circumference and central angle measures allows us to find arc length.

Definition of Arc Length

As an airplane travels around the world, it follows a certain flight path. This path has to follow the contour of our earth, which makes the plane follow a certain arc. This arc length is a portion of the entire circumference of the earth.

Arc length is literally the length of the arc of a portion of a circle. This arc is a part of the total circumference of a circle. This length is measured as a linear distance. Since it is a portion of the entire circumference, we need to first identify the formula used to find the circumference of a circle as well as use the central angle.

Circumference and Central Angle

Circumference is a term used to describe the length around a circle. Circumference is found using this formula:

Circumference Formula

C is for Circumference, d is the diameter and pi, can be rounded to 3.14.

The central angle measure will be given to you and since it is a part of the whole circle, it will be written as a fraction. For instance, if you have a central angle measure of 45 degrees, the fraction would be 45/360.

Finding the Arc Length

An arc length is measured by taking a part of the whole circle. For instance, if you had a central angle measure of 45 degrees, the arc created by this angle would be 45 out of 360 degrees or 45/360 degrees. The arc length would be found by calculating the portion of the circle, that is 45 of 360 degrees of the circle.

Arc length is combining the formula for circumference of a circle with the central angle measure of the circle. The formula for finding arc length is:

Arc Length Formula

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