Calculating the Length of an Arc | Formulas and Examples

Length Of Arc

The length of an arc refers to the distance along a curve or a portion of a circle between two specific points

The length of an arc refers to the distance along a curve or a portion of a circle between two specific points. It is often measured in terms of the units used to describe the circumference of the circle.

To calculate the length of an arc, you need to know the angle subtended by the arc at the center of the circle (in degrees or radians) and the radius of the circle.

There are two formulas you can use to calculate the length of an arc:

1. For an arc measured in degrees:
Arc length = (𝜃/360) * 2πr
where 𝜃 represents the central angle (in degrees) and r is the radius of the circle.

2. For an arc measured in radians:
Arc length = 𝜃r
where 𝜃 represents the central angle (in radians) and r is the radius of the circle.

Note that in both formulas, 𝜃 is the ratio of the subtended angle to a full circle (360 degrees or 2π radians).

To illustrate, let’s consider an example:
Suppose we have a circle with a radius of 5 units and we want to find the length of an arc that is subtended by a central angle of 60 degrees. Using the first formula:
Arc length = (60/360) * 2π(5) = (1/6) * 2π(5) = (π/3)(5) = (5π/3) units

Thus, the length of the arc is (5π/3) units.

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