Finding the Length of an Arc: Calculations and Formulas for Circles

arc of a circle

The arc of a circle is a portion of the circumference of the circle

The arc of a circle is a portion of the circumference of the circle. It can be thought of as a curved segment of the circle between two points on its circumference. The length of the arc is proportional to the angle it subtends at the center of the circle.

To calculate the length of an arc, you need to know the radius or diameter of the circle, as well as the measure of the central angle in degrees or radians. There are two methods to calculate the arc length: using the central angle or using the circumference of the circle.

Method 1: Using the central angle
If you know the measure of the central angle (θ) in degrees, you can use the following formula to calculate the arc length (s):

s = (θ/360) * 2πr

Where r is the radius of the circle.

Method 2: Using the circumference of the circle
Alternatively, if you know the circumference of a circle (C) and the measure of the central angle (θ) in degrees, you can use the following formula to calculate the arc length (s):

s = (θ/360) * C

Keep in mind that the angle θ should be in degrees for these formulas. If you are given the angle in radians, you can convert it to degrees by using the conversion factor: 180°/π radians.

Remember to use consistent units throughout your calculations, whether it is in centimeters, meters, inches, or any other unit of length.

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