Last updated on June 21st, 2020
An arc is any portion of the circumference of a circle. Arc length is the distance from one point to another. Arc length is the distance from one endpoint to the arc of the other. It requires knowing a bit about the geometry of a circle. Here is a step by step guide on how to find arc length.
How to find arc length using a measurement of Central angle in Degrees
- Set up the formula for arc length. Arc length = 2π(r)(Θ/360)
where r equals the radius of the circle and Θ equals the measurement of the arc’s central angle, in degrees. - Plug the given length of the circle’s radius into the formula.
For example, if the circle’s radius is 20 cm, your formula will look like this: Arc length = 2π(20)(Θ/360) - Insert the given value of the arc’s central angle into the formula.
For example, if the arc’s central angle is 145 degrees, your formula will look like this: Arc length = 2π(20)(145/360) - Multiply the radius by 2π. For example 2π(20)(145/360)
2(3.14)(20)(145/360)
(125.6)(145/360) - Divide the arc’s central angle by 360. For example (125.6)(145/360)
(125.6) (0.402) - Multiply the two numbers together. For example (125.6) (0.402)
50.49
How to find arc length using a measurement of Central angle in Radians
- Set up the formula for arc length. The formula is arc length = Θ(r), where Θ equals the measurement of the arc’s central angle in radians, and r equals the length of the circle’s radius.
- Plug the length of the circle’s radius into the formula. For example, if the circle’s radius is 20 cm arc length = Θ(20).
- Insert the measurement of the arc’s central angle into the formula. For example, if the arc’s central angle is 3.72 radians,
(3.72) (20). - Multiply the radius by the radian measurement. (3.72) (20) = 74.4