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