Arc Length Calculator

Calculate the arc length of a circle sector. Enter the degrees of rotation/central angle, and the radius to calculate the arc length and sector area.

Arc Length Formula

The following can be used to calculate the total length of an arc.

L = r * Θ

  • Where L is the arc length
  • r is the radius
  • and Θ is the central angle or angle of rotation.

The length of an arc depends only on the radius of that circle and the central angle of the arc. The arc length is some portion of the circumference. An arc equal to the circumference would have a central angle of 2*PI.

How to calculate Arc Length

Let’s take a look at an example of how you can calculate an arc length.

  1. First, either measure or evaluate the radius or diameter of your circle. This can be chosen instead of measured if you choose so. We will chose 2 meters.
  2. Next, measure or choose the central angle. This is also sometimes referred to as the angle of rotation. We will chose 35 degrees.
  3. Finally, enter the values into the calculator above, or the equation, and we get 1.22 meters.

Now let’s take a look at an example of calculating the arc length when the angle is given in radians.

  1. For this example we first need to measure the angle. Let’s assume we get a measurement of 2.5 radians. First, we need to convert this into degrees. 1 radian is equal to 59.27 degress so 2.5*59.27=143.29.
  2. Next we need to measure the radius. For this example we will assume an extremely large radius of 200meters.
  3. Finally, enter all of the information into the formula or calculator above and we get 500.17 m

More about arc length

Arc length is also related to semi circles. That’s because a semi circle has an arc length that is exactly 1/2 of the circumference of a complete circle. By that logic, the arc length of a quarter circle is exactly 1/4 of the circumference of a circle. You can click on the link about the calculator to learn more about the area of semi circles and it’s relationship to arc length.

If you notice above, the formula for arc length requires both an angle and a radius. These units are actually the 2 units that are used to describe polar coordinates. Therefore, if you have a point with standard Cartesian points, you can convert to polar coordinates and then determine the arc length.

arc length calculator

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