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.

To calculate the arc length, multiply the radius by the angle of rotation in radians.

How to calculate an arc length?

How to calculate 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 choose 2 meters for this example.

  2. Next, measure or choose the central angle.

    This is also sometimes referred to as the angle of rotation. We will choose 35 degrees.

  3. Finally, enter the values into the calculator above, or the equation

    The result is 1.22 meters.

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

    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 degrees so 2.5*59.27=143.29.

  5. Next we need to measure the radius

    For this example, we will assume an extremely large radius of 200meters.

  6. Finally, enter all of the information into the formula or calculator above

    The solution is 500.17m

Can you find the arc length of a circle?

Calculating the arc length of a circle is as simple as calculating the total circumference of that circle. This can be done using the formula 2*pi*r.

Does arc length have to be in radians?

The calculation of an arc length can be done using radians or degrees. To do so, you must be sure the formula is converted if you are using degrees. The calculator above can perform this for you.

What does arc length mean?

An arc length is the total distance traveled along an arc with a specified radius and a central angle.

How does arc length relate to circumference?

An arc length that is equal to a circumference has a central angle of 2*pi radians.

Is arc length equal to radius?

No, an arc length is not equal to the radius, but it is dependent on the radius. The arc length can be calculated by multiplying the radius by the angle in radians.

How is arc length measured?

Arc length is typically calculated using the formula L= r*Θ, but it can also be measured by taking a string along the length of the arc, then straightening that string and measuring the length.


What is an arc length?

An arc length is a measure of the circumference of a portion of a circle enclosed by two radii.

How do i calculate the sector area?

Since an arc length is a portion of the circumference of a circle, the sector area is also a portion of the area of the total circle. It’s equal to the total area multiplied by the fraction of the arc length to the total circumference. This sector area calculator does the math for you.

Should i use Radians or degrees?

Using this calculator, you can actually use either radians or degrees. To convert between the two, simply multiply radians by 57.2958 to get degrees, or divide for the opposite.