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.
- Area of a sector calculator
- polar coordinates calculator
- Midpoint Calculator
- Area of a semi circle calculator
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.
Time needed: 10 minutes.
How to calculate Arc Length
- 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.
- Next, measure or choose the central angle.
This is also sometimes referred to as the angle of rotation. We will choose 35 degrees.
- Finally, enter the values into the calculator above, or the equation
The result is 1.22 meters.
- Now let’s take a look at an example of calculating the arc length when the angle is given in radians.
or 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.
- Next we need to measure the radius
For this example we will assume an extremely large radius of 200meters.
- Finally, enter all of the information into the formula or calculator above
The solution is 500.17m
An arc length is a measure of the circumference of a portion of a circle enclosed by to radii.
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 total circumference. This sector area calculator does the math for you.
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.
Additional information on the 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.
For more math related calculators, click here.
For all calculators, click here.