Arc Length Calculator

This arc length calculator can easily calculate the length of an arc of a circle with the help of central angle and the radius of the circle.

To understand that concept of arc length, first understand what an arc is.

A segment, or part, of a curve is called an arc. It can also be a line graph part. The arc AB is part of a circle in the diagram below.

arc of circle

A minor arc is when the arc of a circle is less than a semicircle, while a major arc is when the arc is bigger than a semicircle. Because the arc AB of the circle is less than a semicircle in the diagram above, it is a minor arc.

The total distance between point A and B is called as the arc length.

Calculator Use

  • This calculator is Extremely easy to use.
  • Simply enter the central angle and the radius of the circle to determine the length of an arc.
  • From the entered inputs, the calculator will display the result as a length of an arc.

Arc Length Formula

The formula to calculate the arc length of a circle is mentioned below.

arc length calculator formula
Note : If central angle is in radians then you can directly multiply it by radius (arc length = central angle x radius)

How to Calculate Arc Length of Circle

Calculating the arc length of a circle is not difficult. You can simply calculate the arc length if you know the radius/diameter and the center angle of the circle. With the help of an example, we will try to explain the topic as simply as possible.

Explaination with Example

We will explain you how to find out the arc length of numbers with a very simple example.

Example 1 : Find the length of an arc of a circle having radius 3 meter and the central angle 25 degree.

Solution :

So that you don’t get confused, we started with a very simple and basic example. First and foremost, determine whether the central angle of the circle is in degrees or radians before attempting to calculate the arc length. Because, in order to compute the arc length of a circle, we must convert the center angle from degrees to radians.

To do so you just have to multiply the value of angle by π/180.

Lets use the above formula to calculate the arc length of circle.

arc length = (central angle x π/180 ) x radius
arc length = (25 x π/180 ) x 3
arc length = (25 x π/180 ) x 3
arc length = (0.43633231299 ) x 3
arc length = 1.308996939 m

Example 2 : Find arc length of a wooden wheel with diameter measuring 3 ft and central angle of 45 degrees.

Solution :

We know that the radius of the circle is the half of the diameter. Hence the radius of wooden wheel is half of 3 i.e, 3/2 = 1.5 ft.

From the formula,

arc length = (45 x π/180 ) x 1.5
arc length = (0.78539816339 ) x 1.5
arc length = 1.1781 ft