Formula to Find Arc Length

The circle is a combination of points in a plane .And all the points are the same distance from a point. This point is called the center of the circle. There are some parts of the circle. These parts are as follows:

  • Center:  Center is a point which is the same distance from all the points of a circle.

In this figure C is the center of the circle.

  • Radius: Radius is a line segment whose one end point is on the circle and one end point on the circle.Here the length of CB is the radius of the circle.
  • Diameter: Diameter is a line segment which is passes through the center of the circle and who’s both end points lias on the circle. Here the length of the EA is the diameter of the circle.
  • Chord: A chord is a line segment whose both the end points lies on the circle.
  • Sector: Sector is a part of the circle which is enclosed by two radii and an arc which is connecting by both the radius.Here ACB is the sector of the circle.
  • Arc: Arc is a part of the perimeter of the circle. Here BFA is the arc of the circle.



We can find the area of the arc length by this formula

            Arc length=`theta/360 * 2 pi r`

Where `theta` = central angle

             r =radius of circle and `pi=3.14`

Another short cut method of finding the length of arc is as follows:

 Arc length=`theta` r

Where  `theta ` is in radian.


Examples to Find the Arc Length:


Que 1.Find the length of arc  if central angle is 120 degrees and diameter of circle is 4cm.


Here  central angle( θ)=120

And diameter(d)=4cm

So radius(r)=4/2=2cm

Arc length=`theta/3260 * 2 pir` 

                   =`120/360 * 2 * 3.14 * 2` 


Que 2:  Find the arc length if central angle is 3 radian and radius is 4cm?

Ans : Arc length= r `theta`

Here r=4cm

And `theta` =3radian

So  arc length=4*3

                        =12 cm


Questions to Find Arc Length:


1) If area of circle is 4cm2 and central angle is 90 degrees than find the value of arc length

Ans  1.77cm

2 )Find the value of arc length if central angle is 180 degrees and radius is 4cm?

Ans 12.56cm