How do you find the radius of a circle given the length of an arc?

2 Answers

The circle with radius #r# has a circumference #2*pi*r# which corresponds to an angle of #360^o#.

If you are given an arc of a certain angle lets say #p^o# degrees which is #l# in length then

#p^o/360^o=l/(2*pi*r)=>r=(360^o*l)/(2*pi*p^o)#

Sep 2, 2016

#r = (180 xxl)/( pi theta)#

Explanation:

You always need another piece of information, just the arc length is not enough - the circle could be big or small and the arc length does not indicate this.

It will help to be given the sector angle.

If you have the sector angle #theta#, and the arc length, #l# then you can find the radius

#r = (180 xxl)/(pi theta)#