# Thread: Finding the Radius when all i have is the arc length

1. ## Finding the Radius when all i have is the arc length

Im not sure if Trig is the right forum to post in, I apologize if I am in the wrong spot....
I have a project at work where I was given the arc lenght of a line and was asked to find the radius of the circle. What is the formula to do this....if it exists?
Thanks
Shante

2. ## Re: Finding the Radius when all i have is the arc length

Originally Posted by Shante
Im not sure if Trig is the right forum to post in, I apologize if I am in the wrong spot....
I have a project at work where I was given the arc lenght of a line and was asked to find the radius of the circle. What is the formula to do this....if it exists?
Thanks
Shante
$s = r\theta$

$s$ is arclength

$r$ is the radius

$\theta$ is the sector angle in radians

3. ## Re: Finding the Radius when all i have is the arc length

The radius can be found as follows

$r= \frac{180\times L}{\pi \times \theta}$

Where L is the arc length and $\theta$ is the angle corresponding to the arc length.

4. ## Re: Finding the Radius when all i have is the arc length

I know i sound like a total novice here, I promise im not, its just been forever since i have even thought about this type of math.....I dont have the angle....is there a way for me to find that....all they told me is they want a 60" arc length but gave me no other information....and in order to bend the piece of metal to that arc length they need the radius....sorry!

5. ## Re: Finding the Radius when all i have is the arc length

Hmm... you need at least two pieces of information to work with. An arc of a given length x (60" in your case) could be any radius, depending on the ange. the smaller the radius. the greater the angle.

Might you know what portion of a circle you need to bend the metal to? Half a circle? A quarter circle? A definition along those lines would give an angle and thus, allow a radius to be calculated.

6. ## Re: Finding the Radius when all i have is the arc length

All they have given me at this point is the arc length, I kept trying to tell them I didnt think that was enough information. I appreciate the help

Thanks