# Formula to find arc radius using arc length, chord length, and/or segment angle

##### New member
I'm attempting to write some code using the Ruby programming language that will give me the radius of an arc but the only pieces of information I have to work with are the arc length (L), the chord length (C), and the circular segment angle in degrees (A):

I'm hoping someone can show me how to insert L, C, and A into a formula that I can use in my code. I'm working with a CAD program that opens up access to certain pieces of information about each arc, but unfortunately radius isn't one of them, so I need to use the information I do have to find the radius.

Thanks so much for your time.

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#### Klaas van Aarsen

##### MHB Seeker
Staff member
Let R be the radius of the arc.
Then the angle A in radians is defined as the arc length L divided by the radius R.
In other words:
$$A = \frac L R\implies R=\frac{L}{A}$$

##### New member
Let R be the radius of the arc.
Then the angle A in radians is defined as the arc length L divided by the radius R.
In other words:
$$A = \frac L R\implies R=\frac{L}{A}$$
@Klaas van Aarsen Thank you! I was able to use your answer to write my desired code section. I just needed to add some language to convert degrees to radians (degrees*pi/180). My finished section of Ruby code looks like this:
Ruby:
arc_length/(arc_angle * Math::PI / 180)
Thanks so much for the help : )

##### New member
Pretty elementary I know, but just in case this helps anyone else:
I feel a little silly in retrospect. I searched all over the place online before posting here. My problem was that I didn't until today understand what a radian was. A radian is essentially defined as the circular segment angle at which the arc length is equal to the radius. I've attempted to illustrate this in the image below:

For me personally, I can then pretty easily go through all the logic like so:
• As most people know, a circle's circumference can be measured by its radius*2*pi, therefore...
• A full circle contains a quantity of radians that can be represented as 2*pi, therefore...
• 360 degrees/(2*pi) or 180/pi gives me the number of degrees in a radian, therefore...
• The inverse of 180/pi or pi/180 will give me the number of radians in a degree
• Knowing my degrees, I therefore know exactly how many radians I'm working with...
• Knowing my arc length, I can then simply divide that by my number of radians to get my radius
Its all quite easily understandable using things I already knew as soon as I understood what a radian was. Thanks again @Klaas van Aarsen for giving me an answer that got me looking in the right place.

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