Find the radius from a chord

By having only two measurments, first the length of the chord and the height of the curve, what is the formula for finding the radius of the circle.

[Robert Fogt]

I am not exactly sure what you mean.

The chord meaures the curve of a sector of a circle? The height is what? The height from the center of the circle or the height from the ends of the chord?

I have a book listing many formulas, but none to help knowing just the length of the arc and the height.

Take a look at the following diagram, and point out all the information you know and I can supply the correct formula.


My guess is you know the height m and the arc length XZ. Is this correct?

Yes that is correct. I know the length of the cord (c) and the height of the arc created by the cord (m). Is there a formula to find the radius with this information?

[Robert Fogt]

Just to make sure we are talking about the same thing, c is a straight line between points X and Z, called the cord, the curved line would be called arc length XZ.

Assuming you know c (not XZ) and m then the formula would be:

r = (m² + ¼c²)/2m

I have the circle and a chord through the circle then i know the hight but how do i fing the radius? Does it have something to do with triangles and the hypotenuse?

[Robert Fogt]

Using the image above, provide the symbols for what you know. I can look up the formula for what you need in my pocket ref. There is a section on circle segments, circle sectors, and circular zones.

Originally Posted by Robert Fogt

Just to make sure we are talking about the same thing, c is a straight line between points X and Z, called the cord, the curved line would be called arc length XZ.

Assuming you know c (not XZ) and m then the formula would be:

r = (m² + ¼c²)/2m

brilliant, thankyou , i needed this info too. spot and many many thanks. Andy

Originally Posted by Unregistered

Yes that is correct. I know the lenght of the chord (c) and the height of the arc created by the chord (m). Is there a formula to find the radius with this information?

Could you please let me know what the formula is by e mail.
[.. guest link removed ..]

[Mrs X]

Bumping for unregistered

I stumbled on this through a google search. I was also looking for the same formula which I couldnt find in any of my study books. It's in the machinist handbook but I dont have one here at home.

Here's the Formula R = ((C/2)² + H²)/2H

So in your case with a chord of 30m and a height of 10m

R = ((30/2)² + 10²)/2*10
R = ((225+100)/20
R = 325/20
R = 16.25m

I know I'm a little late on the thread but should help others.