Finding a Chord Length of a Circle if I have Arc Length and Height?

Aug 2011
I am in the process of making a tent and need to get two curved surfaces to meet.
I need to find the length of a Chord of a circle given that I have the Arc length and Arc Height (that's all), no radius or anything else.

I suspect that I will need a radius to find this. Or am I missing a point here?

The below spreadsheet I found on the web proports to be able to do this but the answer is not correct. The edges of my material does not match up when I calculate the Chord length given that I've entered the Arc Length and the Arc Height.

Does anyone know how to do this?


MHF Helper
Jun 2014
Call the known chord height 'H' and the known arc length 'A'. If we define R as the radius of the arc and theta as the half angle for the arc length, we have two equations in two unknowns (R and theta):

\(\displaystyle R\cos \theta + H = R\)

\(\displaystyle R \theta = A \)

Combine and rearrange to get:

\(\displaystyle A \cos \theta + 2 H \theta = A \)

I don't believe there is a closed-form solution for this, so you will have to solve for theta using a numerical technique. The radius can then be found using \(\displaystyle R = \frac A {\theta} \), and then the chord length will then be \(\displaystyle 2 R \tan \theta\).
Jun 2013
the spreadsheet you referenced seems to give the correct answer.

what values did you try?