I found this on line and thought it was nifty. I was designing my future arches and wanted specific dimensions. For my purposes I am using an oval shape. The basic formula is:
AB = Width of the longest long axis,
CD = Length of the longest short axis
The formula is PI * SquareRoot of 2 * ((1/2 long axis)squared + (1/2 short axis)squared).
Since the arch is only 1/2 the circumference, you would take the answer and divide by two.
For my purposes I am planning on inserting arches into my fence posts which are 6' apart. I want the legs to be 6' apart and the height to be 4' So for my purposes the length of my pvc arch needs to be 8'. If I want 1' tails on both ends that gives me a 10' length of pole with 8 one foot channels.