Radius of an arc

      Formulas for determining the radius of an arc, or "eyebrow"

I would like to know the formula for determining the radius of an arc, or "eyebrow", in cabinetmakers terms. I know it starts with a line connecting two points of the arc and the amount of "rise" within that segment.

Forum Responses
I looked for this formula for a long time and found it in a book called "Pocket Ref" by Thomas J. Glover.

Here is the formula if the line connecting the to points is "A" and the distance from a to the edge of the circle is b (at a 90 degree angle to a)
then (^2 equals "squared"):
(((a/2)^2)+(b^2))/2*b =radius
or half a squared plus b squared divided by 2 times b.
I think the degrees are (atan(a/2)/(r-b))*2

I just draw the horizontal line and then the rise from the midpoint, create a 3 point arc, then ask ACAD what the radius is.

Here is another way:

Square 1/2 of span.
Divide by rise.
Add rise.
Divide by 2.

Rise squared plus half the width squared divided by twice the rise.

The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).

Comment from contributor A:
Another way:

C= chord length
M= distance from chord to edge of circle

C squared divided by 8M + M/2 = R

Comment from contributor B:
To calculate radius of a circle where:
r = radius and is unknown
C = chord length (a line the crosses any two points on a circle)
B = length of perpendicular line from midpoint of chord to edge of circle

r=((4*Bsquared + Csquared)/8B)

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