I've given up trying to construct a formula, but I think that if
you're in a hurry the following should do. You'll need to construct a
look-up table of:

theta vs [sin(theta/2) / theta] (theta in radians)

Calculate 1/2 x c/a, find the value of theta from your look-up table
having that value, then calculate r as a/theta

(I'm naming your circle arc "a", chord "c", and "theta" as the angle
subtended by the chord)

Here's the math:
circle arc: a=r x theta (radians)
or r=a/theta

triangle: sin(A)=opposite/hypotenus
or in this case
sin(theta/2)=c/2 / r


doing the math I get: sin(1/theta)/theta = 1/2 x c/a