This is a tool I came up with and started designing but I didn't end up needing it, so this is incomplete, and you are welcome to finish/remix it. (STEP and F3D files included)

This tool works based on this formula (Description/proof) with the chord length held constant. for the 100 mm version I designed, the formula can be simplified to: R=(1250/h) +(h/2). R is the radius, and h is the arc height. You use it by placing the sharp edges (not the round ones) against the curve and fit calipers against the scale's edge to measure the arc height, plug that value into the formula, and you've found the radius!

There are increments on the scale, so a caliper isn't needed always, also, a caliper relief to measure the arc height more accurately. I was thinking of making more of different sizes and possibly ones where the arc height is held constant, and the chord length is variable. Also debossing size -specific formulas on each different gauge for ease of use. The model is kind of parametric with the maximum diameter the tool can measure controlling the thickness of the tool proportionally.

Again, I did not need this tool so I didn't finish the design and you are free to remix (with proper attribution of course).

Happy Printing!