Daydreaming in geometry class a lifetime ago, I realized the "3 points define a circle" principle could be used equally to measure an arc's radius. I mentally designed the tool presented here, but had no way to actually build it ... until 3D printing.

Touch the tool's 3 disks to a curved surface, and read the radius in centimeters or inches on the dial.

This is a cousin of the "lens clock" your optometrist uses to measure the curvature of a lens.

Update 2015-08-01: Thank you roki@thingiverse for text() tip; posting updated code. Also strengthened hinge, since I had one break.

Update 2016-05-29: Added "inch" version.

Print the stationary part in white, and the moving part in a contrasting color. Default print settings are fine.

Touch the numbers and tick marks with a Sharpie so they're readable against the white background.

Snap the two parts together, and it's ready to use.